MultCraft Internatonal Journal of Engneerng, Scence and Technology Vol, o, 9, -4 ITERATIOAL JOURAL OF EGIEERIG, SCIECE AD TECHOLOGY wwwest-ngcom 9 MultCraft Lmted All rghts reserved Evaluaton of the nformaton servcng n a dstrbuted learnng envronment by usng montorng and stochastc modelng R P Romansky, E I Parvanova Comuter Systems Deartment, Techncal Unversty of Sofa, Bulgara College of Energetc and Electroncs at Techncal Unversty of Sofa, Bulgara Abstract The dstrbuted learnng s an nstructonal model that allows nstructor, students, and content to be located n dfferent nodes n the global network The authors man dea s to organze a dstrbuted learnng envronment (DLE) based on nformaton and communcaton resources of global network n combnaton wth the technologes for vrtual realty and D smulaton In ths reason a concetual model of the DLE archtecture and learnng rocesses s defned, and relmnary nvestgaton s carred out The urose of ths aer s to resent an evaluaton of nformaton servcng n DLE by usng stochastc model desgned on the base of the results from rogram montorng A formalzaton of the DLE rocesses s made and a stochastc model based on the aaratus of Markov s chans and queung theory s desgned The results obtaned from rogram montorng are used for determnaton of the values of the basc model arameters to secure hgh model adequacy The rogram montorng s realzed by usng two rogram alcatons and a relmnary statstcal analyss s made Fnally, an evaluaton of the nformaton servcng n DLE s realzed and the obtaned assessment are resented n sutable manner Keywords: Dstrbuted learnng, nformaton servcng evaluaton, Markov s modelng, montorng, statstcal analyss Introducton The dstrbuted learnng (DL) s an nstructonal model that allows nstructor, students, and content to be located n dfferent, noncentralzed locatons so that nstructon and learnng occur ndeendent of tme and lace (Oblnger, 996; Bowman, 999; Dede, 4) Ths requres buldng a dstrbuted learnng envronment (DLE) based on nformaton and communcaton resources of global network and web-sace, ncludng wreless networks (Predd et al, 6) The develoment of the technologes for vrtual realty and D smulaton (Funkhouser, 5; Berbaum, et al, 8) create a ossblty to organze a vrtual envronment for e-learnng based on comuter generated D models The man dea of the authors of ths artcle s to combne the technologcal rncles of the web-envronment wth the ossbltes for e-learnng based on the vrtual realty and D learnng obects The man goal s to organze DLE and a concetual model (Romansky and Parvanova, 8) and for ths urose rncles of vrtual envronment (Romansky and Parvanova, 9a) are defned A relmnary nvestgaton of the dstrbuted learnng rocesses s needed to secure effectve organzaton of the DLE archtecture In ths reason we carry out dfferent exerments by usng modelng based on determnstc (Romansky and Parvanova, 9b) and stochastc tools The urose of ths aer s to resent an evaluaton of nformaton servcng n DLE by usng stochastc model desgned on the base of the results from rogram montorng The aaratus of Markov s chans (Deshande and Karys, 4) s selected to desgn the model wth the combnaton of the man rncles of queung theory The results obtaned from rogram montorng are used for determnaton of the values of the basc model arameters n order to secure hgh model adequacy The goal of the aer s to resent basc stes of the evaluaton organzaton and summary of the obtaned analytcal assessments In ths reason a formalzaton of the envronment s gven and a Markov s model s desgned The rogram montorng s realzed by usng two rogram alcatons and a relmnary statstcal analyss s made Fnally, an evaluaton of the nformaton servcng n DLE s realzed and obtaned assessment are resented n sutable manner
