VERIFICATION OF BUSINESS RULES USING LOGIC PROGRAMMING MEANS

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3 Sesson 3. Formalzaton and Smulaton of Busness Systems VERIFICATION OF BUSINESS RULES USING LOGIC PROGRAMMING MEANS Henrkas Pranevcus, Regna Msevcene Kaunas Unversty of Technology, Department of Busness Informatcs Kaunas, LT-44029, Lthuana E-mal: {hepran, In ths paper development of the analyss tool for verfcaton and valdaton of busness rules s presented. Formalsm for expressng the busness rules s the predcates logc language. The rules are developed on the framework of Pece Lnear Aggregate (PLA) formalzaton. By the presented approach the PLA based busness process specfcaton s transformed to the set of predcate logc rules descrbng both the specfcaton and the propertes under nvestgaton. The artcle also shows verfcaton and valdaton of the busness rules determned by the clauses of the frst order predcates logc. The convenent nterface of the system s presented. The nterface allows competent user to nterfere, fnd and correct mstakes. The presented approach s llustrated by the example. Keywords: busness rules, verfcaton, valdaton, predcates logc language. Introducton Busness rules and constrants have become a basc topc n systems development and enterprse modellng. The essence of the busness rules s to descrbe and verfy aspects of the busness functons. Busness rules can appear n many dfferent forms, both formal and nformal. Formal methods for descrbng rules are relatvely new and stll beng refned. Systems desgners have long been able to descrbe busness n terms of the structure of the data that enterprse uses and the functons t performs. Unfortunately, the constrants under whch the enterprse operates, they have tended to neglect [-3]. Moreover, dscussons on busness rules frequently concern on that has been done n knowledge-based systems n such area as knowledge verfcaton. There are sgnfcant numbers of artcles on verfcaton and valdaton constructs n knowledge-based systems. Many authors who wrte about the verfcaton and valdaton n knowledge-based systems have ther own defntons of the concepts [4-7]. Busness rules are better understood, when technques and tools are developed. The technques nclude formal methods for descrbng rules, wth tools translatng these formalsms drectly nto other mplementaton constructs. Ths paper employs ntegrated busness process modellng and smulaton framework Pece-Lnear Aggregate (PLA) for formalzaton of busness process and analyss of rules wrtten for the process [8-9]. Specal tools are created for executon of the aggregate models. Our approach s based on usng the frst order predcate logc and programmng language Prolog for constructng of the executable specfcaton [0-2]. By the presented approach the PLA based busness process specfcaton s transformng to the set of predcate logc rules descrbng both the specfcaton and the propertes under nvestgaton. The resoluton method mplemented n Prolog s appled to analyse the rules. The artcle also shows how the system executes verfcaton and valdaton of busness rules determned by the clauses of the frst order predcates logc. The convenent nterface of the system s presented. The nterface allows competent user of the problem doman to nterfere, fnd and correct mstakes. The presented approach s llustrated by the example. 2. Busness Process Modellng n the PLA Notaton Ths paper employs ntegrated modellng and smulaton framework Pec-Lnear Aggregate (PLA) for analyss of busness processes. On the ground of the developed PLA prncples automatc analyss tools are created (see Fgure ). MoSIS (Modellng, smulaton, analyss and mplementaton sute) for busness systems permts to perform man stages of analyss and desgn usng formal methods. The man feature of ths system s all stages of analyss, and desgn of busness processes are performed based on sngle PLA mathematcal scheme. The system conssts of such sub-systems performng the followng tasks: transformaton of system models specfed wth 99

4 The Internatonal Conference Modellng of Busness, Industral and Transport Systems 2008 SDL, ESTELLE, UML languages to PLA model; valdaton and verfcaton of PLA formal specfcatons; smulaton; test creaton; automated software mplementaton. SDL ESTELLE Valdaton & Verfcaton UML PLA Smulaton Numercal models Software mplementaton Creaton of tests Fg.. MoSIS the verfcaton and valdaton tool 2.. PLA defnton PLA s a specal case of automaton models. These system descrbed n any formalsms, one can assocate a transton system of a set of states, a set of ntal states, a set of dscrete actons, a set of dscrete steps a s s. Furthermore, from state s the system can move to state s ' durng a postve amount of tme t n whch no dscrete acton occurs. PLA model s extended automaton model. In the formalsm busness processes are modelled as compostons of aggregates. Each aggregate specfes nteractons among ts partners and each aggregate servce a unque busness process (e.g. processng a payment or shppng). By the PLA approach each aggregate A s vewed a system A = X,Y,E,Z,H, G. In the defnton two sets ( X and Y ) present nput and output sgnals that arrve or ext of the aggregate. The state Z of the aggregate s specfed by dscrete ( D = { d,d 2,, d p }) and contnuous ( W = { w,w2,, w f }) components. It s asserted that from state s the aggregate can nstantaneously move to new state s va the occurrence of event e (see Fgure 2). s 2 s e 2 s 4 s 5 e s 2 s 3 s 3 e 3 s 4 s 6 Fg. 2. State transton usng two events The events can occur when an nput sgnal arrves at the aggregate or when a contnuous component acqures a defnte value. The events E = E E are defned as the sets of nternal ( E ) and external ( E ) events. Transton ( H : E Z Z ) and output ( G : E Z Y ) operators reflect one state to other. The aggregates of the system (of n elements) are connected by channels. Each channel connects a par of contacts: S = A, A,, A, 2 n R, where R : X Y s a fnte set of channels, whch represent connectons between aggregates Example of PLA specfcaton Throughout ths paper we wll demonstrate an example whch ncludes a part of on-lne e-books Sales process busness model. By the model Company sells books to the publc customers usng an electronc 00

5 Sesson 3. Formalzaton and Smulaton of Busness Systems catalogue. Customer orders books mentoned n the catalogue. If the order s acceptable, Order clerk of the Company shps the books and Invoce to Customer. PLA specfcaton of the example conssts of the system S = ( A, A2, R ), where A (Customer), A2 (Company) are aggregates of the busness system; R = {r, r2} presents two channels r (the channel for sendng documents or resources from Customer to Company) and r2 (the channel for sendng documents or resources from Company to Customer). Fgure 3 shows the structure scheme of the PLA model. Order lst A A 2 Customer y x E (E ) x Order Entry Clerk (E ) Invoce Packng Slp Order Entry Clerk (E2 ) y Descrpton of aggregate A = X,Y,E,Z,H, G : Fg. 3. Structure scheme of the example. A set of nput sgnals X = { x }, where x s Invoce document as the nput sgnal. 2. A set of output sgnals: Y = { y }, where y s document Order lst as output sgnal. 3. A set of external events E ' = { e' }, where e ' event descrbes the arrval of the Invoce. 4. A set of nternal events E " = e }, where: e " event descrbes the formng of the Order. { 5. Dscrete component of the state v { k } =, where k s amount of ordered books. 6. Contnuous component of state: zν = { w( e )}, where: w(e ) s moment when starts the event. 7. The ntal state presents the formng of the new Order and amount of ordered books s 0. w( e " ) = ; k = Transton operator H ( e " ) descrbes, that the nternal event Order s formed and amount of ordered books s k = + random( 5 ). The amount of the ordered books y = k s sent to Company (n output operator G( e " ) ). H( e " ): k = + random( 5 ); w( e " ) = y G e " ) : ( = k Specfcaton of other aggregates s presented n [0]. 3. Rule Based Process Model Based on PLA 3.. Rule sets as unts of logc Busness rules can appear n many forms, both formal and nformal. Last provdes natural-language statements wthn a lmted range of patterns. The formal expresson of busness rules needs ether graphcal or formal (logc-based) language. Specal tools are created for executon of the formal models. 0

6 The Internatonal Conference Modellng of Busness, Industral and Transport Systems 2008 By our approach the rules are developed on the framework of Pece-Lnear Aggregate (PLA) formalzaton. The PLA based busness process specfcaton s transformng to the set of predcate logc rules descrbng the specfcaton. By our approach two parts of rules are constructng. One of the part corresponds to the busness process specfcaton, and the second part descrbes statements about the underlyng busness rules. The consstency of the rules s verfed by the resoluton method usng logc programmng language Prolog. The logc programmng language Prolog presents some advantages. The language based specfcaton allows clear separaton of logc and control parts and permts the specfcaton to be more easly mproved. Correspondngly, the logc component specfes rules, whch are used n solvng problems and control component determnes the problem solvng strategy by means n whch that rules are used adapted to new problems. The suggested approach uses busness process rules, based on PLA model. The most convenent way of creatng the rules s to select an approprate pattern from a short lst of avalable patterns. The patterns we cover n the form of the followng predcates: The predcate QX _ name ( nput _ p,nput _ v,w,,w,d,, ) acqures True value when arrve nput sgnal wth value nput _ v at the contact nput _ p of an aggregate wth contnuous and dscrete coordnates of the aggregate state. Smlarly predcate QY _ name ( output _ p,output _ v,w,,w f,d,, d z ) acqures True value when a sgnal wth value output _ v s generated at the pole output _ p of aggregate. f d z The followng predcate QW _ name ( w,,w,d,, ) acqures True value when an nternal f d z event occurred. P(w,..., w f, d,..., d s ). The predcate s True, when are satsfed condtons for the state coordnates. These predcates are used n rules of transton and output operators. They depend on occurrence of external and nternal events. The followng rules are possble:. The external event changes the state coordnates and the output sgnal s sendng: QX_name (x,..., x,..., xm, w,..., wf,d,...,ds ) P ( w,...,w,...,wf,d,...,ds ) QY_name (y',..., y',..., yn', w',..., wf',d',...,ds' ). 2. The external event changes the state coordnates wthout the output sgnal: QX_name (x,..., x,..., xm, w,..., wf,d,...,ds ) P ( w,...,w,...,wf,d,...,ds ) QW_name ( w',..., w',...,wf',d',...,ds' ). 3. The nternal event changes the state coordnates and the output sgnal s sendng: QW_name ( w,..., w,...,wf,d,...,ds ) P ( w,...,w,...,wf,d,...,ds ) QY_name (y',..., y',..., yn', w',..., wf',d',...,ds' ). 4. The nternal event changes the state coordnates wthout the output sgnal: QW_name ( w,..., w,...,wf,d,...,ds ) P ( w,...,w,...,wf,d,...,ds ) QW_name ( w',..., w',...,wf',d',...,ds' ). In the aggregate system the aggregates are connected by communcaton channels. The channels communcaton of system s descrbng usng the followng predcates: the frst predcate OY _ name _ descrbes the aggregate (that marked as name _ ) whch generates an output sgnal on the output _ p contact, the next predcate of the aggregate (that marked name _ 2 ) on whch arrves an nput sgnal on the nput _ p contact. Communcaton of output pole output _ p of aggregate wth name name _ and nput pole of aggregate wth name _ 2 s descrbed by a logc formula: QY _ name_( output _ p, output _ v, w,,w,d,, ) QX _ name _ 2 nput f d z _ v, w,,w f,d,, d z ,,w f, d,, d z ( _ p, nput ) Here w,,w f,d,,d z, w states.. are contnuous and dscrete coordnates of the aggregates 02

7 Sesson 3. Formalzaton and Smulaton of Busness Systems 3.2. Example of rule based specfcaton In the example of aggregate specfcaton presented above transton operator H( e " ) descrbes, that the nternal event Order s formng and amount of ordered books s equal + random( 5 ). H( e " ) : k = + random( 5 ); w( e " ) = G( e " ) : y = k By the presented approach the operators above are transformed to the rule: QW_A(w, k) w 0 next_k = random(5) + next_w = QY_A(next_k, next_w, next_k) The rule declares: f aggregate s wth name A coordnates are (w and k, where w s nternal event Order s formed and k s amount of ordered books) and the nternal event s not equal 0, then the new amount of ordered books s generatng and new order of books s preparng. 4. Rules for Verfcaton of Busness Rules Verfcaton and valdaton of the busness process conssts of verfyng that a model satsfes the propertes by explorng all ts reachable states. Ths requres that ths state space be fnte and tractable. The reachable states analyss s based on the concept of global state, whch s a composton of local states of aggregates. By the gven approach reachable states tree s generated and then analysed. Analysng the reachable states tree, the followng propertes can be observed: ) completeness, 2) deadlock freeness, 3) tempo blockng freeness, 4) lvelness, 5) termnaton or cyclc behavour, 6) boundedness, etc. Invarant approach s used to analyse ndvdual propertes of the aggregate models. The nvarant s an asserton descrbng correct system state and remanng true n spte of events takng place and of transtons from one state to another. By our approach the set of rules of general and ndvdual propertes under nvestgaton are the followng:. Intal state statement presents what concrete ntal values must to be of all aggregates (global) coordnates: Q_global ( w0,..., w0 f, d0,..., d0s,...,w0,..., w0 f,d0,..., d0 ). n sn 2. Fnal state statement also presents what concrete termnal (T) values must to be of all aggregates (global) coordnates: Q_global ( wt,..., wt,dt,..., dt,...,wt,..., wt,dt,..., dt f s fn sn. 3. Boundedness rule demonstrates boundares for dscrete coordnates of the all aggregate state: Q_global ( w D = {d,...,d f,...,w,d,...,d } s,...,d s,...,w n,..., w n f n,d n,...,d there predcate D = {d,...,d,...,d } demonstrates boundares for the dscrete coordnates. s 4. Deadlock statement shows, that when all the contnuous coordnates n global state are equal 0, then the executon s False. Q_global ( 0,...,0,d,...,d s,...,0,...,0,d n,...,d 5. Invarant rules demonstrate general (or ndvdual) condtons: n s n ) n s n ) ) f Q_global ( w,..., w,d I = {d,...,d,...,d }. s,...,d s,...,w n,...,w n fn,d n,...,d nsn ) 03

8 The Internatonal Conference Modellng of Busness, Industral and Transport Systems Verfcaton of Busness Rules 5.. Verfcaton and valdaton tool Verfcaton and valdaton tool s created on the means of logc programmng language Prolog. The tool provdes convenent user nterface for automatc analyss of the busness rules. The verfcaton and valdaton tool conssts of the followng components: translator, knowledge base and user nterface (see Fgure 4). PROLOG system Knowledge base PLA framework Specfcaton Translator Rules of the Specfcaton Rules of Propertes Reachable states formng rules Users nterface INTERF Fg. 4. Structure of the Verfcaton and Valdaton tool The translator automatcally generates Prolog rules from the aggregate specfcaton. The translator also provdes ntellgent edtor. Predcate logc system Prolog s used for analyss of the rules base. The consderable attenton s pad to user nterface and user dalog. The user of the verfcaton and valdaton tool have ablty not only to derve concluson from exstng data n the knowledge base, but also to gve explanatons how and why correspondng solutons have been made User nterface of the tool In addton to other features the presented tool has to provde ablty for user to nterfere n certan stage of PLA specfcaton analyss. For example, n certan stage of analyss user can ask the system to explan how one or another presented soluton of the problem was derved, f t s not clear (therefore, queston how s mplemented). Whle askng queston how expert system wll present the lst of rules used n goal satsfyng process. The latter lst s presented n drect order. Durng problem soluton process system may request addtonal nformaton, whch s needed to make concluson. If t s not clear to user why the system gave the correspondng request, the user may also ask the system queston why. In ths case system wll present nference chan stpulated by queston why, n other words, the user wll receve the lst of rules used to fnd the goal. In how queston s case expert system presents the lst of rules n drect order but n why queston case the lst of rules wll be presented n ndrect order. The rule, whch satsfes fnal goal, s at the bottom of the presented lst. The dfference between mentoned questons s presented on Fgure 5. Goal Rule No. Rule No. 2 Concluson The problem s Request to user Request to user Rule No. 3 how why Rule No., Rule No.2, Rule No.3. Rule No. 3, Rule No. 2, Rule No.. Fg. 5. How and why questons 04