4 Romansky and Parvanova/ Internatonal Journal of Engneerng, Scence and Technology, Vol, o, 9, -4 Formalzaton and Abstract Descrton The concetual model for organzaton of DLE s roosed n (Romansky and Parvanova, 8) and conssts of some basc comonents students, teachers, clents, nformaton and educaton resources, communcaton tools, etc The DLE s an nteractve envronment for knowledge resentaton and servcng based on requests sent by users The access to the learnng resources could be realzed from dfferent remote nodes by communcaton resources of Internet The man comonents defned n ths concetual model are users, nformaton learnng resources and communcaton medum All these comonents could be descrbed as dscrete ndeendent obects wth ther own nternal structure and functonalty Ths formulaton ermts to buld an abstract model of DLE as an ordered dscrete structure DLE {U, R, T, D} (Fgure ) based on the followng formalzaton: a) abstract obect: Set of ndeendent users U {U / }, U ; Set of dstrbuted learnng resources n dfferent nodes of the DLE R {R / M}, R ; Set of network communcaton tools (transmtters) T {T q / q K}, T ; Dstrbutor (D) that routs all nformaton obects n the communcaton medum by usng nformaton n the ackets a) nteractons between defned abstract obects: requestng a learnng resource ntalzed by user req:u R (for U U & R R); resondng by sendng the requested learnng obect (nformaton block) Inf:R U (for U U & R R) Users U { U / } U U U Dstrbuted Users req D Dstrbutor Transmtters T { Tq / q K} T T q Inf Communcaton Medum Resources R { R / M} R R R Dstrbuted Educaton System Fgure Abstract model of educaton rocess n the DLE The nformaton servcng n the DLE has a stochastc nature Ths ermts to use a stochastc aaratus for modelng of the DLE comonents and nteracton In ths reason, the aaratus of Markov s chans s sutable for the descrton of system behavor as a sequence of dscrete states <S(), S(),, S(k),> for each sequence of tmes t <t <<t k <t k < For model desgnng s necessary to defne a fnte set of dscrete states {s, s,, s n } resentng the man events or stuatons n the educatonal rocess and determnng the matrx of transtve robabltes Ρ{ :[S(t k )s ] [S(t k )s ]} and vector of ntal robabltes P { (), (),, n ()} The stochastc analytcal model of the servcng n the DLE could be defned by usng the followng formulas: formula for comoste robablty: n ( k) ( k ) ;,,, n; condton for normalzaton: Stochastc modelng by usng Markov s chan n ( k ) ;,,, n Model defnng Two basc stuatons could be realzed n the dstrbuted learnng envronment (Fgure ): (a) remote access of multle users to selected nformaton-learnng resource stuated n node of the global network; (b) remote access of only one user to multle nformaton-learnng resources stuated n dfferent nodes of the global network
Romansky and Parvanova/ Internatonal Journal of Engneerng, Scence and Technology, Vol, o, 9, -4 5 U U U D&T R a) mult-user remote access to selected dstrbuted resource U D&T R R M R b) one-user remote access to multle dstrbuted resources Fgure Abstract resentaton of the remote access to the learnng resources To descrbe the stochastc nature of the nformaton servcng two basc ntenstes are defned the ntensty of the nut flow of requests () and ntensty of the flow of servcng n the node of the requested resource () It s ossble each learnng resource R n the DLE to be requested by dfferent number of users and ths number could be from (mnmum) to (maxmum) Each new user wll generate request wth the ntensty After the full servcng of each user request by the resource (by the server n the node) the Markov s rocess wll be returned to the revous state by the ntensty In ths reason the stochastc nature of the nformaton servcng n the DLE could be descrbed by Markov s model shown n the Fgure S S S S Fgure Markov s chan model of the mult-user access n DLE The stochastc nvestgaton s connected to the determnaton of assessments for the arameters for the steady-state regme assessments of the fnal robabltes for all defned states n the Markov s model It s known that to ensure the steady-state regme t s necessary to by realzed the condton / <, e < The general Markov s model s resented below: for ; ) ( () After some transformatons of the () we defne the next form of the Markov s model: ) ( ; ) ( ) ( for () The theory of robabltes gves some assessments for the man stochastc arameters f that could be nterreted n our case: Exectaton of the number of the actve users E[] av /(-) /(-); Varance of the number of the actve users V[] av av ;
6 Romansky and Parvanova/ Internatonal Journal of Engneerng, Scence and Technology, Vol, o, 9, -4 Exectaton of the number of the users watng servcng E[W] W av /(-); Exectaton of the watng tme for servcng E[T W ] / /[ (-)] The stochastc analyss of the nformaton servcng n the learnng envronment s carred out n three basc drectons: Analyss of the nfluence of the number of actve users; Analyss of the user s access to the resources; Analyss of the nfluence of the learnng contents sze Prelmnary model soluton The relmnary soluton of the Markov s model s made for ts verfcaton and to defne the model senstvty In ths reason concrete values for the basc model arameters are acceted: ; (the average tme between user s requests s s); 6 (the average tme for a request servcng s 5s) / < The Markov s model s the followng:,,6 (,,6) (,,6),,,6,6,5,5,5 () The analytcal soluton of the model gves the assessments for the fnal robabltes resented n the Fgure 4 Each value for the (,,,) resents the robablty of the number of actve users n the steady-state regme The measures of the stochastc arameters values are: number for E[] and V[]; second for E[W] and E[Tw],6,5,5,5 Value of the robablty,4,,,,7,,7 Value,5,5,5,67 E[] V[] E[W] E[Tw] Probabltes for the actve users stochastc assessments a) assessments of the fnal robabltes Fgure 4 Results obtaned by the model soluton b) assessments of the stochastc arameters Organzaton of the stochastc evaluaton To organze the adequate analyss of the nformaton servcng n the dstrbuted learnng envronment based on the defned stochastc model s necessary to determne the adequate values for the man model arameters ntenstes of the nut requests flow and of the servcng n the resource s nodes One of the sutable manners for determnng of these arameters s by usng rogram montorng n the real dstrbuted medum In ths reason, an organzaton of the montorng exerments and relmnary statstcal analyss of the measured data are resented n the next secton 4 Montorng and relmnary statstcal analyss 4 Montorng organzaton A rogram montorng of the network traffc arameters s organzed to collect real data for nformaton rocesses and dstrbuted servcng (Romansky, 6) The measurement s realzed n two drectons to collect detals for the frames assed va network medum and to determne statstcal data about communcaton and servcng arameters An adequate exermental lan should be defned to obtan correct assessments for the robablty dstrbuton of the nvestgated arameters (n artcular, for the ntenstes of the nut request flow and of the servcng rocesses)
7 Romansky and Parvanova/ Internatonal Journal of Engneerng, Scence and Technology, Vol, o, 9, -4 The montorng of network traffc arameters and characterstcs of the dstrbuted nformaton servcng could be made by usng dfferent rogram tools for measurement, regstraton and analyss, for examle: Webserver Stress Tool (HTTP clent-server tool); Irs (measurement and control of network traffc); Dstnct etwork Montor (ackets catchng and analyss of the network rotocols); Mcrosoft Performance Montor (standard nstrument of the Wndows T system); Mcrosoft etwork Montor (tycal network analyzer