9 Sesson 3. Formalzaton and Smulaton of Busness Systems 5.3. Example of user nterface Example of the user nterface shows dalog between system and user durng the specfcaton analyss. The example (see Fgure 6) of the user nterface shows dalog between system and user durng analyss. By the nterface user can ask the system to explan how or why presented soluton of the problem s derved. In queston case why the system lsts predcates wth dscrete and contnuous coordnate values n ndrect order of nference. INTERF s a smple PROLOG shell. Please, enter one of the commands: help. load. analyze. how. or why. > load. Please, enter the name of knowledge base n sngle commas (for example: books_order.pro.): > books_order.pro. > analyze. -->+ - [] - [] - [] W? (yes/why/end) >> yes. --> [] W? (yes/why/end) >> why. r(,,[],0,,25,2) qw(,,[],0,,25) qt(,[],[],[],0,35) r(,[],[],[],0,35,) -->3+ - [ ] - [] - [0 0] W Fg. 6. Example of the user nterface 6. Conclusons In ths paper we set out for usng a busness rule model to represent control flow of busness processes. In partcular we demonstrate how the busness rule based model defnes busness model and the state transtons of the busness model. The formalsm for expressng the busness rules s the predcates logc language. The rules are developed on the framework of Pece-Lnear Aggregate formalzaton. By the presented approach the PLA based busness process specfcaton s transformed to the set of predcate logc rules descrbng both the specfcaton and the propertes under nvestgaton. The artcle also shows verfcaton and valdaton of busness rules. The convenent nterface of the system s presented as well. Our presented approach has some advantages: Ths allows clear separaton of busness process logc and rules that constran the busness process. Furthermore applcaton of PLA approach allows automated analyss of general propertes (completeness, deadlock freeness, termnaton, boundedness) and ndvdual propertes of the rule based specfcatons. The user of the verfcaton and valdaton tool has ablty not only to derve concluson from the exstng data, but also to gve explanatons how and why correspondng solutons have been made. The approach permts the rule based specfcaton to be more easly mproved modfyng rules when changng busness polces wthout the need to change the process defntons. References. Vanthenen, J., Goederter, S. and Mues, C. Experences wth Modellng and Verfcaton of Regulatons. In: Internatonal Workshop on Regulatons Modellng and ther Valdaton & Verfcaton (REMO2V '06), n conuncton wth the 8th Conference on Advanced Informaton System Engneerng (CASE '06), Luxembourg, Luxembourg, 2006, pp

10 The Internatonal Conference Modellng of Busness, Industral and Transport Systems Goederter, S., Vanthenen, J. Rule-based busness process modellng and executon. In: Proceedngs of the IEEE EDOC Workshop on Vocabulares Anthologes and Rules for the Enterprse (VORTE 2005). CTIT Workshop Proceedng Seres (ISSN ), Defnng Busness Rules. What are they really? The Busness Rules Group: Fnal Report revson.3, July, Preece, A. Foundaton and Applcaton of Knowledge Base Verfcaton, Internatonal Journal of Intellgent Systems, Vol. 9, 994, pp Plant, R. T. Methodologes for the development of knowledge-based systems, : The Knowledge Engneerng Revew, Cambrdge Unversty Press 8. Cambrdge, 2003, pp Tsa, W.T., Vshnuvaala, R., Zhang, D. Verfcaton and valdaton of knowledge-based systems. IEEE transactons on knowledge and data engneerng, Vol., No, 999, pp Tsa, J.P., Lu, A., Juan, E., Sahay, A. Knowledge-Based Software. Archtectures: Acquston, Specfcaton and Verfcaton, IEEE Transactons on Knowledge and Data Engneerng, Vol., No, 999, pp Pranevcus, H. Aggregate approach for specfcaton, valdaton, smulaton and mplementaton of computer network protocols: Lecture notes n Computer Scence No502. Sprnger-Verlag, 99, pp Pranevcus, H. Formalzaton and smulaton of busness process. In: Modellng and Smulaton of Busness Systems. Internatonal Conference. 2003, pp Pranevcus, H., Msevcus, P.V., Msevcene, R. Transformaton of aggregate specfcatons to the predcate logc models. In: The Internatonal Workshop on Harbour, Martme and Multmodal Logstcs Modellng and Smulaton. 2003, pp Pranevcus, H, Msevcene, R, Janusauskate, Z. Usng pece-lnear aggregate model for resource-eventagent busness process analyss. In: Informaton technologes 2006, Internatonal conference. 2002, pp Pranevcus, H, Msevcene, R, Mlcute, V. Use of aggregate specfcaton and logc programmng for knowledge base valdaton and verfcaton. In: Internatonal Conference on Modellng and Smulaton of Busness Systems. 2003, pp

11 Sesson 3. Formalzaton and Smulaton of Busness Systems MODELLING OF RAILWAY SCHEDULE IN TEMPORAL DATABASES Eugene Kopytov, Vasls Demdovs,2, Natala Petukhova 2 Transport and Telecommuncaton Insttute Lomonosova, Rga, LV-09, Latva Fax: E-mal: [email protected] 2 State Jon-Stock Company Latvan Ralway Turgeneva 2, Rga, LV-547, Latva Fax: E-mal: [email protected] The gven paper deals wth the ssues of buldng a temporal database for the ralway schedule. For the mathematcal descrpton of the ralway schedule system, we suggest to use set theory and algebra of logcs. We defne the perodcty parameters and temporal elements and formulate the rules of ther calculaton. We also gve practcal examples on defnng the dates on whch the set verson of the tran schedule becomes actual. Keywords: ralway transportaton, schedule, temporal database, statement of comparson, perodcty. Introducton The gven paper consders the task of supportng the ralway schedule n nformaton systems (IS). The man problems of holdng the schedule n the database are connected wth the great number of ts varants condtoned by season changes of the ralway changes, dfferent days of the week, planned and unplanned repar works, re-arrangng holdays and weekdays and other factors. The schedule-supportng task can be solved by means of a calendar statng the ply of each tran on each day of the year. However, the number of entres descrbng on what day, at what tme and at what staton each tran wll be havng a stop, wll approxmately equal the product of the number of trans by the average number of stops and by the number of days covered by the schedule. Wth ths approach we wll need about 2 mllon records to hold the local Latvan ralway schedule n the relatonal database and for larger ralway companes the volume of the correspondng database wll ncrease by about ten tmes. Moreover, holdng the schedule for several years wll ncrease the number of records up to hundreds of mllons. However, the man problem of the above approach les no so much n the volume of the stored data but n the trustworthness of these data and n the operatveness of enterng changes n the schedule. When these changes are frequent, the task becomes much more complcated. The above crcumstances have served the bass for carryng out the gven research, n whch we suggest the prncple of realzng the schedule system on the bass of the temporal database prncples [, 2]. In the gven paper, the authors consder the ssues of buldng a temporal database (TDB) of the ralway schedule wth the use of the perodcty parameters and temporal elements. The suggested approach s appled n desgnng the nformatonal system of the nland Latvan ralway tran schedule. 2. Desgnng a Temporal Database Model n the System of the Ralway Schedule Prncples of desgnng a temporal database assume that the database holds all obects versons and access to all of them s avalable for the user []. The TDB peculartes are frst of all connected wth usng the stored obects of the temporal database for the VIEW. The man concept n the temporal model s lfespan. It means the duraton of tme perod assocated wth the exstence of the obect n a concrete state. The example of temporal relaton Tran schedule constructed for dfferent tme perods s shown n Fg.. The authors also use the relatonal envronment for developng the system of the ralway schedule. To realze temporal prncples n the frame of the relatonal model, the authors of the paper suggest an open model wth an Abstract Obect Identfer (AOID) []. The gven model provdes the support of the mult-verson of the obect and mnmzng expenses for mtaton of DELETE and UPDATE operatons wth the transton of the old verson to shadow area. In ths model lfespan of the obect s descrbed through lfe spans of all ts propertes, defned n dfferent relatons and havng tme attrbutes DATE_START (tme of lfespan start) and DATE_STOP (tme of termnaton). Realzaton of the temporal logcs usng some elements of actve databases n analytcal applcatons and real tme tasks has been performed on the bass of trggers and Java Stored Procedures [, 2]. 07

12 The Internatonal Conference Modellng of Busness, Industral and Transport Systems 2008 Fg.. The three-dmensonal temporal relaton Tran Schedule Let us consder a mathematcal descrpton of the suggested model. We have the totalty of m obects (trans), whch s descrbed by the relaton RO ( A, A2,,..., Am ), where A, A2,..., Am are the relaton attrbutes characterzng the obect propertes, e.g. data about the tran stops. A classc relatonal approach assumes that the relaton RO has m of tuples one for each obect. In the perod of the database lfespan the stored obects (tran schedules) are subect to constant changes, correspondngly there change the tuples of the relaton RO, whch correspond to the changed obects. The outdate nformaton about the changed obects s no longer kept n the database (DB). To keep the complete hstorc nformaton about the DB obects we need to support several obect versons n the relaton, whch may be acheved by ncludng some addtonal attrbutes n the relaton RO. To keep the complete hstorc nformaton about the obects, let us use the relaton of the type: R A, A,..., A, AOID, t, t ), () ( 2 m s e where AOID s an abstract obect dentfer; t s and t e are correspondngly DATE_START and DATE_STOP of the stored obect versons lfespan. One of the serous problems occurrng n the consdered IS of the ralway schedule s connected wth the overlappng of the obects lfespans, when one schedule overlaps another (see Fg. 2). The pecularty of the gven stuaton s that, the obect when changed cannot lose the actualty of ts state ether n the past or n the future for a certan perod only t s substtuted by another verson. As a result, more than one actual tuple descrbng dfferent versons of the same obect s property can exst at one tme. The latter contradcts the very dea of TDB, therefore t s necessary to trace and settle such stuatons by makng specal data queres. To explan the consdered case we refer to example shown n Fg. 2. We assume that the varable t n means the moment of revewng. The season ralway schedule s fxed n February for the perod from the moment t to t 6. Later on n March, the schedule s changed for the perod from the moment t 2 to t 4, and then n Aprl, we make one more change for the perod from t 3 to t 5. For the nqury of the tran traffc at the moment t n, we ll get the schedule fxed n February for [t, t 6 ], at the moment t n2 the schedule fxed n Aprl for [t 3, t 5 ], and at the moment t n3 we agan have the schedule for [t, t 6 ]. Fg. 2. Crossng of Obect Lfespans n DB of the Ralway Schedule System 3. Usng the perodcty prncple n the ralway schedule In practce, the tran may have smultaneously several vald schedules for a long perod. In ths stuaton, every schedule s fxed wth the account of the days of traffc and wth the use of dfferent perodcty 08

13 Sesson 3. Formalzaton and Smulaton of Busness Systems characterstcs, for example: on the weekdays, on the rest-days, on the partcular rest-days, on the frst weekday, on the last day of the weekend (whch sometmes may be Monday), on the even, on the odd days, etc. Let us take as an example a mult-varant tran schedule presented n Fg. 3. A we can see, for the tran numbered n there are two basc schedules, one for the weekdays wd, the second one for the rest-days rd. Both schedules are actual n the tme perod [t, t 4 ], but n dfferent weekdays. Then, for repar works we make a change n the schedule of the gven tran on Tuesdays and Thursdays for the tme perod from t 2 to t 3. Thus, n the tme perod [t 2, t 3 ] we already have three actual schedule versons vald for the days, whch correspond to the characterstcs wd, rd and Tue,Thu, wth only one schedule verson wd or rd, or Tue,Thu vald for one day. Fg. 3. Varety of the tran schedule vald versons: wd, rd and Tue, Thu We shall llustrate the former statement wth the dagram n Fg. 4, n whch the axs Day of Week shows the weekdays n the followng sequence: Monday, 2 Tuesday, etc. The granularty level of ths schedule equals one day; therefore, we can state that tme n our system has a dscrete character and the versons possess the property of perodcty. As we can see n the fgure, on dfferent weekdays, one verson from the three s the actual tran schedule, and the other two are n the shadow zone at the moment []. Here, the tran schedule for Tuesdays and Thursdays (characterstc Tue,Thu) overlaps the weekday schedule wth the characterstc rd (see Fg. 4). Fg. 4. Perodcty n the tran schedule However, except perodcal versons of the tran schedule, there may be one-tme schedule changes. These are referred to holdays and addtonally fxed holdays or cancelled holdays. Pont out such case of the schedule change when a weekday changes place wth a rest-day. Thus, for example, n 2007, n Latva, Monday Aprl 30 (weekday) changed place wth Saturday Aprl 4 (rest-day). As a result, the trans of the Aprl 30 schedule pled accordng to the Aprl 4 (rest-day) schedule and vsa versa. Such changes or specal fxatons sometmes cause paradoxes. For example, n 2007 Monday November 9 was fxed as an addtonal rest-day and all trans on ths day pled accordng to the November 8 (rest-day) schedule, whch caused the perodcty falure as t s shown n Fg. 5. It should be added that some trans wth the perodcty of the Sunday day were cancelled on November 8 due to the fact that a regular Sunday day s also the last rest-day of the week and addtonal Sunday day trans are fxed to carry passengers from tradtonal places of rest on these days. 09

14 The Internatonal Conference Modellng of Busness, Industral and Transport Systems 2008 Fg. 5. Falure n the perodcty of the tran schedule For the correct work of the schedule system wth the account of all the above non-trval rules, we need a clear formalzaton of the task settng and descrbng the schedule temporal model. For ths, we wll take a group of sets characterzng the rules of formng the trans traffc perodcty, the ralway obects and the schedule system as a whole. 4. Formalzaton of the Schedule Model 4.. Mathematcal descrpton of the ralway schedule system To descrbe the obects and the rules we wll take a number of basc sets: S = s, s,..., s } s a set of all ralway statons, where k s the power of set S; { 2 k N = { n, n2,..., nm} s a set of the ralway trans where m s the power of set N ; We wll defne the tran wth number n N by the vector of the followng type: ( n) ( n) ( n) ( n) v = { < s, T >, < s2, T2 >,..., < s α, Tα > }, where the couple < s, T > defnes the -th tran stop, n partcular, the name of the staton s ( n) S and the tme of the tran departure T ; α s the number of the tran stops on the schedule v. For the tran numbered n, we can keep several schedule versons characterzed by the valdty perod, tme of fxaton and perodcty. Correspondngly, we take the followng schedule parameters: t s s start tme when the schedule verson comes nto acton; t e s end tme when the schedule verson expres; t fx s fxaton tme,.e. the moment of enterng the gven verson of the tran schedule n the database; C s the perodcty characterstc used to defne the days for whch the gven schedule wll be vald. Characterstc C presents a logcal expresson consstng of one or more statements of comparson, whch are connected by the logcal operatons, and (see [4]). Each statement s an elementary parameter of the p perodcty and defnes belongng of the day to a partcular group, for example, the day s an even day of the week ; t may be true or false. Elementary perodcty parameters form such a set of attrbutes on whch base we can buld logcal expressons settng any more complcated perodcty. We are gong to consder dfferent varants of the perodcty parameter gven by the set P = { p, p2,..., pπ } where π s the set power; the set elements are the followng statements: ed s any weekday (used n case of daly tran ply); wd s work day (used n case of work days ply); rd s rest-day ; Mon, Tue, Wed, Thu, Fr, Sat, Sun are the correspondng weekday ; pd s the even day of the week ; nd s the odd day of the week ; lh s the last rest-day of the week ; fw s the frst work day of the week ; etc. To dentfy a concrete verson of the schedule for the tran wth number n N we wll use the tuple (n) n, C, t fx, ts, te. Then, the -th verson v of the schedule for the tran number n N wll be defned by the tuple: v ( n) ( n) ( n) { n, C, t, t, t, s, T, s, T,..., } ( n) fx s e 2 2, = s α T α. (2) 0

15 Sesson 3. Formalzaton and Smulaton of Busness Systems ( n) ( n) n Let {, ),..., ( n v v v ) } ( 2 V = g be the set of all versons of the schedule for tran wth number n N, where g s the set power equal to the number of versons of then-th tran schedule; then { } ( n ) ( n2, ),..., ( n V V V m ) V = s a set of all versons of all trans schedules. Then, we ntroduce the sets characterzng exceptons n the perodcty fxed drectly. ( C) C {, } ), ( C ex ex ex ) ( 2, EX ( C) = θ s a set of days-exceptons, whch are gven the C characterstc, where θ s the power of set EX (C). Specal example of the set EX (C) are gven by the set ( wd ) { } wd ) ( wd EX ( wd ) = ex ), ex2,..., exw settng addtonally fxed work days by the perodcty ( rd ) characterstc C = wd and the set { } rd ) ( rd EX ( rd) = ex ), ex2,..., exq determnng addtonally fxed rest-days wth the perodcty characterstc C = rd ; EX = { C, EX ( C), C2, EX ( C2),, Cl, EX ( Cl ) } s the set of all exceptons for smlar perodcty characterstcs, where l s the power of the set EX ; the elements of set EX re-defne the perodcty attrbutes for the dates ndcated n EX (C). Z = { z, z2,..., zμ} s the set of dates transferred (changed) n the trans schedule, where z s a couple of days d,d 2 determnng that the schedule fxed for d date s now fxed for the d2 date; μ s the power of set Z Formalzaton of the perodcty model To defne the tme n whch the verson of a partcular tran schedule becomes actual for the whole perod of ts lfespan, we wll use the noton of temporal elements TE [3]. Element TE (C) for C = wd s a fnte (wd) (wd) unon of ntervals t durng wd s actve: t... tλ and TE(wd) also can be denoted by the set { ( wd ) ( ) },..., wd t tλ. In ths way TE (C) for C = wd, C = rd and C = Tue Thu (see Fg. 4 and Fg. 5) can be defned as follows: {,...,[64,68],[7,75],..., } TE ( wd) = t s t e, (3) {,...,[69,70],[76,77],[83,84],.. } TE ( rd) = t s., t e, (4) {,...,[65,65],[67,67],.. } TE ( Tue Thu) = t s., t e, (5) where [64,68] s the tme nterval expressed n days of the year (64 Monday, 68 Frday, t s and t e are denoted as the start and end ponts of the nterval t = [ t s, te]. As t s seen from the formulae (3) (5), temporal elements TE of the schedule versons possess perodcty, therefore, to get the whole set of the TE values, we ntroduce the extenson functon Ext ( C) [3]. E.g., f C = Mon Wed Fr s the defnton of Monday, Wednesday and Frday, Ext ( C) gves as output the set of all Mondays, Wednesdays and Frdays n the tme nterval of the followng schedule verson. The perodc event n the tme range [ t, t4] wll be presented as a par [ t, t4 ], C, and the set of the TE (C) values n the gven tme range as the extenson functon Bounded Extenson n the format BExt ([ t, t4], C). Wth the employment of the used defntons and functons, we defne the temporal element for the perodcty characterstc C n the tme range t, t ] as follows: [ s e ([ t, t ], C) EX ([ t, t ], C) EX ([ t, t ], ) TE( C) = BExt C, (6) s e s e s e where EX ([ ts, te], C) EX ( C) s the set of exceptons of the perodcty characterstc C actng n the perod ( C) ( C) of the schedule verson valdty: EX ([ t, t ], C) = { ex ex [ t, t ]} ; s e s e (C) ex C s the set of days whch are subect to the change of the perodcty attrbutes except the C characterstc. Thus, the expressons (3), (4) and (5) wll look as follows: ([ t, t ], Mon Tue Wed Thu Fr) EX ([ t, t ], wd) EX ([ t, t ], ) TE( wd) = BExt rd ; (7)

16 The Internatonal Conference Modellng of Busness, Industral and Transport Systems 2008 ([ t, t ], Sat Sun) EX ([ t, t ], rd) EX ([ t, t ], ) TE( rd) = BExt wd ; (8) ([ t, t ], Tue Thu' ) EX ([ t, t ], Mon Wed Fr Sat ) TE( Tue Thu) = BExt Sun. (9) Example. Calculaton of the temporal element for even days of the month, except Tuesday, can be presented as follows: ([ t, t ], pd Tue) EX ([ t, t ], nd ) TE( pd Tue) = BExt Tue. (0) For perodcty characterstcs we have formulated the gven essental rule: coverngs of the temporal scale, whch correspond to the perodcty characterstcs C and C never overlap, n other words Ext ( C) Ext( C) =. Examples of calculatng the perodcty characterstc C are llustrated n table. Table. Examples of performng a complement operaton on on the C statement Statement C Statement C wd rd rd wd Mon Tue Wed Thu Fr Sat Sun Tue Thu Mon Wed Fr Sat Sun pd Tue nd Tue It s sgnfcant that we wll be usng temporal elements n order to defne actual versons of the trans schedule. Thus, the verson of schedule v for tran number n N, defned by expresson (2), may be specfed usng a temporal element: v ( n) ( n) ( n) { n, TE( C, t fx ), s, T, s2, T2,..., s α T α } =, (), where temporal element TE ( C, t fx ) s formed wth the account of the fxaton tme t fx of schedule v and defnes all the dates for whch the gven verson s actual. () Temporal element TE ( C, t fx ), besdes perodcty attrbute characterstcs and date changes, takes nto account the cases of the schedules overlap. When spottng such conflcts, smlar dates are excluded n that of the two temporal elements, whch fnds correspondence wth the earler fxaton tme t fx. Then, the defnton () TE ( C, t fx ) presents a recursve functon. Recursve essence s also found n the fact that n calculatng of one temporal element there are used the temporal elements of later versons, whch elements, n turn, are defned n the same way: TE( C, t ( ) fx v V ( v ) ( ) fx ) = TE( C ) TE( C, t ), (2) where V ( v ) s the set of versons of the schedule for n-th tran, whch tme perods cover partly the perod of verson v and elements of V ( v ) are fxed later than verson v ; the set V ( v ) can be found by formula: { ( n ) ( ) ( ) ( ) ( ;[, ] [, ) ] ( ) ( v v V t t t t t t ) } V ( v ) = > ; (3) v V ( v ) TE( C, t ( ) fx ) s e s e fx fx defnes the set of dates, for whch versons of the schedule v V v ) are actual and whch overlap the schedule v and have hgher prorty. (n) The condton of recurson termnaton s fulflled when such a verson of the schedule vlast V for (n) tran wth number n s reached for whch we wll not spot any other verson of ths tran schedule v V, ( last) s ( last) e ( ) s ( ) e satsfyng the condton: [ t, t ] [ t, t ] t > t, here last. Then, from (3) we have V ( ) =. v last ( ) fx ( last) fx ( 2

17 Sesson 3. Formalzaton and Smulaton of Busness Systems Let us note that after the correcton of TE(C) accordng to the formula (2), temporal elements of dfferent schedule versons for one tran never overlap,.e. we satsfy the rule: ( ) ( ) fx fx TE ( C, t ) TE( C, t ) = for, =,2,... g;. To take nto account all date changes, the temporal elements of versons for schedule transformed as follows: v V (n) should be ( ) fx ( ) + = TE( C, t fx z z TE ( C, t ) ) ; =,2,..., g, (4) where ( ) z = { d z =< d, d 2 >, z Z, d 2 TE( C, t fx )} s the set of dates, whch should be excluded from the temporal element of verson v snce they subect to change; + ( ) z = { d z =< d, d >, z Z, d TE( C, t )} s the set of dates, whch should be ncluded n the temporal 2 fx element of verson v snce ts temporal element TE ( C, t fx ) comprses the date whch schedule s standard for the date to be updated. Fg. 6 llustrates the schedule change from Frday Aprl 3 to Saturday Aprl 4, whch means excludng Aprl 4 from the temporal element of schedule #2 for the rest-days (rd) and ncludng t n the temporal element of schedule # for the weekdays (wd). Functon BExt( [ ts, te], C) defnes the dots of the tme perod wthn the dapason [ t s, te ], respondng the perodcty characterstc C. The bass of the functon s checkng every dot x [ t s, te] for correspondence to the logcal expresson C. Ths check means ncludng the revewed date x n every statement ncorporated nto C ; as a result, we get a certan complcated statement C(x) bult on the base С for day х. () Fg. 6. Schedule change of one day for to another The result C ( x) = True means that day x satsfes the perodcty characterstc of schedule C, whle C ( x) = False means that for day x another verson of the schedule s actual. Then, the set of dots of the tme axs wthn the dapason t, ] correspondng to the perodcty attrbutec s calculated n the followng way: [ s te ( x [ t, t ]) C( x) x BExt([ t, t ], C). (5) s e s e For an example of calculatng accordng to formulae (5), we consder the defnton of dates n the dapason [ t s, t e ], whch are the workdays and the even days of the month. We may put down the soluton of ths task as follows: [( x s pd) ( x s wd) ] x BExt([ t, t ], pd ) ( x [ t, t ]) wd. (6) s e s e Generally, n calculatng the expresson C (x), we have, at frst, to work out all the elementary expressons p (x) consttutng t, and then to subect the receved results ( True or 0 False) to the 3

18 The Internatonal Conference Modellng of Busness, Industral and Transport Systems 2008 operatons, and formng the expresson C. Let us note that p (x) means the expresson bult on the bass of the perodcty parameter р for day x. For calculatng the expressons p (x) for the maorty of possble elements of the set P, t s enough to know the coordnates of the revewed dot on the tme axs. For example, f we know the date, we can calculate out the day of the week and thus, to check t for the correspondence to the perodcty attrbutes Mon, Tue, Wed, Thu, Fr, Sat and Sun, and usng the rule of correlaton of the weekdays to defnng the rest days, we can check t for the correspondence to the attrbutes wd and rd. Stll, there are such attrbutes for whch check up t s not enough to know the coordnates of the revewed dot, and we need to know perodcty attrbutes of the other days. The examples of such complcated perodcty are the frst and the last days of the rest-days group. To defne them, we need to know the perodcty attrbutes of the adacent days: the day before the revewed date n case of the day of the rest-days group and the day after the revewed date for the last day of that group. Dffculty s added by the fact that for these adacent days there mght have been fxed changes or substtutons, and we need to take nto account the perodcty attrbutes of all these changes. For each element p P, there s a specal rule of calculatng f p (x). Examples of ths calculatons rules are shown n table 2. In the gven expressons we use the functons WeekDay (x) and DayOfMonth (x) returnng for the date x, correspondngly, the day of the week and the number of the day n the month, as well as the functon Mod (a, 2) returnng remander after number a s dvded by 2. Table 2. Examples of rules for calculatng belongng of the date x to the elements of the set P Perodcty attrbutes p Rules of calculatng the attrbute f p (x) Day of week: p = dw { Mon, Tue, Wed, Thu, f dw (x) = WeekDay (x) Fr, Sat, Sun} Attrbute type of day (of ether a rest-day or a workday): wd, f WeekDay( x) { Mon, Tue, Wed, Thu, Fr}; f (x) p = td { wd, rd} td = rd, otherwse Day s even and odd: pd, f Mod( DayOfMonth( x)),2) = 0; p = pn { pd, nd} f pn (x) = nd, otherwse The last holday: lh, f WeekDay(x) { Sat, Sun} p = lh f lh ( x) = WeekDay( x + day ) { Mon, Tue, Wed, Thu, Fr};, otherwse where x + day the day followng the day x Every day: p = ed (x) = ed f ed Example. The tran ples on even days of the month except Tuesday. To work wth the schedule of the gven tran, we need to defne the dates from the dapason [ ; ], whch satsfy the perodcty characterstc s an even day of the month and not Tuesday. For the gven perodcty attrbute we have C = pd Tue, then the check up of the dates correspondence to the gven perodcty characterstc comes down to calculatng the expresson C(x) of the type C( x) = ( f ( x) = pd) ( f ( x) = Tue) : pn dw C(' ') = [( f (' ') = pd) ( f (' ') = Tue)] = True ; pn dw = C(' ') = [( f (' ') = pd) ( f (' ') = Tue)] = 0 False ; pn dw = C(' ') = [( f (' ') = pd) ( f (' ') = Tue)] = 0 False. pn dw = We cannot but notce that n the gven tme dapason only one date consdered perodcty characterstc. The resultng s as follows: x = ' ' BExt([ ; ], pd Tue). x =' ' satsfes the 4

19 Sesson 3. Formalzaton and Smulaton of Busness Systems 5. Examples of Calculatng Temporal Elements Let us consder an example of calculatng temporal elements for dfferent versons of the schedule for the tran numbered n. The set of versons of tran schedule wth dfferent perodcty s schematcally presented n Fg.3 and Fg.5. As we can see n Fg. 3, the tran has three schedules v,v2 and v 3. Let us fx two versons of the schedule v and v 2 wth the correspondng perodcty attrbutes wd and rd on the perod from November to November 30, 2007; the tme of fxaton of these versons s October 0, 2007 correspondngly at 2:00 and 4:00, and the thrd verson v3 wth the attrbute Tue,Thu for the perod from November 5 to 25, 2007 s fxed on November 2, Then we have: t ='0..07', t 2 ='05..07', t 3 ='25..07' and t 4 ='30..07'. Fg. 5 shows the tme perod November 5 25, 2007, when three schedules v,v2 and v3 were n use; here: on the axs Days of week corresponds to Monday November 5, 2007; 2 corresponds to Tuesday November 6, 2007, etc. Accordng to formulae (2) we can descrbe each schedule verson: v v v { n wd, ' : 00', '0..07', '30..07, s, ' : 05',,,' 2 :5' } =, s0 { n rd, ' : 00','0..07 ', '30..07, s,' : 00',,,' 2 :2' } 2 =, s0 { n ( Tue Thu),' : 00','05..07', '25..07, s,' :0',,,' 2 : 2' } 3 =, s0 Note that n gven examples we show only the frst and the last stops of the tran schedules to smplfy the data presentaton. Snce November9, 2007 was announced a rest-day n Latva, on that day the trans were plyng n conformty wth the rest-day schedule. Therefore, n our case we have a non-empty set of exceptons for restdays; n other words we have EX ( rd) = { 9. }. Note that here and further on, we do not menton the year 2007 to smplfy the data presentaton. Calculaton of the temporal element for the schedule verson v 3, fxed after the frst two versons, s made pretty smply accordng to formula (5), snce we do not need the temporal elements of the other schedule versons here: (3) (3 (3) ([ t ), t ], C ) TE( C3, t fx ) = TE( C3) = BExt s e 3 EX ([ ts, te ], C3) EX ([ ts, te ], C3) = BExt([5., 29.], Tue Thu) EX ([5., 29.], Tue Thu) EX ([5., 29.], Mon Wed Fr Sat Sun rd) = {6., 8.,3.,5., 20., 22.} = (3) (3) {6., 8.,3.,5., 20., 22.}. To calculate the temporal element of the schedule v 2, we need to know the temporal element of verson v 3 the only verson of the schedule, whch was fxed later: TE (3) ( C2, ' : 00' ) = TE( C2 ) TE( C3, t fx ) = (2) (2) (2) (2) (2) (2) ([ t, t ], C ) EX ([ t, t ], C ) EX ([ t, t ], C ) BExt s e 2 s e 2 s e 2 TE( C3) = BExt([0., 30.], rd) EX ([0., 30.], rd) EX ([0., 30.], wd) TE( C3) = { 3., 4., 0.,., 7., 8., 24., 25.} {9.} {6., 8., 3., 5., 20., 22.} = { 3., (3) 4., 0.,., 7., 8., 9., 24., 25.}. The schedule v s the earlest one, and to calculate ts temporal element we need the temporal elements of the schedules v2 and v 3 : TE( C () (2) (3), t fx ) = TE( C) ( TE( C2, t fx ) TE( C3, t fx )) = () () () () () () (2) ([ t, t ], C ) EX ([ t, t ], C ) EX ([ t, t ], C ) ( TE( C, t ) TE( C )) BExt s e s e s e 2 fx BExt([0., 30.], wd) EX ([0., 30.], wd) EX ([0., 30.], rd) ( TE( C,' : 00') TE( C ))= 2 3 (3) 3 ; = ;. 5

20 The Internatonal Conference Modellng of Busness, Industral and Transport Systems 2008 { 0., 2., , 2.-6., , } {9.} ({3., 4., 0.,.,7., 8.,9.,24., 25.} {6., 8., 3., 5., 20., 22., 27., 29.}) {0.,2., 5., 7., 9.,2.,4.,6.,9., 2., 23., 26., 28., 30.} = 6. Defnng an Actual Schedule Verson Presence of the temporal element allows smplfyng sgnfcantly many of the temporal functons, such as defnng an actual obect verson, defnng the dots on the vald tme axs when a partcular obect verson comes out of the shadow zone. Thus, to defne the actual schedule verson for the tran wth number n we suggest usng functon ActVer() of the type: ( ) ( n ) v f x TE( C, tfx) ; ActVer( x, V ) = otherwse (7) where x s the date whch schedule you have to know. (n) (n) The resultng of the functon ActVer( x, V ) s the element of the set v V presentng the sought for actual verson. If the tran does not ply on the gven date x, the functon wll gve back the empty set. The guarantee of only one actual verson n acton s the condton of non-overlappng ТЕ of all versons of the tran schedule (see rule n the secton 4.2.). 7. Conclusons In the paper we have shown the possblty of usng the theory of sets and the algebra of logcs for the descrpton of the ralway schedule system. Realzaton of the mathematcal model of ralway schedule s performed n the envronment of the temporal database, for whch we have defned the perodcty parameters and temporal elements and formulated the rules of ther calculaton. The suggested schedule s support system may serve not only as an nformatonal schedule system but also as a part of the management system makng t possble to model the ralway schedule by automatcally generatng changes optons n case of announcng an addtonal rest-day and as a part of an analytcal system for analyzng and predctng passengers flows. Further step of the present research wll be amed at reachng effcent solutons for realzng the gven system wth the use of modern database technologes. References. Kopytov E., Demdovs V., Petoukhova N. Method of Temporal Databases Desgn Usng Relatonal Envronment. In: Scentfc Proceedngs of Rga Techncal Unversty Computer Scence: Appled Computer Systems. Rga: Rga Techncal Unversty, 2002 Seres 5, Vol. 3, pp Kopytov E., Demdovs V., Petoukhova N. Use of Temporal Databases Prncples n Informaton Systems of the Latvan Ralway. In: Proceedngs of VII Internatonal Conference TransBaltca Rga: RMS Forum, pp (In Russan) 3. Novkov F. Dscrete Mathematcs for Programmers/ Sankt.Pt. Pter, 2000, 304 p. (In Russan) 4. Terenzan P. Symbolc User-defned Perodcty n Temporal Relatonal Databases. IEEE Transactons on Knowledge and Data Engneerng. Vol. 5, Issue 2, 2003, pp