n the basc verson of Wndows T); LAAlyzer (nstrument of ovell for long tme observaton of the network traffc), etc 4 Program alcaton for statstcal analyss Two ndeendent rogram alcatons are desgned for nterretaton of montored data and to determne basc statstcal assessments etmontor s an alcaton for data nterretaton of real network traffc regstered by usng the standard montorng rogram Dstnct etwork Montor The alcaton s develoed by usng Vsual C 6 and MFC lbrary of classes It gves nformaton about acket length, tme, source and destnaton of the ackets, rotocol tye, etc and resents grahcal vsualzaton of the man statstcal assessments (Fgure 5) Fgure 5 Interretaton of montored data by etmontor etwork Analyzer s an alcaton realzed by usng of C# n the Mcrosoft Vsual StudoET envronment It analyses emrcal data from montorng and calculates basc statstcal assessments (average value, correlaton, varaton, regresson) The alcaton ermts to determne the functonal deendency between two arameters (varables) as a regresson lne based on the x (q) for q,, (Fgure 6) regstered emrcal data { }
8 Romansky and Parvanova/ Internatonal Journal of Engneerng, Scence and Technology, Vol, o, 9, -4 Fgure 6 Intal forms of the etwork Analyzer 4 Prelmnary statstcal analyss Some of the basc statstcal arameters are resented below: number of actve users (users); bandwdth for server (server bandwdth) and user access (user bandwdth); average value of the tme for nformaton obect selecton (average clck tme); watng tme for the selecton actvaton (clck tme); tme for URL nterretaton by usng DS server of the clent machne (tme for DS); tme to connect wth the server of the selected obect (tme to connect); average tme for request servcng (average request tme); tme for the frst byte recevng of the resonse from the server (tme to frst byte TFB); average acket length; The statstcal analyss that s carred out usng etwork Analyzer s based on the formulas resented n table Parameter Exectaton for x (average value) Varance for x Mean square devaton Coeffcent of varance Covaraton between x and x Coeffcent of correlaton Model of smle lne regresson (b dslacement; b coeffcent of regresson) Table Basc statstcal assessments Analytcal formula EX ( q ) x x _ av x DX q q DX C V x av ( q ) [ x x ] ( q ) ( q ) [ x x ][ x x ] q r x b b x ; ; b x b b x The exerments smulate access to www-obect and they are carred out for values of the number of actve users from to Ths ermts to analyze the users number nfluence on the other statstcal arameters Some of the statstcal assessments for the functonal deendency between arameters, calculated by usng etwork Analyzer, are resented n Fgure 7
9 Romansky and Parvanova/ Internatonal Journal of Engneerng, Scence and Technology, Vol, o, 9, -4 server bandwdth f(users) clck tme f(users) tme to connect f(users) Fgure 7 Assessment obtaned by regresson analyss Statstcal analyss of the measured data that was carred out usng etwork Analyzer ermts us to determne basc stochastc arameters for nvestgaton of the desgned Markov s model The ntensty of the nut flow of requests () could be determned on the base of the calculated average values for the montored arameters average clck tme (4,8 s), clck tme (4,88 s), tme to DS (,8 s) and tme to connect (,8 s) These values ermt to determne, s - In the same way, the ntensty of the flow of servcng n the node of the requested resource () could be connected to the arameter average request tme (4,8 s) whch determnes value, s - These values for the ntenstes defne /,5 s - All assessments are summarzed n table Table Assessments obtaned durng the relmnary statstcal analyss [s] users average clck tme clck tme tme to DS tme to connect average request tme,57,4,8 5,6,76,47 5 5 4 4,9, 4 6 5,8,, 5 8 6 6,,9,9 6,, Average: 4,8 s 4,88 s,8 s,8 s T S 48 s Total