21 Sesson 3. Formalzaton and Smulaton of Busness Systems SIMULATION OF BUSINESS PROCESS USING PLA FORMALISM Henrkas Pranevcus, Vytautas Plkauskas Kaunas Unversty of Technology, Busness Informatcs Department Studentu 50, Kaunas LT Lthuana E-mal: Whle creatng busness process smulatons models, BPMN descrptons of those models are used. Smulaton model creaton means assgnng parameters to BPMN model. BP-PLA graphc language s developed for creatng smulaton models. The summarzng aggregates smulatng BPMN model elements were created whle developng metamodel of that language. Two types of aggregates, such as: BP generator and busness process behavour mtator were dstngushed n the mplemented system verson of smulaton modellng. The named aggregates were formalzed usng PLA method and were mplemented n PLA modellng system. BP smulaton model PLA descrpton s obtaned from BPMN model n BP-PLA language. Ths descrpton s automatcally transformed nto program code of smulaton model. Provded method for smulaton model creaton s llustrated wth ol-flled wagon outpour n to the ol termnal smulaton model. Keywords: busness process modellng, smulaton, pece-lnear aggregate, doman specfc language. Introducton Accordng to [-2] a busness process s a set of partally ordered actvtes that are amed at reachng a goal. The man concepts of the busness process are: Goal or obectve of the process. It means that after the process has completed t s possble to know f the process has acheved ts goal. Actvty or task. It changes the state of the process n some way. Tme an axs whch the partal order refers to. The tme can be regarded as beng absolute or relatve, dscrete or contnuous, nternal or external. State. It s a characterstc of the process. It can be fnal (the goal has been reached) or ntermedate (the goal has not been reached yet). Event. A moment of tme at whch the state of the process changes. Process type. Processes that are smlar by ther goals and actvtes are unted n such types. These concepts are smlar to concepts that are used to descrbe a dynamc system whch changes states on the way to reachng ts goal. Smulaton models can provde the most accurate and nsghtful means to analyze and predct the performance of busness processes [3]. A smulaton s an mtaton of a system. A smulaton of a department, responsble for payng accounts, would mtate the behavour of such department and portray ts dynamcs. In the past few years, several new software tools have been developed specfcally for modellng busness processes. Most of these tools defne busness processes usng graphcal symbols or obects, wth ndvdual process actvtes depcted as a seres of boxes and arrows. Specal characterstcs of each process or actvty may then be attached as attrbutes of the process. Busness process smulaton software tools can be dvded nto three maor categores [3]: Flow Dagram Based smulaton tools; System Dynamcs Based smulaton tools; Dscrete Event Based smulaton tools. The most capable and powerful tools for busness process smulaton are the Dscrete Event drven smulaton products. These tools provde modellng of entty flows wth anmaton capabltes whch allow user to see how obects are routed through the system. Some of these tools even provde obect-orented and herarchcal modellng whch smplfes development of large busness process models. Most of the exstng semantc models, languages and logcs dedcated for descrbng and reasonng about tme-based systems, mplctly vew executon as an alternatng sequence of nstantaneous dscrete actons and contnuous phases durng whch tme advances. To each system descrbed n any of these formalsms, one can assocate a transton system or automaton consstng of a set of states, a set of ntal states, a set of dscrete a d actons, a set of dscrete steps s s, and a set of tme-passage steps s s. It s asserted that from state s the system can nstantaneously move to state s va the occurrence of the dscrete acton a. Furthermore, from state s the system can move to state s durng a postve amount of tme d n whch no dscrete acton occurs. These transton systems provde a very abstract vew of the orgnal system behavour, n whch many aspects, such as the number of parallel components, the communcaton between these components, the way n whch a system evolves durng the contnuous phases, etc., are no longer represented. In ths paper Pece-Lnear Aggregate formalsm (PLA) [4] wll be used for creatng dynamcal models of busness process. Motvaton for usng formal methods s: Permt an unambguous formal descrpton of a system beng analyzed; 7

22 The Internatonal Conference Modellng of Busness, Industral and Transport Systems 2008 Model propertes can be analyzed usng mathematcal proof technques; Formal descrpton approach s a theoretcal background for developng computerzed formal specfcatons analyss software tools (valdaton, verfcaton, smulaton). PLA s a specal case of automaton models. The state of the aggregate can change n two cases only: when an nput sgnal arrves at the aggregate or when a contnuous component acqures a defnte value. The Pece-Lnear Aggregates are based on Pece-Lnear Markoff representaton. The scheme for creatng a model for smulatng busness process (BP) s gven n Fgure. BPMN Descrpton BPMN-PLA Descrpton PLA Smulaton System PLA of BPMN Elements BP Smulaton Model Fg.. The scheme for creatng BP smulaton model BP-PLA graphc language was created for the expanson of BPMN model. Language was developed by deployng Mcrosoft Tools for Doman Specfc Languages [6]. Whle creatng metamodel of the graphc language, the summarzng aggregates, smulatng BPMN model elements, were created. In the mplemented verson of smulatons system two types of aggregates: Busness Process Generator and Busness Process Behavour Imtator were dstngushed. The frst aggregate smulates BPMN Start Event element. The second aggregate smulates the followng BPMN elements: Actvty, Sequence flow, Message flow, AND Gateway, Exclusve Gateway and End Event. The named aggregates were formalzed usng PLA method and mplemented n PLA modellng system. PLA descrpton of BP smulaton model was obtaned by descrbng BPMN model n BP-PLA language. Ths descrpton was automatcally transformed nto program code of the smulaton model. The BP smulaton model was obtaned by applyng PLA smulaton modellng framework. The rest of the paper s structured as follows: Secton 2 descrbes PLA formalzaton approach, Secton 3 presents obect orented model of PLA that had been used for developng Busness Process Smulaton Modellng System. Secton 4 presents how the smulaton model s obtaned by deployng our created smulaton system BP-PLA and usng BP BPMN descrptons. Secton 5 presents an example of methodc for creatng smulaton model of busness processes n transhppng ol termnal. 2. PLA Smulaton System The aggregate approach for a system specfcaton s appled by representng a system as a set of nteractng Pece-Lnear Aggregates (PLA) [4]. The PLA s understood as an obect defned by a set of states Z, nput sgnals X and output sgnals Y. The aggregate functon s defned n a set of moments n tme t T. The states z Z, the nput sgnals x X, and the output sgnals y Y are consdered to be tme functons. Along wth these sets, transton H and output G operators are also used. Smulaton modellng system was mplemented n Mcrosoft.NET 2.0 envronment n C# program language [5]. The system has a lbrary composed of basc classes for aggregate smulaton. For the mplementaton of aggregate connecton scheme there were three dedcated classes used (Fg. 2): SmulatonModel aggregate smulaton model basc class; Aggregete aggregate basc class; OutputPont aggregate nteracton pont class. The aggregate connecton n the aggregate system s mplemented by the SmulatonModel class whch contans an aggregate lst modelaggregates. In ths lst aggregates belongng to the Aggregate are kept. Aggregaton obects and SmulatonModel classes are created durng the creaton of aggregate connecton, whch s formed n the AddAggregate method. These are then placed nto the modelaggregates lst. After that, the aggregate obects are connected to the closed system by deployng OutputPont class (.e. aggregate nteracton pont). The obect method nsde ths class ConnectTo() s connected to the closed system usng the connecton channels. The aggregate nteracton whle communcatng through aggregate connecton channels s mplemented by the nteracton pont obect method Output(). 8

23 Sesson 3. Formalzaton and Smulaton of Busness Systems Fg. 2. The dagram of aggregate connecton scheme mplementaton classes SmulatonModel class method ntalze() s created for the aggregate system ntalzaton (.e. ntal aggregate system state) settng. The mplementaton of ths method calls ntalze() methods of each aggregate obect n the modelaggregates lst. The followng classes for the aggregate external event generaton and t s processng n the lbrary are descrbed (Fg. 3): ExternalEvent external event class; ExternalEventHandler delegate of aggregate external event processng method; AgEventArg the base class of message transfer between aggregates. The generaton of aggregate external events s ntated by the aggregate message transformer n the method Send() whch moves events to the approprate nteracton pont obect. The outgong message s the obect wthn AgEventArg. The structure of ths message n the nteracton pont obect method output() s placed nto the newly generated outer event ExternalEvent type obect. Wthn ths obect there are as many external events generated as there are saved references n nteracton pont obect attrbute targeteventhandlers. The references to the delegate ExternalEvenHandler of the approprate outer event processng method are saved n ths attrbute. All generated external events are placed and saved n the queue SmulatonMoel.externalEventQueue tll they are selectng for processng wth NextExternalEvent() method from SmulatonModel class. Fg. 3. The dagram of external events mplementaton classes 9

24 The Internatonal Conference Modellng of Busness, Industral and Transport Systems 2008 The followng classes for the generatng and processng aggregate s nternal events are dstngushed (Fg. 3): InternalEvent nternal events class; ContousCoordnate abstract contnuous coordnates class; InternalEventHandler delegate of aggregate nternal event processng method; ControlSum class of control sum; ControlSequence class of control sequence. Aggregate nternal event generaton s ntated by aggregate controllng sum ControlSum method CreateInternalEvent(w). The tme moment of the expected nternal event s set by ths method s parameter w. One of the further mentoned methods can be used for settng parameter w of control sequence ControlSequence class obect: Next() generates random number equally dstrbuted n the nterval (0, ); Next(double a, double b) generates random number equally dstrbuted n the nterval (a, b); Next(double b) generates random number equally dstrbuted n the nterval (0, b); NextExp(duoble m) generates random number equally dstrbuted accordng the exponental law wth the mean m. Generated nternal event s put nto the sorted lst of nternal events nternaleventquque. The sortng s made accordng the nternal event attrbute W. Internal event for the processng s selected by SmulatonModel class method NextInternalEvent(). 3. BP-PLA Smulaton Systems Whle creatng metamodel of the grapc language, the summarzng aggregates, smulatng BPMN model elements, were created. In the mplemented verson of smulatons system two types of aggregates: Busness Process Generator and Busness Process Behavour Imtator were dstngushed. The frst aggregate smulates BPMN Start Event element. The second aggregate smulates the followng BPMN elements: Actvty, Sequence flow, Message flow, AND Gateway, Exclusve Gateway and End Event. Fg. 4. The dagram of nternal event mplementaton class 20

25 Sesson 3. Formalzaton and Smulaton of Busness Systems 3.. Aggregate for BP generaton Aggregate generator mplements BPMN start event,.e. creates a new BP nstance that s provded by the number of -th queue (unque dentfer). Ths number dentfes approprate BP process nstance n the smulaton model (BP). The BP performance traectory s defned by (Fg. 5): PB 2 3 N = a,a,a, a, where: a s the dentfcaton of -th actvty n BP traectory; N s the number of actvtes n BP traectory. a 3 BP a a 2 a 4 a 5 a 6 a 7 BP 2 a 2 a 2 2 a 2 3 a 2 4 a 2 5 a 2 6 a 2 7 PB τ Fg. 5. BP performance traectory The followng performance duratons are defned for each actvty element of that performance traectory: = τ, τ,, τ 2, τ 3 where τ s the duraton of a actvty. BP process s defned by two sequences a τ BP = BP, BP. N Characterzed sequences are generated accordng to the schedule formed n advance or accordng to the dstrbuton law that defnes the tme moments when new processes appear. Generated sequences are output sgnals of Generator aggregate ( y = BP ) Aggregate for mtaton of BP behavour The structural scheme for busness process behavour aggregate s gven n Fgure 6. The presented scheme pctures n-channel servce system that s composed of: Servce devces R, =,n ; Prorty queues Q, =, m ; Buffer groups { B,B 2, B } B =, =, m. k Servce devces R are used for BPMN actvty performance modellng. Actvty can be performed n any free servce devce. If all the devces are busy, BP s put nto queue. If the servce devce s busy, relatve prortes can be assgned to queued actvtes. The prorty queues were ntroduced for mplementaton of prorty servce. Buffer groups are used for the smulaton of BPMN element s AND Gateway BP-PLA graphc language BP-PLA graphc language was created for descrbng BPMN model expanson. Mcrosoft Tools for Doman Specfc Languages (DSL) were used for the composton of ths language [6]. Usng DSL, users can desgn graphcal languages and generate code and other text output from the doman-specfc languages. DSL tools consst of: A proect wzard creatng a fully confgured soluton. There user defnes a doman model; A graphcal desgner for defnng and edtng doman models; Desgner defntons n XML. The code for mplementng desgners s generated from these defntons so that one can defne a graphcal desgner hosted n Mcrosoft Vsual Studo wthout manually wrtng any code. A set of code generators that take a doman model defnton and a desgner defnton as nput and produce code mplementng both of the components as output. The code generators also valdate the doman model and the desgner defnton. 2

26 The Internatonal Conference Modellng of Busness, Industral and Transport Systems 2008 Servce devces Buffer groups Prorty queues Fg. 6. The structural scheme of BP behavour aggregate BP-PLA graphc language doman model defnton s gven below. BPPLA model conssts of two types of aggregates (Fg. 7): AgrStart s used to smulate BPMN Start Event element; AgrFlow s used to smulate BPMN flow elements. Aggregate AgrStart has an output OutPort, whle AgrFlow has both nput and output ponts InPort. Aggregate s nput and output ponts are connected wth Connecton channels, whch are used for message transmsson between aggregates (Fg. 8). Message receved va InPort s transmtted to BPMN element Actvty. Ths BPMN element can transmt the message further to another aggregate va OutPort. Fg. 7. Dagram of BP-PLA graphcal language for aggregates defnton Fg. 8. Aggregate and Actvty nterconnecton dagram 22

27 Sesson 3. Formalzaton and Smulaton of Busness Systems A dagram of BPMN elements (EndEvent, Actuvty, Gateway) s presented n Fgure Smulaton Model of Ol Termnal Ol products are transported to the ol termnal by trans. When a tran arrves, the representatve of the ralway gves the load documents to the termnal operator. After that the data of load arrval and delvery notes are entered nto nformatonal system of the termnal. At the same tme customs procedures are Fg. 9. Dagram of BPMN elements beng completed. The worker of the strategc management department groups the delvered wagons nto groups wth no more than 32 wagons n each. In ths way all the wagons are empted n two turns. After the message about assgned groups reaches ralway staton servce, wagons are delvered to the overhead road for the outpour. The needed tanks are prepared before outpour, ther level s fxed, and the route for product pumpng by the ppes s set, needed bolts are opened, the outpour devces n the overhead are connected, the steam s passed, and the pumps are swtched on. The wagons are checked, steam pass s swtched off, bolts are closed, transhpment devces are dsconnected, and the van dspatch documents are formalzed. The ralway staton servce takes the wagons from the termnal operators and draws the documents for further wagon transportaton. A busness process BPMN dagram of ol pourng out of the wagons nto reservors s presented n Fgure 0. Fg. 0. BPMN dagram for ol outpour from wagon to termnal tank Whle creatng the smulaton model, the followng ol termnal resource requrements had to be evaluated: Two workng places for the document processng n the strategc management department exst: arrval data flng (aggregate ManDep), and wagon groupng nto groups (aggregate ManDep2); One workng place for document processng n customs s foreseen (aggregate Custom); Two platforms are used for transhpment of ol n termnal (aggregate Platform); 23

28 The Internatonal Conference Modellng of Busness, Industral and Transport Systems 2008 One locomotve for wagon transportaton between ralway staton and transhpment platforms s used (aggregate Locomotve). A BP-PLA model dagram was created usng these constrants (Fg. ). Fg.. BP-PLA model dagram Usng the dagram a software code of the smulaton model was generated. Smulaton results An ncome from wagon unloadng,.e., ol pourng out from wagons nto termnal reservors, was calculated durng smulaton. The ncome depends on unloaded amount of ol. Income dependences of per loadng coeffcent (K) n dfferent envronment temperature condtons (T) are presented n Fgure T(+0) T( 0 ) T(-0) ,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 Fg. 2. Smulaton results ncome The ncome dependences are presented usng relatve percentage values. It s consdered that 00 percent ncome s at 20 Celsus envronment temperature (there s no need to warm wagons before pourng out) and whle pourng out pers are fully loaded,.e., when K=. Dependences of formed ol pourng expenses from per load coeffcent (K) n the dfferent envronment temperature condtons (T) are presented n Fg. 3. Pourng expenses depend on the amount of the poured ol and expendtures for wagon warmng tll the requred temperature before the pourng begns. Warmng expenses arse when ol n wagons s gettng cold whle watng for the pourng to begn. These expenses are presented usng the same relatve values as for ncome n Fg. 2. Dependences of the dfference between receved ncome and pourng expenses on per loadng coeffcent (K) n the dfferent envronment temperature condtons (T) are presented n Fg. 4. Ths dfference s presented usng the same relatve values as for ncome n Fgure 2. 24