tme T R 9,95 s, s -,7 s - 5 Evaluaton of the stochastc arameters of the nformaton servcng n DLE 5 Analyss of the nfluence of the number of actve users ( const; var) The nvestgaton s carred out for constant value,5 and dfferent number of the actve users from to The goal s to evaluate the nfluence of the arameter on the stochastc assessments of the fnal robabltes for steady-state regme The calculatons are realzed on the base of the man formula (for,,, ) see () Examles for some of the calculatons are resented below and all obtaned assessments are summarzed n table : ( ) /(),67, : and ( ) /(,75),57,9 and,4 : ( ) /(,875),5,7,, and,7 : ( ) /(,9995),5,5,,5, etc
4 Romansky and Parvanova/ Internatonal Journal of Engneerng, Scence and Technology, Vol, o, 9, -4 Table Evaluaton of the fnal robabltes for steady-state regme 4 5 6 7 8 9,67,,57,9,4,5,7,,7 4,5,6,,6, 5,5,5,,6,, 6,5,5,,6,,, 7,5,5,6,6,,6,8,4 8,5,5,5,66,,57,78,9,96 9,5,5,5,66,,57,78,9,95,98,5,5,5,65,,56,78,9,95,98,49 average,5,65,8,66,,7,8,9,95,98,49 The average values of the determned fnal robabltes for steady-state regme and grahcal nterretaton of the functons () for,,,4 are shown n Fgure 8 The results show that for <4 the number of actve users has a lttle nfluence on the fnal robabltes and for 5 the robablty for mult-user access to the nformatonal resources s ractcally equal to zero,6,8,5,7,4,, fnal robabltes,6,5,4,,,, P P P P4 P5 P6 P7 P8 P9 P 4 5 6 7 8 9 number of actve users Average values of the fnal robabltes Fgure 8 Interretaton of the obtaned assessments functons () for,,,4 5 Analyss of the user s access to the resources ( var; const; const) The exerments are carred out for dfferent values of the ntensty (average tme between two requests from 5,55 s to s) and the ntensty of servcng s fxed as average value, s - All assessments obtaned by the analytcal analyss are summarzed n table 4 and some of them are grahcally nterreted n Fgure 9 Table 4 Assessments from the analytcal evaluaton for var E[] V[] E[W] E[Tw],8,9,9,6,4, 9 9 8, 45,6,8,4,7,,7 4,,4,7,9,8,9,4, 5,76,67,67,,6,46,7,7,,5,75,9,5,,,5,5,7,,7,5 5,8,4,6,5,,4,67,,7,,6,,7,,6,,4,6,,4,4,,8,6,,,5,,5,5,,,9,9,9,9,,,,56
4 Romansky and Parvanova/ Internatonal Journal of Engneerng, Scence and Technology, Vol, o, 9, -4 E[] E[W] Probablty,,9,8,7,6,5,4,,, 9 8 7 6 5 4,,,4,6,8,,,4,6,8 4 5 6 7 8 9 Intensty of the request flow Intensty x, Fgure 9 Grahcal nterretaton of the fnal robabltes and exectatons for users 5 Analyss of the nfluence of the learnng contents sze ( var; const; const) The exerments are carred out for dfferent values of the ntensty of servcng (the average tme of request s servcng deends on the sze of the learnng content n the searate nodes of DLE and range from s to 8 s) and the ntensty of nut flow of requests s fxed as average value, s - The man assessments obtaned by the analytcal analyss are summarzed n table 5 and some of them are grahcally nterreted n Fgure Table 5 Assessments from the analytcal evaluaton for var E[] V[] E[W] E[Tw],5,8,4,7,,7 4,,5,67,4,8,9, 6,6,54,75,57,48,7,6,9, 4,8,76 7,57,,5,5,7,,7,5 5,,5,4,6,5,,4,67,,7,67,,,68,,7,,49,7,6,64,5,86,7,,6,,4,56,,4,4,5,75,9,5,,,44,8,67,5,,8,6,,,5,,5,5 E[] E[W],9 4,5,8 4,7,5,6 Probablty,5,4 Probablty,5,,5,,,5,5,5,75,,5,,5,4,5,5,5,75,,5,,5,4,5 Intensty of servcng Intensty of servcng 6 Conclusons Fgure Grahcal nterretaton of the fnal robabltes and exectatons E[] and E[W] The followng conclusons could be made from the study conducted: The rocesses n the DLE have a stochastc nature that determnes the usefulness of a stochastc aaratus lke the Markov s chan In ths case the theory of Markov s stochastc rocesses s combned wth the rncles of queung theory for servcng of an nut flow of requests Ths combnaton ermts to use the model from Fgure defned by () and ()
4 Romansky and Parvanova/ Internatonal Journal of Engneerng, Scence and Technology, Vol, o, 9, -4 The evaluaton n ths aer s dfferent from the nvestgatons resented n (Romansky and Parvanova, 9b), and ermts to comare the man results of servcng and to defne the secfc arameters for DLE organzaton n a real medum To defne the frame of the current nvestgaton a relmnary model soluton s made and rogram montorng s realzed The statstcal analyss of the montored data n art 4 ermts to determne the functonal deendency of the man arameters by the number of actve users and to defne the tendences for regresson and varaton needed for the next stochastc evaluaton 4 The stochastc evaluaton shows that the number of actve users has a lttle nfluence on the varaton of the other arameters of the educaton servcng n DLE Ths fact ermts to use a fxed value for durng the evaluaton of the nfluence of nut requests and servcng ntenstes 5 The assessments n arts 5 and 5 ermt to determne the range of varaton for some mortant stochastc arameters lke the stuaton of servcng n steady-state regme, exectaton of actve users E[], exectaton of watng users E[W], etc These analytcal assessments defne the otmal frame of servcng n DLE determned by ranges,s - ±,s - and,s - ±,5s - References Berbaum, A, Just C, Hartng P, Menert K, Baker A, Crus-era C, 8 VR Juggler: a vrtual latform for vrtual realty alcaton develoment Int l Conf on Comuter Grahcs and Interactve Technques (ACM SIGGRAPH ASIA 8), Sngaore, Artcle 4 Bowman, M, 999 What s Dstrbuted Learnng ews & Advce from the Technology Collaboratve, Vol II, o, -5 Dede, C, 4 Dstrbuted-learnng communcatons as a model for educaton teachers Proc of Socety for Informaton Technology and Teacher Educaton Int l Conf, Chesaeake, VA, - Deshande, M, Karys G, 4 Selectve Markov models for redctng Web age access ACM Trans on Internet Technology, Vol 4, o, 6-84 Funkhouser, T, 5 Shae-based retreval and analyss of D models Communcaton of the ACM, Vol48, o 6, 58-64 Oblnger, DG, Maruyama, MU, 996 Dstrbuted learnng CAUSE Professonal Paer Seres, o 4, -7 Predd, J B, Kulkarn SB, Poor HV 6 Dstrbuted Learnng n Wreless Sensor etworks IEEE Sgnal Processng, Vol, 4, 56-69 Romansky, R, 6 An organzaton of rogram montorng and dstrbuted servcng evaluaton Proceedngs of the 7 th Internatonal Symosum on Intellgent Systems (ITELS 6), Russa, 6 June 6, 5-4 Romansky, R, Parvanova, E, 8 Concetual model of dstrbuted archtecture for D smulaton learnng Proceedngs of the Internatonal Scentfc Conference UITECH 8, Gabrovo, Bulgara, Vol III, 87-9 (n Bularan) Romansky, R, Parvanova, E, 9a Generaton of vrtual learnng envronment on the nternet usng VRML Proceedngs of the rd Int l Conf SAER-9 (n the frame of Int l Conf on Informaton Technologes), St Konstantne and Elena, Bulgara, 4-9 Romansky, R, Parvanova, E, 9b Determnstc nvestgaton of dstrbuted learnng envronment by usng Petr nets model 5 th Internatonal Conference E-Learnng and the Knowledge Socety Berln, Germany, August Setember 9 (acceted for ublshng) Bograhcal notes Assoc Prof Dr Rad P Romansky s workng n the Comuter Systems Deartment of the Techncal Unversty Sofa, (Bulgara) He has engaged n teachng and research actvtes snce the last 8 years Hs felds of scentfc nterest are Informaton and etwork Technologes, Comuter Modelng, Comuter Archtectures, Data Protecton, Aled Informatcs, etc He has over 5 ublshed books and over 5 ublcatons n varous natonal, nternatonal conferences and ournals Assst Prof Elena I Parvanova s workng n the College of the Energetc and Electroncs at the Techncal Unversty of Sofa (Bulgara) She s PhD student n the feld of the dstrbuted learnng and D Smulaton The scentfc felds are D Smulaton, Vrtual Realty, Multmeda, Informaton Technologes, etc Receved: August 9 Acceted: Setember 9 Fnal accetance n revsed form: Setember 9