29 Sesson 3. Formalzaton and Smulaton of Busness Systems T(-0) T( 0 ) T(+0) ,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 Fg. 3. Smulaton results expense 5 T(+0) T( 0 ) T(-0) 0 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9-5 Fg. 4. Smulaton results dfference 5. Conclusons The BP-PLA language created by authors for desgn of smulaton models s presented n the paper. The language uses PLA modellng concepts. It permts to expend busness process descrptons n BPMN. Ths extenson permts to automate the generaton of smulaton model programs. References. Krkova, M., Makna, J. Renassance of Busness Process Modellng. In: Proceedngs of 3th Internatonal Conference on Informaton Systems Development Advances n Theory, Practce, and Educaton (ISD 2004) Vlnus, 2004, pp F-R.Ln, M-Ch. Yang, and Y-H. Pa. A generc Structure for busness process modellng. Busness Process Management Journal Vol. 8(), 2002, pp Hlupc, V., Vreede G-J., Orson A. Modellng and Smulaton Technques for Busness Process Analyss and Re-Engneerng, Internatonal Journal of Smulaton Systems Scence and Technology, Vol. 7 (4-5), 2006, pp Pranevcus H. Aggregate Approach for specfcaton, Valdaton, Smulaton and Implementaton of Computer Network Protocols. Lectures Notes n Computer Scence No 502, Sprnger, 992, pp Pranevcus, H., Plkauskas V., Gugns G. Creatng Smulaton Models Specfed by PLA Usng UML. In: Internatonal Conference on Operatonal Research: Smulaton and Optmsaton n busness and Industry. Kaunas: Technologa, 2006, pp Greenfeld J., Short K., Cook S., Kent S.: Software Factores: Assemblng Applcatons wth Patterns, Models, Frameworks, and Tools. Wley Publshng, 2004, 25 p. 25

30 The Internatonal Conference Modellng of Busness, Industral and Transport Systems 2008 MODELLING AND ANALYSIS OF BUSINESS RULES USING KNOWLEDGE BASED AND FORMAL APPROACHES Henrkas Pranevcus, Germanas Budnkas Busness Informatcs Department, Kaunas Unversty of Technology Studentu 56-30, Kaunas, Lthuana Phone: E-mal: {henrkas.pranevcus, The paper presents an approach that apples knowledge based and pece-lnear aggregate (PLA) formal approaches for modellng and analyss busness rules. In our technque, busness rules are represented by producton rules usng concepts of PLA model. A knowledge base of the busness rules s analysed by checkng ts consstency (statc propertes) and dynamc constrants (dynamc propertes). The analyss s performed by applyng decson table verfcaton method and reachable state valdaton method and supportng tools PROLOGA and CLIPS. The proposed approach s llustrated by an example. Keywords: busness rules, PLA, knowledge base, decson table, consstency and dynamc constrants. Introducton Busness rules are sgnfcant for enterprses because they defne how they are dong busness. They are also popular n the nformaton system communty as they are able to make applcatons flexble. One of the most mportant parts n the development of nformaton systems s problem representaton and analyss of doman descrptons, whch, n our case, are expressed n a form of busness rules. Possble nconsstences lke redundances, contradctons or mssng rules as well as dynamc falures lke nablty to reach a defned goal should be corrected as early as possble to mnmse cost of the development. Checkng for consstency as well as dynamc constrants s emphassed n formal methods and formal specfcatons. The most popular formal specfcaton languages beng used for descrpton of the systems are SDL, Lotos, Estelle, PLA [], [2], [3]. Checkng of busness rules consstency s hghly mportant. Examples of related works could be [4], [5], [6], [7], [8]. The use of models (especally formal ones) whle representng and analysng busness rules s propagated n [9], [0] as t smplfes the rule formalsaton and ensures hgher clarty and consstency of the rule descrptons. PLA s a formal state-based model. It s successfully used for formal specfcaton, valdaton and smulaton of complex system ncludng computer network protocols, transport systems, medcal applcatons, etc. for several decades. Use of PLA model n representng and analysng busness rules should gve us an advantage of a use of formal model as well as accompanyng analyss technques. In ths paper we wll explore the possbltes to use PLA and related technques for busness rules. Busness experts fnd dffcult to understand formal specfcaton languages. Many authors (e.g. Bruynooghe et al. []) beleve that the declaratve style of descrpton that s used n knowledge bases s more understandable and acceptable than the procedural style (the latter s used n PLA formal specfcaton languages). Ths s because a problem s descrbed at the knowledge level at whch the knowledge engneer specfes expertse [2]. Representaton of knowledge used n knowledge-based systems (KBS) s close to the way of thnkng by a human. Condtonal and sequental parts of the most busness rules correspond to a structure of a producton rule representaton. In ths way, representaton of busness rules by producton rules s natural. State structure, condtons for state changes due to ncomng requests and nternal events are strctly defned n the PLA model. Addng the PLA model to the representaton process assgns extra value n terms of easer to represent a structure of busness processes expressed usng busness rules, ther nteracton; easer to perform checkng. Our approach for representng busness rules s based on producton rule representaton and PLA model elements. Ths approach s explaned n secton 2. Busness rules consstency s expressed usng general propertes non-redundancy, non-conflctness, non-defcency. The consstency of busness rules s checked by transformng PLA KB productons to decson tables (DT) and applyng tabular statc verfcaton technque that s mplemented n Prologa system. The consstency checkng technque s descrbed n secton 3. Dynamc constrants of busness rules are expressed usng general dynamc propertes absence of statc deadlocks, fnal state reachablty, boundedness, and completeness. The constrants are checked usng expert system that s bult by combnng PLA KB wth knowledge base of dynamc propertes and valdaton method. The technque s presented n secton 4. Secton 5th llustrates the proposed technque wth the example of busness rules descrbng goods orderng regulatons used by a frm manager. Relaton of the proposed approach to other works s dscussed n secton 6. Concluson sums up the paper. 26

31 Sesson 3. Formalzaton and Smulaton of Busness Systems 2. Busness Rules Representaton Usng Concepts of PLA Model Accordng to the revew made n [5] classfcaton categores of BR nclude the followng: rules descrbng stuatons (e.g. state changes due to busness events), constrants, facts assertng structure, terms correspondng to actors, events, parameter values, actons, etc. These concepts and rules already present n the state-based formal pece lnear aggregate PLA model [3]. The model defnes notons that can be successfully appled for busness rule representaton and analyss. Input and output requests, ther structure, nternal and external (busness) events along wth ther cause, actvtes, computatonal parameters, state structure and rules descrbng how state s changed, actors and ther nterconnecton are all defned n the formal PLA model. As was stated early, representaton of busness rules n a declaratve way by usng productons s natural and wll be used n our approach. Therefore, we propose for each rule category to use an approprate rule template, whch can be seen as a sentence pattern that tells how to descrbe the rules that belong to a partcular category. Further we present examples of busness rule categores and how they are represented by rule templates expressed n a form of knowledge base based on PLA model (PLA KB) predcates and productons. Busness rule category Incomng request Actor's state State change and output of the request after occurrence of an external event PLA KB predcate or producton c IncomngRequest ( a, x,, x c ), c c x where a symbolc name of the th actor; x,, components of the request. c c cc dc State ( a, w,, w, d,, d ), c where cc c w,..., w and d dc,..., d are actons and computaton parameters descrbng the state. c c IF IncomngRequest ( a, x,, x ) cc dc and State ( a, w,, w, d,, d ) c c c cdc cc and Aux ( a, w,, w, d,, d ) c cc dc THEN State ( a, w*,, w *, d *,, d * ) and OutcomngRequest ( a, y,, y ) where predcate Aux descrbes auxlary condtons that check state values. c c oc The representaton usng PLA KB s performed by puttng knowledge of busness rules to correspondng elements of PLA KB whch form and structure are defned wth respect to formal PLA model. Such a way of representng the busness rules by puttng ther knowledge to the constructs of the defned structure s suggested n [9], [0], as t smplfes the rule formalsaton and ensures hgher clarty and consstency of the rule descrptons. After creaton of the PLA KB, t s checked for consstency and dynamc falures by analysng ts general statc and dynamc propertes correspondngly. 3. Checkng of Busness Rules Consstency Busness rules consstency means that the busness rules are expressed n the rght way. Checkng ths property s known as verfcaton [4]. Consstency of busness rules usually s expressed n terms of nonredundancy, non-conflctness, non-defcency [5]. These constrants by ther nature correspond to the ones that are analysed whle checkng statc propertes (.e. performng statc verfcaton) of rule bases. As t was mentoned earler, busness rules n our approach are represented by producton rules of PLA KB. Snce most of nconsstences n rule-based systems can be solved usng decson tables (DT) [3] and the tabular verfcaton technque s computersed n Prologa system [4], our approach employs these facltes. Therefore, n order to perform checkng of consstency of busness rules represented n PLA KB, ts producton rules have to be transformed to Prologa DTs. As stated n [3], a DT s equvalent to a set of producton rules. Consstency constrants for DTs have drect correspondences to the ones, defned for rules, whch make the PLA KB. In our technque, consstency checkng s performed n Prologa system. The system uses sngle ht DT representaton. In a sngle ht table each possble combnaton of a condton can be found n exactly one and only one column. The transformaton to Prologa DTs s specfc wth respect to the PLA model and employs some of ts concepts that have been mentoned n the begnnng of ths secton. Producton rules are transformed to the DTs of certan groups thus enablng to fully explot advantages of tabular representaton to perform consstency checkng. 27

32 The Internatonal Conference Modellng of Busness, Industral and Transport Systems 2008 Statc verfcaton technque for analyss of PLA KB s based on [3], [4] works. Further we present a porton of ths technque. A subsumed column par n a sngle ht DT s represented by sngle column that corresponds to several PLA KB productons. Thus, the subsumed column par anomaly s detected f several PLA KB productons correspond to the same DT column. Full descrpton of the PLA KB statc verfcaton technque as well as transformaton steps of PLA KB constructs to sngle ht DTs are presented n [5], [6]. 4. Checkng Dynamc Constrants of Busness Rules The dynamc constrants (or propertes) are those characterstcs of a rule-based system that can be evaluated only by examnng how the system operates at a run tme. The most common technques of valdaton and verfcaton that have been developed for use on KBS are dentfed n [7]. A detaled revew of specfc methods and supportng tools can be found n [8]. Functonal valdaton of the PLA KB s carred out usng the expert system n CLIPS (C Language Integrated Producton System). CLIPS s a tool for productve development and delvery of expert systems [9]. The expert system s bult by combnng statcally verfed PLA KB wth a KB of dynamc propertes and valdaton method (KB DPVM) [6]. Inference n the expert system for functonal valdaton s performed usng forward-channg strategy oned wth a reachable states method [5]. The dea behnd ths method s a constructon of a correspondng graph of global states of the model (.e. the nvestgated busness process) under analyss. Constructon s started wth the predefned ntal global state. All possble transtons from the gven state are analysed. Repeatedly generated (accordng the model functonng) states that have been already analysed are excluded from the analyss. The reachable states graph s constructed tll the fnal state s reached or some of the valdated dynamc propertes are not satsfed. Whle makng the nference, rules of PLA KB, whch descrbe both busness processes and dynamc propertes, are actvated and executed. The scheme below llustrates how functonal valdaton n the expert system s performed. The defned KB DPVM, whch s mplemented n CLIPS, may be used for varous knds of applcatons. The nstances of dynamc propertes are the absence of statc deadlocks, fnal state reachablty, boundedness of countable state parameters, and completeness. Valdaton method, n whch all reachable states are analysed, s mplemented n the KB DPVM. In a vew of analyss of the executon paths, ths method s smlar to functonal valdaton method suggested by Preece et al. [20] that analyses the sequences of rules that must fre to acheve a goal. When performng the on of PLA KB wth KB DPVM, the needed adaptaton changes are mnor they are an adaptaton of descrpton of dynamc constrants for a specfc busness process. For nstance, n order to check the boundedness property, ndvdual bounds have to be defned. Havng combned the KB DPVM wth the PLA KB, the expert system (ES) n CLIPS s bult. The ES uses CLIPS nference engne that s based on the forward channg strategy. If the valdated dynamc constrants are volated, the expert system generates a correspondng report and a desgner corrects the KB accordngly. Begn KB DPVM s supplemented wth predcates about: ntal and fnal states; auxlary knowledge for reachable states graph constructon; auxlary knowledge for check of dynamc propertes Executon of PLA KB productons that descrbe busness processes. Generaton of new global state. Removng of newly generated states that already have been analysed Incluson of already analysed global states nto a set of analysed global states. Checkng for dynamc propertes One of the propertes under analyss s not satsfed N Y End Fg.. Schematc llustraton of the analyss of dynamc propertes n the valdaton expert system 28

33 Sesson 3. Formalzaton and Smulaton of Busness Systems 5. Illustraton of the Proposed Technque For llustraton of the proposed technque we employ busness rules descrbng automoble spare parts orderng regulatons used by a frm manager. The rules are the followng. A customer orders an tem (or tems). At the frst, the manager searches for t n a local store. If the search fals, the tem s ordered from a warehouse; otherwse t s ordered from the local store. If an amount of the requested tems s greater than the local store has, partal orderng (from the local store and then from the warehouse) s requested. Local store may have up to 00 tems. A fragment of the busness rules represented by PLA KB s gven n Table. Table. PLA KB fragment of goods orderng regulatons Busness rule PLA KB predcates and rules State of the aggregate LocalStore s charactersed by predcate State: Item search n a local store, order from a warehouse, order from a local store, partal order from the warehouse and local store, search result and amount of the requested tems. State(LocalStore, search, order_ws, order_ls, porder_ws, porder_ls, search_res, tem_amount) For the brefness, afore-defned predcate wll be denoted as State_C. A customer orders an tem (or tems). At frst, the manager searches for t n a local store. If the search fals, the tem s suppled from a warehouse. If the search fals, ; otherwse t s suppled from the local store. If an amount of the requested tems s greater than the local store has, partal order (from the local store and then from the warehouse) s requested. IF IncomngReqest (LocalStore,tem_number, amount) and State_C THEN search * = True and State_C IF EndOfOperaton (LocalStore,Search) and State_C and search_res = False THEN order_ws * = True and State_C IF EndOfOperaton (LocalStore,Search) and State_C and search_res = True and tem_amount > 00 THEN porder_ls * = True and State_C IF EndOfOperaton (LocalStore,POrderFromLocalStore) and State_C THEN porder_ws * = True and State_C Two PLA KB productons descrbng end of search n a local store are represented by a decson table (see Table 2). Table 2. Decson table descrbng end of search n a local store. EndOfOperaton (LocalStore,Search) True False 2. ^State_C True False - 3. search_res True False tem_amount 00 > porder_ws * = True.. x.. 2. porder_ls * = True. x State_C. x x The decson table shows that no rules correspondng to the frst row. Thus, a defcency case mssed rule presents n the KB. Such verfcaton report presents Prologa system. Therefore, the KB has to be supplemented wth a correspondng rule. Next we present a producton rule of KB of dynamc propertes and valdaton method that checks dynamc constrant absence of deadlocks: 29

34 The Internatonal Conference Modellng of Busness, Industral and Transport Systems 2008 IF State(parrent_state, current_state, LocalStore, search, order_ws, order_ls, porder_ws, porder_ls, search_res, tem_amount ) AND search = Inactve AND order_ws = Inactve AND order_ls = Inactve AND porder_ws = Inactve AND porder_ls = Inactve THEN Valdaton_Result ( Deadlock presents n state & current_state & whch s orgnated from & parrent_state). 6. Related Works General structures of the predcates and rules for KBs of applcaton and valdaton are defned n both technques too. Our approach s smlar to [2] snce they all use the decson table (DT) for representaton of state-based systems. Mappngs between rules and DTs n order to elaborate advantages of tabular representaton are used n our and [22] approaches. Our approach as well as many others, example of whch s [23], explots advantages of tabular representaton n order to perform verfcaton by transformng certan representaton to DTs. Whle performng statc verfcaton of PLA KB, we use results of Vanthenen et al. [4], whereas when analysng the dynamc constrants we use the reachable state method that s smlar to the functonal valdaton method suggested by Preece et al. [20] n a vew of analyss of executon paths. Rule manager [24] checks for the same set of anomales as our proposed technque does. The followng anomales are beng explored: contradctons, redundances, and ncompleteness. Our approach s smlar to that of [25] snce they both offer the use of declaratve languages for a descrpton of the user needs. We use PLA model concepts for representaton of the obect structure, whle Specht [25] use obect as theory model. In our approach, n contrast to the compared one, we emphasse verfcaton of the created declaratve descrpton. Bergeron et al. [26] state that statc and dynamc analyses are complementary. They propose to use statc analyss frst. In our work at the begnnng of the checkng we use statc verfcaton technque that complements the functonal valdaton. Our approach, as another ones (e.g. [27], [28], [29]), uses statc and dynamc analyses n a par n order to comprehensvely analyse the applcaton beng developed. 7. Conclusons In ths paper we have presented a technque for representaton and analyss of busness rules. Usng the llustratve example we showed as follows: PLA model can be successfully used as a background for busness rules representaton; It gves us the followng benefts: o PLA related valdaton method for analyss of dynamc propertes usng reachable states graph can be successfully appled whle checkng general dynamc constrants of busness rules,.e. absence of statc deadlocks, fnal state reachablty, boundedness of countable state parameters, and completeness; o Tabular verfcaton method can be successfully appled for analyss of statc constrants of busness rules expressed n PLA knowledge base. These constrants are non-redundancy, non-conflct/ness, non-defcency Applcaton area of the approach proposed are busness rules descrbng nteractons between structural parts of a system or organsaton. Ths statement s based on a fact that PLA model s prmarly suted for specfcaton and analyss of complex systems nteractng between themselves. The scalablty of the proposed technque s lmted by software tools that are used n creatng the specfcaton. The lmtaton requrements for these tools are defned n [3], [9]. References. Facch, C., Haubner, M., Hnkel, U. The SDL Specfcaton of the Sldng Wndow Protocol Revsted. Techncal Report TUM-I964. Munchen: Techncal Unversty, Spraks, P., Tampakas, B., Antons, K. Hatzs, and K.Pentars, G. Specfcaton Languages of Dstrbuted and Communcaton Systems: State of the Art. ESPRIT Long Term Research proect Nr report Pranevcus, H. Formal specfcaton and analyss of computer network protocols: Monograph. Vlnus: Technologa,

35 Sesson 3. Formalzaton and Smulaton of Busness Systems 4. Spreeuwenberg, S. Usng Verfcaton and Valdaton Technques for Hgh-qualty Busness Rules, Busness Rules Journal, Vol. 4, No 2, Halle, B. Busness Rules Appled: Buldng Better Systems Usng the Busness Rules Approach. John Wley, Date, C.J. What not how: The busness rules approach to applcaton development, Addson-Wesley Longman, Basley, D. A Metamodel for Busness Vocabulary and Rules: Obect-Orented Meets Fact-Orented, Busness Rules Journal, Vol. 5, No 7, Gerrts, R. Verfcaton of Busness Rules Utlzaton, Busness Rules Journal, Vol. 4, No 2, Baec, M., Krsper, M. A methodology and tool support for managng busness rules n organsatons, Informaton Systems, Vol. 30, No 6, 2005, pp Martn, J., Odell, J. Obect-Orented Methods, a Foundaton. NJ: Prentce-Hall, Englewood Clffs, Bruynooghe, M., Pelov, N., Denecker, M. Towards a more declaratve language for solvng fnte doman problems. In: ERCIM/ COMPULOG Workshop on Constrants. 999, pp Velde, W.V., Aamodt, A. Machne learnng ssues n CommonKADS, KADS-II/ TII.4.3/ TR/ VUB/ 002/ Vanthenen, J. Prologa v.5 User s manual. Katholeke Unverstet Leuven, Vanthenen, J., Mues, C., Wets, G. Inter-tabular Verfcaton n an Interactve Envronment. In: 4th European Symposum on the Valdaton and Verfcaton of Knowledge Based Systems. Katholeke Unverstet Leuven, 997, pp Budnkas, G. Development and analyss of aggregate specfcatons usng knowledge bases: PhD dssertaton. Kaunas: Kaunas Unversty of Technology, Pranevcus, H., Budnkas, G. Creaton of Estelle/Ag Specfcatons Usng Knowledge Bases, Informatca, Vol. 4, No, 2003, pp Preece, A. Evaluatng Verfcaton and Valdaton Methods n Knowledge Engneerng, Mcro-Level Knowledge Management, 200, pp Preece, A., Shnghal, R. Foundaton and Applcaton of Knowledge Base Verfcaton, Internatonal Journal of Intellgent Systems, No. 9, 994, pp CLIPS Reference Manual, Basc Programmng Gude Preece, A., Grossner, C., Radhakrshnan, T. Valdatng Dynamc Propertes of Rule-Based Systems, Internatonal Journal of Human-Computer Studes, No. 44, 996, pp Arentze, T., Borgers, A.W.J., and Tmmermans, H.J.F. The ntegraton of expert knowledge n decson support systems for faclty locaton plannng, Computers Envronment and Urban Systems, Vol. 9, No 4, 995, pp Chambers, T.L., Parknson, A.R. Knowledge representaton and converson for hybrd expert systems, Journal of Mechancal Desgn, Vol. 20, No 3, 998, pp Degelder, J., Steenhus, M. A knowledge-based system approach for code-checkng of steel structures accordng to Eurocode 3, Computers and Structures, Vol. 67, No 5, 998, pp Rule Manager, User manual Avalable Specht, G. O!-LOLA - Extendng the Deductve Database System LOLA by Obect-Orented Logc Programmng, Informatca, Vol. 9, No, 998, pp Bergeron, J., Debbab, M., Desharnas, J., Erhou, M., Lavoe, Y., Tawb, N. Statc detecton of malcous code n executable programs, Internatonal Journal of Requrement Engneerng, 2004, pp M, P., Scacch, W. A Knowledge-based Envronment for Modellng and Smulatng Software Engneerng Processes, IEEE Trans. on Knowledge and Data Engneerng, Vol. 2, No 3, 995, pp Regnell, B, Runeson, P. Combnng Scenaro-based Requrements wth Statc Verfcaton and Dynamc Testng, In: 4th Internatonal Workshop on Requrements Engneerng: Foundaton for Software Qualty. Psa, Italy, 998, pp Wang, T.-H., Edsall, T. Practcal FSM Analyss for Verlog, In: IEEE Int'l Verlog HDL Conf. and VHDL Users Forum. Los Alamtos, Calforna: IEEE Computer Soc. Press, 998, pp

36 The Internatonal Conference Modellng of Busness, Industral and Transport Systems 2008 VARIOUS ASPECTS OF SIMULATION S USAGE TO CREATE REAL SOLUTIONS WITH DARSIR CONCEPTION AS AN EXAMPLE Vadm Zuravlyov, Eleonora Latsheva 2 Rga Techncal Unversty Pernavas -2, Rga, LV-02, Latva Phone: E-mal: [email protected] 2 Meza /3, Rga, LV-048, Latva Phone: E-mal: [email protected] Nowadays concepts of desgnng data management systems and technologes exst, and they can be used to create new real solutons wthout usng typcal programmng. In ths work authors present one of the ways to create real solutons the usage of smulatons. Dfferent technologes can be used to enable necessary functonalty, but the authors have chosen Rado Frequency Identfcaton (RFID), as the most perspectve drecton nowadays. One of ther concepts of desgnng data management systems, that authors want to present, s a Data-And-Rules-Save-In-Resource ( DARSIR ) [] concepton, that can be used wth RFID technology. Man case of ths concept s to acheve unversalty, flexblty, not usng other sources (such as database) to accept the decson that the nformaton (attrbutes and rules) s saved n RFID tag. In ths work authors present varous aspects of smulaton's usage to create a soluton. Authors also present the man steps from smulaton creaton to real soluton. Keywords: DARSIR concepton, Rado Frequency Identfcaton, XML, Resource Physcal Mark-up Language, smulaton. Introducton Nowadays one of the most mportant tasks that many specalsts are tryng to decde n nformaton technologes s foundng an easy way for creatng new real solutons. Varous concepts of desgnng data management systems and technologes exst, and they can be used to create new real solutons wthout usng typcal programmng. In ths work authors present one of the ways to create real soluton usage of smulatons. Dfferent technologes can be used to enable necessary functonalty, but authors have chosen Rado Frequency Identfcaton (RFID), as the most perspectve drecton nowadays. Ths technology s chosen n []. RFID s an automatc dentfcaton method, whch reles on storng and remote data retrevng wth the use of devces called RFID tags. RFID tag s possble to place n physcal obect, embeddng n physcal obect or to construct nteracton wth other physcal obects (for example sensors). The approach gves a varety of archtectural solutons. One of ther concepts of desgnng data management systems, that authors want to present, s a Data- And-Rules-Save-In-Resource ( DARSIR ) [] concepton, that can be used wth RFID technology. Man case of ths concept s to acheve unversalty, flexblty, not usng other sources (such as database) to accept the decson that the nformaton (attrbutes and rules) s saved n RFID tag. Ths concept data storage type provdes releve transformaton from smulaton scheme to real solutons. In ths work authors present varous aspects of smulaton's usage to create a soluton Authors present ther opnon for man steps from smulaton creaton to real soluton. In ths paper the man elements of DARSIR concepton, data storage type, attrbutes, rules etc. are descrbed, workng prncples of the real soluton and smulaton are shown. For better understandng of practcal usage, last step s the descrpton of a concrete problem: t s necessary to organze regulaton of temperature nsde. Authors are descrbng aspects of smulaton s creaton of ths task, as well as the real soluton of t n RPML, whch s a fnal result. 2. Descrpton of the Concepton The frst step of smulaton s usage for soluton creaton s defnng key elements of concepton. The key elements of the DARSIR concept are resources. A resource s any obect of the lvng or lfeless nature, whch s nvolved n workng process of nformaton system. The nformaton of a concrete resource and ts nterrelatonshp wth other obects (or types of obects) must be stored n ths resource. Dfferent technologes can be used to enable necessary functonalty, but authors have chosen Rado Frequency Identfcaton (RFID), as ths technology s chosen n []. RFID (see more n [2]) s an automatc dentfcaton method, relyng on storng and remotely retrevng data usng devces the so-called tags. Basc element of ths technology s a tag, t s an obect that can be attached to or ncorporated nto a product, anmal, or person for the purpose of dentfcaton usng rado waves. It s possble to store up to Mb data n each tag. Such sze of data allows untng the lst of attrbutes (data) wth functonalty (rules) n resource. 32

37 Sesson 3. Formalzaton and Smulaton of Busness Systems 3. Workng Prncples of the Real Soluton and Smulaton Next step of our process s defnng workng prncples of concepton and ways of smulaton usage n creaton of new real soluton. The DARSIR concept workng process key element s RFID reader. RFID reader has a bult-n embedded system that loads to and carres out rules from RFID tags. To load rules from RFID tags, they must be located n RFID reader workng zone. If RFID readers are connected n network of RFID readers, that RFID readers realze RFID tag nformaton (attrbutes and rules) exchange. Resources (RFID tags) are mportant for real soluton and smulaton, because for creaton of workng process s necessary to change nformaton (attrbutes and rules) only n resources (n RFID tags). Other elements of workng process (such as RFID reader) usually do not need any modfcatons. 4. The Structure of Stored Informaton Further t wll be necessary to defne the structure of stored nformaton n smulaton. From the prevous chapters t s known, that all nformaton that can be changed, s stored n resources (RFID tags). And all nformaton that s needed n real soluton customer must edt n smulaton scheme. It s not possble to create fnshed real soluton f ths condton s not executed Next step s to descrbe format of storng nformaton n concepton. In the DARSIR concepton nformaton s stored n resource n PML (Physcal Mark-up Language) the format modfcaton of XML. PML s descrbed n [3] as a smple, general language for descrbng physcal obects for use n montorng and control of a physcal envronment partcularly through the Internet. Applcatons nclude nventory trackng, automatc transacton, supply chan management, machne control and obect-to-obect communcaton. In the DARSIR concept descrpton artcle [] s represents a new modfcaton of PML, that s been developed for ths concept, that calls s RPML (Resource Physcal Mark-up Language). Further n ths document the authors gves examples n the language RPML, but the places, where syntax concdes wth the offcal verson of the language PML, wll not be separately descrbed (t s possble to fnd them on offcal page [3]). To create real soluton t s necessary to create RPML document for each element from the fnshed smulaton model and load t n approprate RFID tag. RPML documents have the attrbutes and rules, man types for them and knds of stored nformaton wll be defned n the followng chapters. 4.. Attrbutes Each resource has own unque features, but t s possble to emphasze some standard knds of such features: Physcal any resource possesses physcal propertes, t s possble to fx from what materal the resource s made, the length of the resource, etc. Sensors the resource can have bult-n sensor (such as thermometer, hydrometer) or many sensors; the current value of sensor s stored n resource as attrbute. Entty the resource can have ts owner (t can be the person, the organzaton, the country, etc.), so here such parameters, as a name of the owner, the name of the organzaton, the address, etc., are regstered. Locaton the coordnates of a resource concernng the readng out devce, t can be n 2D (X and Y), also n 3D (X, Y and Z) coordnates. Confguraton resource can consst of another resources (e.g. pallet shpment), here the unque numbers of other resources can be lsted. Hstory parameters of any knd, that has tmng component, when these parameters have been fxed. It s very mportant to remember, that memory of a resource s lmted and consequently t s necessary to lmt fnal number of possble records Varables any program can be stored n a resource, and for ts work varables are necessary. There are standard types of varables (such as Integer, Strng, Date, etc.), and also non-standard such as arrays (defned n PML). So far the authors have descrbed the basc knds of features, but there are also other, not lsted knds of features. All of ths depends on defned tasks and on varants of ther soluton. It would also be desrable to note, that exst tags that communcate wth the carrer. The typcal example of such tag s sensors. For example, the thermal sensor control can wrte down a current condton of temperature n the tag. Also any mechansm (beng carrer of tags) can wrte down on t the nformaton. For example, the prnter can wrte down on the tags the workng condton of tself (such as prntng, on, off, watng, error etc.). Some standard knds are possble to use n smulaton as statc data, such as: physcal, entty. But some standard knds are possble to change n smulaton process, such as: sensors, locaton, confguraton, hstory and varables Rules In smulaton, rules can be created by smulaton s languages. In ths chapter authors are defnng format, how smulaton rules must to be converted for creaton of real soluton. 33

38 The Internatonal Conference Modellng of Busness, Industral and Transport Systems 2008 The deology s smlar to usual programmng languages, and analogcal examples n programmng language C ++ are specfed for better understandng of the chapter. In a resource the rules are presented as the program, n the form of XML. The executable block of the program, called "task", can be defned as procedure. The very frst executable task n a resource s called "man". In the own task there s an opportunty to apply some knds of operatons:. Executable actons whch can execute resources. Typcal actons: to nclude, to swtch off, to start, etc. 2. Boolean the Boolean operators, consstng of condton and task that wll be executed (or on the contrary not to be executed) f condton s true. 3. Predefned the bult n operators who are predetermned by the system (for example, for defnton of dstance between two resources, operaton "Locate" s used). The syntax of the task: <task label = "procedure" varable="value">.. <return type = "varable">value</return> </task> By the tag "task" t s defned the workng block, where the name of the task (procedure) s requred to be defned. Then the names of varables wth ther values are lsted. The authors want to emphasze that t s necessary to defne those varables whch are transferred nto "task". Insde of the procedure there are operatons. If t s necessary to return any values, then the type of procedure (type) or the name (varable) or the returned value (value) are defned. If ths task s used as a condton n verfyng operaton, then the last value n the last tag "return" s consdered. The syntax of the checkng operaton: <f label = "name" condton="condton"> <true>..</true> <false>..</false> </f> By means of tag "f" t s possble to defne a condton. Condtons of comparson are set by an alphabetc combnaton: EQ (=), GT (>), LT (<), GE (=>), LE (<=), NE (<>). If the condton s true, then the workng block, that s located n the tag "true", s to be executed. Otherwse, the block of the tag "false" must be executed. Verfcaton operaton has a name on whch t s possble to dentfy verfcaton operaton (name). If the tags "true" and "false" don t exst, tag "true" wll be consdered. 5. The Smulaton Creaton from Real Soluton Sometmes customers have stuatons, when they have real soluton ready and need to do some changes for ths soluton wth smulaton usage. For ths functonalty wth smulaton usage t s possble to have the followng stuatons and possble decsons: Real soluton s created by DARSIR concepton the best way n ths stuaton, s possble to transfer all attrbutes and rules from resources to smulaton scheme; Real soluton wth all elements wth bult-n RFID tags n ths stuaton t s possble to load some part of attrbutes n smulaton scheme, as physcal (f present RFID dentfcaton owner type descrpton), sensors (f present), entty (f present n RFID tag), locaton (possble defne by RFID readers), confguraton (possble defne by RFID readers), etc.; Real soluton all elements wthout bult-n RFID tags n ths stuaton frst step s bult-n RFID readers, t s possble to load some part of attrbutes n smulaton scheme (but usually less than n prevous stuaton), as physcal (f present RFID dentfcaton owner type descrpton), sensors (f present), locaton (possble defne by RFID readers), confguraton (possble defne by RFID readers), etc. 6. The Example So far, the theoretcal bass of the varous aspects of smulaton s usage for creaton of real soluton wth DARSIR concepton was brefly descrbed n ths document. For better understandng of the practcal usage of the smulaton for creatng real soluton wth DARSIR concept authors descrbed a concrete problem, and ts soluton n RPML wth remarks of smulaton creaton. Condton of the problem: t s necessary to organze regulaton of temperature nsde. Intal data are the condtoner (downturn of temperature), a heater (rse of temperature) and thermo sensor (capable to take temperature). Frst of all the authors need to defne attrbutes that can be used to solve the problem. In thermo sensor there s already been one parameter "Temperature", that changes on demand of attrbutes from the envronment. There are also 2 parameters: "Mn" (admssble mnmum) and "Max" (admssble maxmum). 34

39 Sesson 3. Formalzaton and Smulaton of Busness Systems Example: <mat label = "thermosensor"> <extrude type = "Temperature"> 0 </extrude> <nteger label = "Mn"> 20 </nteger> <nteger label = "Max"> 2 </nteger> </mat> Smulaton creaton process s dependent on smulaton language. It s reason why authors can only defne attrbutes, whch must be used n smulaton. There s defned one sensor type attrbute and two attrbutes of varable type. The next step s defnton of accessble executable operatons. The condtoner and a heater have two executable operatons "On" and "Off" that allow swtchng on and off these devces. There wll be a control block (or n other words workng algorthm) n thermo sensor:. If value of the parameter "Temperature" s greater then value of the parameter "Max", then swtch off the heater and swtch on the condtoner. 2. If value of the parameter "Temperature" s less then value of the parameter "Mn", then swtch off the condtoner and swtch on the heater. In RPML t looks as: <task label = "man"> <f label = "Hot" condton = "Temperature GT Max"> <msr label = "Heater.Off"></msr> <msr label = "Condtoner.On"></msr> </f> <f label = "Cold" condton = "Temperature LT Mn"> <msr label = "Condtoner.Off"></msr> <msr label = "Heater.On"></msr> </f> </task> In smulaton t s mportant to defne the correct executable actons, so they can execute resources they need. If smulaton have some errors n names that mean that n transformaton process from smulaton to real soluton ths error must be fxed. After that t s necessary to realze mechansm for name correcton checkng. 7. Conclusons Varous aspects of smulaton s usage for creaton of real solutons of DARSIR concepton as example are descrbed n ths artcle. It s one of the possble easy ways for creatng new solutons wthout usng typcal programmng. Authors have chosen one of the concepts of desgnng data management systems. The choce s Data- And-Rules-Save-In-Resource ( DARSIR ) [] concepton, that can be used wth RFID technology. Ths concept data storage type provdes releve transformaton from smulaton scheme to real solutons. In ths artcle authors present ther opnon for man steps from smulaton creaton to real soluton. Man elements of DARSIR concepton, data storage type, attrbutes, rules etc. are descrbed here. Workng prncples of the real soluton and smulaton are shown. For better understandng of practcal usage, last step s descrbed as concrete problem: t s necessary to organze regulaton of temperature nsde. Varous aspects dscussed n ths artcle can be used as a practcal gude for the mplementaton of Data- And-Rules-Save-In-Resource as the easy way of creaton new real soluton. Such smulaton task can be easly created wth user-frendly graphcal nterface. Acknowledgements Ths work has been partly supported by the European Socal Fund wthn the Natonal Programme Support for the Carryng out Doctoral Study Programme s and Post-Doctoral Researches proect Support for the Development of Doctoral Studes at Rga Techncal Unversty. References. Zuravlyov, V. Man prncples of a new concept of desgnng data management systems. In: The 7 th nternatonal thematc ssue Computer Scence of the RTU scentfc proceedngs seres Appled Computer Systems; 47 th RTU Internatonal Scentfc Conference, Rga, Latva, October 2-4, Rga: Rga Techncal Unversty, Sandp Lahr. RFID sourcebook. N.J., IBM, London: Upper Saddle Rver, The Physcal Markup Language 35

40 The Internatonal Conference Modellng of Busness, Industral and Transport Systems 2008 FORMAL DESCRIPTION OF DYNAMIC FEATURES IN PLA Henrkas Pranevcus, Dalus Makackas 2, Agne Paulauskate-Tarasevcene 3 Department of Busness Informatcs, Faculty of Informatcs Kaunas Unversty of Technology Studentu 56, Kaunas, Lthuana Tel , fax E-mal: [email protected], 2 [email protected], 3 [email protected] Dynamc structure systems are systems wth capabltes to change not only ther behavour n tme but all structure as well. For expandng range of specfed systems formal notaton has to be extended wth opportuntes to descrbe all futures of such systems. We present extended PLA formalsm DPLA, whch s able to specfy systems that can change ther structure dynamcally. Operators, for defnng the actons of structural changes n DPLA, are presented. A formal descrpton of structural changes n DPLA specfcaton s defned usng Z specfcaton language. Keywords: mult-agent systems, formalzaton, DPLA, dynamc structure, Z. Introducton Dynamc structure systems are systems wth capabltes to change not only ther behavour state n tme but all structure as well. More often we need to specfy systems whch are nteractve n dynamc envronment changng type and number of ts attrbutes, where obects are changng ther structure n tme and can perform autonomously (.e., mult agent systems)[]. A deep understandng of dynamc data structures s partcularly mportant for modern, obect-orented languages as well [2], [3]. Whereas such systems mostly are large, complex and crtcal, there exsts motvaton for formal specfcaton. Most of formal methods are able to specfy statc structure systems. Dynamc structure s an mportant capablty, related to herarchcal structure, for smulatng complex systems. For expandng range of specfed systems, formal notaton has to be extended wth opportuntes to descrbe all futures of such systems. A pece-lnear aggregate (PLA) s tmed automata based specfcaton formalsm, whch s wdely used for creatng smulaton models (often smulaton of computer network protocols) and ther valdaton. PLA s very mportant for desgn complex real tme systems, but only statc structure. In ths paper extended PLA formalsm DPLA s presented, whch s able to specfy systems that can change ther structure dynamcally. For dynamcs n DPLA, we create four protocols for defnng the sequence of actons of structural changes: the creaton of relatonshps (CR), the deleton of relatonshps (DR), the creaton of new aggregates (CA), and the deleton of aggregates (DA). A formal descrpton of structural changes n DPLA specfcaton s defned usng Z specfcaton language. Fnally, an example of the use of these extensons s ncluded. 2. Formalzaton Possbltes of Dynamc Structure Systems Most of formal methods enable the specfcaton of statc structure systems, whch mean that dynamc features of systems are complex to descrbe or can t be descrbed at all. For expandng the range of specfed systems, formal notatons should be extended wth capabltes to descrbe all features of such systems. For example, to descrbe dynamc structure systems, the classcal notaton of DEVS (dscrete event system specfcaton) was extended by addng specal functons (4). In dyndevs structural changes are nvoked by a model transton functon ρ α, whch generates ncarnatons of dynamc DEVS and a network transton functon ρ N, whch keeps the state and structure of models that belongs to the composton of network. Usng the dynamc DEVS notaton the exstng models can be deleted or new created, couplngs between models added and removed. Such capabltes of dyndevs are also useful for modellng MAS [5] whch, besdes ther specfc features, such systems are prmarly dynamc systems wth capabltes to change not only ther state n tme, but all the structure as well. For varous experments, the system JAMES (A Java-Based Agent Modellng Envronment for Smulaton) was created [6] n whch agents are modelled as tme trggered state automata. The vrtual envronment allows creatng dfferent scenaros and testng the behavour of agents. Another popular DEVS varaton parallel dynamc structure of dscrete events specfcaton network (DSDEN) [7] where dynamc structure system network s defned wth specal component (network executveχ) and structure functon (whch maps the network structure states set S χ and set of network structures * ) 36

41 Sesson 3. Formalzaton and Smulaton of Busness Systems Dynamc structure systems are also modelled wth dfferent Petr Nets (e.g. dynamc Petr Nets, Coloured Petr Nets, hgh level Petr Nets). In DPN, the structure of the net can be changed dynamcally, by nsertng or deletng a transtons or places [8]. For example, modellng MAS wth hgh level Petr Nets t can be concluded that ndvdual agents are modelled as tokens so that they mgrate from one component to another by transton frng at runtme [9]. It s dffcult to determne whch methods are better than others, because all these formal methods specfyng dynamc structure systems hghlght and test dfferent features of such systems. As a result of the overvew, we can make a consumpton that automaton based formal methods are really sutable for descrbng dynamc structure systems, ncludng mult-agent systems. That s the reason for decdng to use the formal method PLA for dynamc structure systems formalzaton. 3. Dynamc Approach of PLA A pece-lnear aggregate (PLA) s tmed automata based specfcaton formalsm, whch s wdely used for creatng smulaton models (for smulaton of computer network protocols often) and ther valdaton [0]. In the applcaton of the aggregate approach a system s represented as a set of nteractng pece lnear aggregates. The PLA s taken as an obect defned by a set of states Z, nput sgnals X, and output sgnals Y (Fg. ). The aggregate functonng s consdered n a set of tme moments t T. The state z Z, nput sgnals x X, and output sgnals y Y are consdered to be tme functons. Apart from these sets, transton H and output G operators must be known as well. Fg.. Scheme of aggregate 3.. DPLA: Dynamc PLA The dynamc structure s an mportant capablty, related to the herarchcal structure, for smulatng complex systems. PLA s very useful for desgnng complex real tme systems, but only for statc structure systems. In dynamc structure systems the envronment s varyng n tme changng the number of ts attrbutes (e.g. new obects are added or removed). For specfyng dynamc structure systems we modfy some components of the orgnal PLA and add some extra operators. The dfference between PLA and DPLA (dynamc PLA) s presented below on Fgure 2. Dfferently from orgnal PLA, n DPLA the number of events, nput, output sgnals, controllng sequences, dscrete and contnuous component may vary n tme. Each aggregate can have chldren aggregates n ts content. dyndevs notaton s smlar to DPLA, but dfferently from dyndevs coupled model (whch s lke a frame of ts component), a parent aggregate s an ordnary aggregate wth ts own nternal events, external event, outputs, nputs and so on []. added In DPLA there are two types of dynamc structural changes: The level of a sngle aggregate: Structural changes of a sngle aggregate (.e. a new ntal state can be E ( tm + ) = E ( tm ) e or deleted E ( tm + ) = E ( tm ) / e ). The level of aggregate system: Structural changes between two or more aggregates (.e., a new lnk between aggregates can be added, or an exstng lnk deleted; also new aggregates can be created A t ) = A( t ) ( A : type ) or elmnated A t ) = A( t ) /( A : type ) ). ( m m 0 new ( m m 0 old 37

42 The Internatonal Conference Modellng of Busness, Industral and Transport Systems 2008 PLA DPLA Input sgnals X = { x, x2,..., xn } Input sgnals X ( tm ) = { x, x2,..., xn } Output sgnals Y = { y, y2,..., y N } Output sgnals Y ( t m ) = { y, y2,..., y N } ' ' ' ' ' ' External events E = { e, e2,..., en } External events E '( tm ) = { e, e2,..., en } " " " " " " Internal events E " = { e, e2,..., ef } Internal events E "( t m ) = { e, e2,..., e f } Dscrete component Dscrete component ν ( tm) = { ν( tm), ν( tm)..., ν p ( tm)} ν ( tm ) = { A( tm ), R( tm )..., ν p ( tm )} Number of system aggregates Set of chldren aggregates K A( t m ) = ( Ag _ name) Matrx of nput sgnals Set of relatonshps R = { r }, =, L, =, 2 R( tm ) = ( name: source _ Ag t arg et _ Ag) * * R : Y X, where Matrx of output sgnals * * Y = H = { h }, =, K, =, max{ M K } YA, X = X A K A A( tm) A A( tm) Contnuous component " z ( t ) = { w( e, t )} ν m Controllng sequences e " { ξ ( ) } f m Contnuous component " z ( t ) = { w( e, t )} Controllng sequences " ( ) V ( t m ) = { e { ξ }} Intal state z ( t m ) Intal state z ( t m ) Transton operator H [ z( t m, e )] Transton operator H [ z ( t m, e )] Output operator G z ( t m, e )] Output operator G z ( t, m e )] [ ν m f m [ Fg. 2. Comparson of PLA and DPLA 3.2. Protocols and Z schemas of structural changes For external structural changes n DPLA, we create four protocols, defnng the sequence of such actons: the creaton of relatonshps CR, the deleton of relatonshps DR, the creaton of new aggregates CA, and the deleton of aggregates DA [2]. Some constrans are appled to avod conflct. For example, an aggregate whose A ( t m ) = can t delete or add other aggregates. Only coordnator can create and delete aggregates from ts own set of chld aggregates A ( t m ). If one aggregate, whch belongs to one coordnator, decded to create a new lnk wth the aggregate, n ts turn whch belongs to the second coordnator, t has to be removed from the content of the frst coordnator and after that to be added to the second one (Fg. 3). Add Ag2 K K2 Ag Ag2 Ag4 Ag5 Ag3 K K2 Ag Ag4 Ag5 Ag3 Ag2 Fg. 3. Structural changes n coordnator level These protocols are usable for realzaton of DPLA, but wrtng specfcaton usng ths notaton s more practcal to nclude operators for such actons of system structural changes. For ths purpose we decded Z formal language [3] for formal descrpton of operators DR, CR, DA and CA, whch corresponded to the protocols. These common operators sgnfcantly reduce specfcaton sze, because we have to be predefned ust 38

43 Sesson 3. Formalzaton and Smulaton of Busness Systems one tme. Performng structural changes by these operators, an aggregate can evolve n the process and dfferently from dyndevs, we don t have to predefne all possble models varatons of each aggregate. CR operator s presented on Fgure 4. Operator keeps all the nformaton needed for creatng a new lnk. The name of lnk name, assocated aggregates source_ag and target_ag has to be denoted. CR=(name: source_ag target_ag) The man condton s that both aggregates must belong to the same coordnator. The new lnk s added to the coordnator s set of relatonshps R(t m ). In general case, f an aggregate gets a request to add new lnk, t checks: f the request ncludes the sgnal wth ts name equal to target_ag; f the request ncludes the sgnal wth ts name equal to source_ag. In the frst case, the nput sgnal s added to the set of nput sgnals X and addtonal transton operator H for processng ths sgnal. In the second case, the new output sgnal s added to the set of output sgnals Y, and addtonal output operator G, whch generates the new sgnal. All transton and output operators whch are added must be predefned n specfcaton of aggregate. Durng structural changes these operators are added to the man H and G sets of aggregate. CR c : A a : A a : A r? : CR result!: REZ a c. chld a c. chld r?.source = a.my_id r?.target = a.my_id c.r = c.r r? ( a. Y = a. Y { r?. sgnal} ~ a. E = a. E a. E a. E = a. E E? a. z = a. z ( a. X = a. X + + { e ( R R )} a. H : a. E a. z a. z a. G : a. E a. z a. Y ) { r?. sgnal} a. E = a. E a. E a. E = a. E a. H : a. E a. z a. z) ~ e E 2 { e ~?} result! = error Fg. 4. Z schema of CR operator DR c : A a : A a : A r? : DR result!: REZ a c. chld a c. chld r. source = a. my _ ID r.target = a. my _ ID r c. R c. R ( a. Y = a. Y / = c. R /{ r?} { r?. sgnal } a. G : a. E a. z a. Y ) ( a. X = a?. X / { r?. sgnal } a. E = a. E a. E a. E = a. E a. H : a. E a. z a. z) result! = error Fg. 5. Z schema of DR operator 2 {} e ~ Appropratve 3 cases for source aggregate (Table ) and for target aggregates s defned n ths operator (Table 2). Below all cases for source aggregate are lsted:. If output operator G, whch generates the new output sgnal, s nvoked by event e, whch exsts n aggregate e E( t m ) at the moment tm, where E ( t) = E' ( t) E ( t). For example, transport A has event mlk delvery every mornng, durng whch t delvers mlk to some stores y(mlk). Store B wants to create a lnk wth t and get a mlk as well x(mlk). Table. Addton of new lnk new n pont of source aggregate 2 3 Cases H( e):... G( e) : y( new) Actons The new output sgnal s added to the set of output sgnals of source aggregate Y ( tm+ ) = Y ( tm ) new. Output operator G s added to the set of output operators G t = G t G e ( ) ( ) ( ) m+ m H ( e ) : The new output sgnal and the new nternal event, durng whch new output sgnal s? generated, are added Y ( t... m ) = Y ( tm ) new, + E ( tm ) = E ( tm ) e?. Transton H and + G tm + = G tm G e e? E ( t m )? and H ( tm + ) = H ( tm ) H ( e ) G( e? ) : y( new)?. Snce the set of nternal events s changed, the state of an aggregate s changng as well z ( tm+ ) = z( tm ) w( e? ( tm )) H ( e... e? E ( t m ) G( e ) : y( new)? output G operators are ncluded to the addtonal sets of aggregate ( ) ( ) ( )? ) : The new output sgnal and G operator are added Y ( tm ) = Y ( tm ) new G( t ) = G( t ) G( ) m m e? +,. Whereas, doesn t exsts the external event, after whch processng, + the new output sgnal s generated, extra CR has to be nvoked for ths external event. 39

44 The Internatonal Conference Modellng of Busness, Industral and Transport Systems If source aggregate s output operator G, whch generates the new output sgnal, s nvoked by nternal event e, whch doesn t exst n the aggregate e E ( t m ) at the moment tm. For example, nternal event of transport A mlk delvery every mornng, whch generates sgnal y(mlk) doesn t exst at the moment. Store B wants to create a lnk wth t and get mlk. 3. If source aggregate s output operator G, whch generates the new output sgnal, s nvoked by nternal event e, whch doesn t exst n the aggregate e E ( t m ) at the moment tm. For example, external event of transport A a permt of mornng delvery, after whch output sgnal y(mlk) can be generated doesn t exst n aggregate at the moment. Store B wants to create a lnk wth t and get mlk. At the pont of target aggregate the structural changes are more general; new nput sgnal and H(new) operator has to be added. We are not nterested f appropratve G(new) generates any sgnals or not, because we don t nclude t to the G operators set. For example, store B wants to get mlk x(mlk) from transport A. Table 2. Addton of new lnk new n pont of target aggregate Cases H (new):... Actons The new nput sgnal s added to the set of nput sgnals of target aggregate X ( tm+ ) = X ( tm ) new. Transton operator H s added to the set of output operators H t = H t H new ( ) ( ) ( ) m+ m DR operator s presented on Fg. 5. Operator keeps all the nformaton needed for deletng a lnk. The name of lnk name, assocated aggregates source_ag and target_ag has to be denoted. DR=(name: source_ag target_ag) The man condton s the same as n CR operator; both aggregates belong to the same coordnator. If an aggregate gets a request for a lnk deleton t checks, f the request ncludes such a sgnal, where ts name s equal to source_ag. If t s true, then addtonal output sgnal s removed from ts output sgnals set Y, and output operator G for ths sgnal generaton. If ts name s equal to tartget_ag, and removes addtonal nput sgnal wth transton operator H for denoted sgnal. Meanwhle, coordnator removes denoted lnk from ts set of relatonshps. Appropratve 3 cases for source aggregate (Table 3) and 2 for target aggregates are defned n ths operator (Table 4).. If source aggregate s output operator G, whch generates the old output sgnal, s nvoked by event e, whch changes the state of the source aggregate. For example, transport A has event mlk delvery every mornng, durng whch t counts days of mornng shft Count ( tm+ ) = Count( tm ) + and delvers mlk to some stores y(mlk). Store B wants to delete a lnk and refuse delvery of mlk x(mlk). 2. If source aggregate s output operator G, whch generates the old output sgnal, s nvoked by nternal event e, whch doesn t change the state (nether contnuous nor dscrete component) of the source aggregate. For example, transport A has event mlk delvery every mornng, durng whch t doesn t change hs state and generates sgnal y(mlk) only. Store B wants to delete a lnk wth t and refuse delvery of mlk x(mlk). 3. If source aggregate s output operator G, whch generates the old output sgnal, s nvoked by external event e, whch doesn t change the state (nether contnuous nor dscrete component) of the source aggregate. For example, transport A gets external event a permt of mlk delvery every mornng, durng whch generates sgnal y(mlk). Store B wants to delete a lnk and refuse delvery of mlk x(mlk). Table 3. Deleton of lnk old n pont of source aggregate 2 3 H ( e) : Cases ( t ) z( t ) z m+ m G( e) : y( old ) H ( e ):? ( t ) = z( t ) z m+ m G( e ) : y( old)? H ( e ):? ( t ) = z( t ) z m+ m G( e ) : y( old)? Actons The old output sgnal s deleted from the set of output sgnals of source aggregate Y ( tm + ) = Y ( tm )/ old. Output operator G s deleted from the set of output operators G t G t G e ( ) ( ) ( ) m + = m / The old output sgnal and nternal event, durng whch ths sgnal s generated, are deleted Y ( tm + ) = Y ( tm )/ old, E ( tm + ) = E ( tm )/ e?. Transton H and output G operators are deleted as well G( tm + ) = G( tm )/ G( e? ) and H ( tm + ) = H ( tm )/ H ( e? ). Snce the set of nternal events s changed, the state of an aggregate s changng as well z ( tm+ ) = z( tm )/ w( e? ( tm )) The old output sgnal and G operator are deleted Y ( tm ) = Y ( tm )/ old G( t ) = G( t ) G( ) m +, + m / e?. Whereas, external event, after whch processng, the old output sgnal s generated doesn t change the state of aggregate, extra DR has to be nvoked for ths external event. 40

45 Sesson 3. Formalzaton and Smulaton of Busness Systems Two cases for the target aggregate usng DR operator are defned below n Table 4. In ths case we are nterested f the output operator of the deleted sgnal generates any sgnal or not.. If operator G of deletng sgnal doesn t generate any sgnal. For example, store B wants to delete a lnk wth transport A, refusng delvery of mlk. 2. If operator G for deletng sgnal generates external sgnal. For example, store B wants to delete a lnk wth a transport A, refusng delvery of mlk, but store B gettng a mlk from transport A x(mlk) dstrbutes t to others stores y(dstrbute). Table 4. Deleton of lnk old n pont of target aggregate 2 H( old) :... G( old) : H ( old) :... G( old) : y Cases ( ) Actons The old nput sgnal s deleted from the set of nput sgnals of target aggregate X ( tm + ) = X ( tm )/ old. Transton operator H s deleted from the set of transton H t H t H old operators ( ) ( ) ( ) m + = m / The old nput sgnal and the other sgnal, whch s generated by output operator G of old sgnal, are deleted X ( tm + ) = X ( tm )/ old, Y ( tm + ) = Y ( tm )/ y( ). Transton H and output G operators of old sgnal are deleted as well G( tm + ) = G( tm )/ G( old) and H( tm + ) = H( tm )/ H( old). Whereas, G operator generates a sgnal, t has to be removed. Extra DR s nvoked for ths external event Usng CA operator (Fg. 6), only coordnator can create chldren aggregates of lower level, defnng the name of the new aggregate and ts type. Coordnator creates new aggregate, adds t to the set of ts chldren aggregates A ( t m + ) = A( t m ) { new : type } and creates relatonshps R( tm + ) = R( tm ) { dyn _ struct : new 0, dyn _ struct*: 0 new, done*: new 0} for dynamc structural changes dyn_struct, dyn_struct*, done*. All aggregates n DPLA have these sgnals by default. Deletng aggregates wth operator DA (Fg. 7), prmarly all lnks wth an aggregate, whch has to be deleted, are removed usng DR operator. After that coordnator start structural changes n ts level: deletes ths aggregate from ts set of chld aggregates and removes default lnks wth t. CA c : A a? : CA r, r : R result!: REZ a? c. chld c. chld = c. chld c. R = c. R result! = error { r, r } { r, r } r. source = c. my _ ID r.target = a?. my _ ID r. source = a?. my _ ID r.target = c. my _ ID DA c : A a? : DA r, r : R result!: REZ a? c. chld c. chld = c. chld / a?. z' = NULL { r, r } result! = error { a } r. source = c. my _ ID r.target = a?. my _ ID 2 r2. source = a?. my _ ID r2.target = c. my _ ID c. R = c. R/ 2 Fg. 6. Z schema of CA operator Fg. 7. Z schema of DA operator schema The above-mentoned three messages common for all DPLA specfcatons, whch nvoke defned operators: (dyn_struct) ncludes the nformaton of what structure changes are expected: CR, DR, CA, DA. All other messages nclude such nformaton as well. An aggregate nforms ts hgher level aggregate coordnator about expected structural changes; (dyn_struct*) an aggregate (coordnator) requests ts addtonal chldren aggregates to make structural changes; (done*) an aggregate nforms ts coordnator about executed structural changes. 4. Applcaton: the Populaton of Lve Organsms Chosen applcaton represents the populaton of lve organsms (.e. cells, brds or anmals). Ths scenaro conssts of three types of organsms (male form and female form) and a famly, whch conssts of more than one organsm. All organsms subsst on food, gven by surroundng envronment. Envronment has lmted recourse of food, whch means that f organsm s populaton grows too large, some of them won t survve. Every organsm, whch s not n famly have the man goal to make a par wth another organsm. Two organsms n famly can reproduce and ncrease populaton. 4

46 The Internatonal Conference Modellng of Busness, Industral and Transport Systems 2008 Fg. 8. An example n DPLA In DPLA specfcaton, every organsm s consdered as an aggregate (Fg. 8). All aggregates nteract n envronment, whch s defned as hgher level aggregate, contanng lower level aggregates all organsms and famles. All sngle aggregates start thers exstence from the lookng for par. An aggregate- organsm sends sgnal to ts coordnator-envronment wth a request to fnd avalable organsm for copulaton. Whenever t gets a name of avalable aggregate, t sends the sgnal to coordnator wth request to add new relatonshps. Ths sgnal nvokes structural changes (CR). Aggregate- Envronment Aggregate-Organsm H (dyn _ struct ) = CR : H ( your _ par ) = a : par (tm + ) = a G (dyn _ struct ) : y (dyn _ struct*) = CR H (done *) = CR : Envronment (t m + ) = (CR, (Envronment (tm ))) G ( your _ par ) : y (dyn _ struct ) = CR propose : my _ ID a here, CR = answer : a my _ ID H (dyn _ struct *) = CR : G (done *) : Organsm (tm + ) = (CR, (Organsm (t m ))) G (dyn _ struct *) : y ( done*) = CR If an aggregate, ntated communcaton gets a postve answer for copulaton, t starts creaton of famly; otherwse t removes relatonshps wth a aggregate and starts ts search for a par anew. After two organsms create a famly, they procreate offsprng, whch means that new aggregate s added n a famly aggregate. In DPLA specfcaton creaton of new aggregate n famly s nvoked by CA operator. H (e ) : Chld (tm+ ) = famly (t m+ ) = (CA, ( famly (t m ))) Chld (tm+ ) = Chld (t m ) w(e, tm+ ) = t m + ξ A(tm ) = 2 # G (e ) : y = here, CA = (name* : ORG ) A(tm ) 2 # A new organsm, added nto the famly, grows up after some perod. From ths moment t can exsts as a sngle aggregate. For such exstence chld aggregate has to be removed from Famly content and moved up to the coordnator Envronment. From ths stuaton another group of structural changes transportaton was detected. To mprove functonalty of DPLA we decded to add new protocols: move up MU and move down MD. In these protocols actons are based on above descrbed operators DR, CA. In MU protocol (Fg. 9) an aggregate Ag, sends the sgnal to ts coordnator AB wth a request to be moved up from a current level. Coordnator deleted all lnks wth ths aggregate and removes aggregate Ag from the set of ts chldren aggregates. After that, the hgher coordnator A adds aggregate Ag to ts set of chldren aggregates and creates default lnks wth t. In MD protocol (Fg. 0) an aggregate, whch wants to move, has to know want knd of aggregates exsts n the same level of herarchy. For ths purpose Ag sends the sgnal Vew to the coordnator. Coordnator responds to ths message sendng the names of ts chldren. Aggregate Ag has to choose one of the chldren of ts coordnator AB. Coordnator deletes all lnks wth Ag and removes t from ts chldren set. Whenever 42

47 Sesson 3. Formalzaton and Smulaton of Busness Systems aggregate s removed from the content of AB, the new coordnator Ag2 adds the new aggregate Ag to the set of chldren aggregates. Fg. 9. MU protocol Fg. 0. MD protocol In our specfcaton grown chld leaves the famly and starts to exst as a normal organsm. The grown chld nvokes MU operator and CR operator for communcaton wth the new coordnator. H ( grown):... G( grown ): y( dyn _ struct ) = MU y( dyn _ struct) = CR food : my _ ID 0 fnd _ par : my _ ID 0 CR =, MU = ( my _ ID your _ food :0 my _ ID your _ par : 0 my _ ID All organsms can de n two ways: starvaton or after defned lfetme. Frst way. e Internal event, whch defnes nutrton stage of organsm. If the organsm s not dyng form hunger, sends sgnal for a food to ts envronment; otherwse t starts structural changes wth DA operator. H ( e ): G( e ): Re s( tm+ ) = Re s( tm ) θ y( food), Re s( tm ) > 0 Re s( tm ) > 0 w( e, tm+ ) = tm + α y( dyn _ struct) = DA, Re s( tm ) < 0 z ( e υ, tm+ ) = Re s( tm ) < 0 here, DA = ( my _ ID : ORG) here, Res(t) food resources; Second way: e 2 nternal event, whch defnes death of organsm. The organsm termnates all nternal events and sends sgnal to envronment for structural changes. ( e2 ): z ( e, t ) H υ m+ = G( e 2 ): y ( dyn _ struct) = DA The above-mentoned approach permts usng a sngle mathematcal scheme to create models both for smulaton and valdaton. The occurrence graph enabled us to valdate specfcaton and to analyse such features of the system as accessblty, necessty of contnuous coordnates, bound of state coordnates, deadlocks and loops. Ths valdaton method s mplemented n specfcaton analyss tool PRANAS2, based on the aggregate approach. 5. Conclusons In ths paper, the dynamc approach of the formal method PLA s presented for formalzaton of dynamc structure systems. DPLA has enabled us to descrbe the structural changes of such systems. New two communcatons protocols MU, MD are presented, whch enable us to defne such structural changes as transportaton of aggregates nto the new postons. These protocols as prevous, defne the order of the actons for dynamc structure changes applyng some constrans (.e., only coordnator can remove ts chldren aggregates) to avod the conflcts. Z schemas allow us to descrbe the presented protocols n formal descrpton; 43

48 The Internatonal Conference Modellng of Busness, Industral and Transport Systems 2008 ncludng operators whch correspond to them. Usablty of defned operators enable us to specfy structural changes of systems (add of new aggregates, delete aggregates, add new lnks etc.) sgnfcantly to reduce the sze of DPLA specfcaton, to mprove functonalty and to formalze systems n compact, readable descrpton. We represent DPLA and new operators usng a concrete applcaton, whch nvolves varous knds of structural changes. References. Fox, J., Beverdge, M., and Glasspool, D. Understandng ntellgent agents: analyss and synthess, AI Communcatons, Vol. 6, 2003, pp Brandt, Joel R. Run-tme modfcaton of the class herarchy n a Lve Java Development Envronment. Washngton Unversty, Department of Computer Scence and Engneerng, USA, Guéhéneuc, Y.G. Dynamc class modfcaton and creaton n Java Rohl, M., Uhrmacher, A.M. Controlled Expermentaton wth Agents Models and Implementatons. In: 5th Internatonal Workshop. Engneerng Socetes n the Agents World. Toulouse, France, October, 20-22, Uhrmacher, A.M. A System Theoretc Approach to Constructng Test Beds for Mult-Agent Systems. In: Dscrete Event Modellng and Smulaton Technologes. A Tapestry of Systems and AI-Based Theores and Methodologes: A Trbute to the 60th Brthday of Bernard P. Zegler: Lecture Notes on Computer Scence. New York: Sprnger, 200, pp Schattenberg, B., Uhrmacher, A.M. Plannng Agents n James. In: Proceedngs of the IEEE, Vol.89, No2, February, 200, pp Barros, F.J. Representaton of Dynamc Structure Dscrete Event Models: A Systems Theory Approach. In: Dscrete Event Modellng and Smulaton: Enablng Future Technologes. Sprnger Verlag, 2000, pp Graff, C.J., Gardna, C. Dynamc Petr Nets: new modellng technque for sensor networks and dstrbuted concurrent systems. In: Mltary Communcatons Conference, 2005, MILCOM 2005, IEEE, Vol., 2005, pp Xu, D., Deng, Y. Modellng moble agent systems wth hgh level Petr Nets. In: Proc. IEEE Internatonal Conference on Systems, Man and Cybernetcs (SMC 2000), Vol.5, 8 th -2 th October, pp Pranevcus, H. Formal specfcaton and analyss of Computer Net Protocols: aggregate method. Kaunas, Lthuana: Technologa, p.. Uhrmacher, A.M. Dynamc Structures n Modellng and Smulaton A Reflectve Approach. In: ACM Transactons on Modellng and Smulaton, Vol., No2, Aprl 200, pp Pranevčus, H., Makakas, D., Paulauskatė-Tarasevčenė, A. Mult-Agent Systems Formalzaton Usng Formal Method DPLA. In: The 2st annual European Smulaton and Modellng Conference. St. Julan, Malta, October 22-24, Malta, 2007, pp Potter, B., Snclar, J., Tll, D. An Introducton to Formal Specfcaton and Z. Trowbrdge, UK: Prentce Hall, p. 44