Parametric model of IP-networks in the form of colored Petri net

Transcription

1 Parametri model of IP-networks in the form of olored Petri net Shmeleva T.R. Abstrat A parametri model of IP-networks in the form of olored Petri net was developed; it onsists of a fixed number of Petri net nodes and is invariant regarding the topology of the network, number of attahed routers and terminal equipment. The build parametri model does not require the modifiation of its struture that redues the model onstrution time for a network with an arbitrary number of devies and allows the performane evaluation. The model adequay is onfirmed omparing with real-life networks. Introdution The protool IP, desribed in the doument RFC 75, is the most widespread and in-use protool of the network layer. The basi funtion of it is the maintenane of interfaes with data-link tehnologies and with protools of the transport layer, in partiular with the protool TCP. Great suesses were attained by VoIP, whih is used by millions people either straight or indiretly. Important funtion of IP protool it the routing on the basis of whih any devie of a network exnges information with any other devie. An express evaluation of QoS in the proess of the networks design is an important sientifi problem, espeially for VoIP. The olored Petri nets [] and CPN Tools [] are suessfully used for the modeling of loal area Ethernet networks [], bakbone TCP/IP and MPLS networks [], Bluetooth pionets [5], as well as for performane and QoS evaluation. In the mentioned papers the modular approah is put in the basis of the teleommuniation networks models onstrution: the model of a network is assembled of before built submodels of the networking and terminal devies. However, the substantial lak of this approah is the neessity of model redesign for every new struture of the network, and also plenty of Petri net elements is used omparatively, that slows the proesses of models onstrution and analysis onsiderably. Presented in [6] the parametri model of swithed Ethernet has the fixed struture for an arbitrary topology, it is invariant regarding the network topology and amount of the onneted networking and terminal devies. The purpose of the present paper is the onstrution of IP-networks parametri model in the form of a olored Petri net. The ontribution of the present paper is the parametri model of IP-network whih as a fixed struture for any given IP-network and onsists of Petri net nodes. The model supplied with measuring fragments provides the performane evaluation diretly in the proess of simulation. Model of IP-network The parametri priniple whih was presented on the models of Ethernet [7] is applied for the IP-networks parametri model onstrution. As distint from the priniple of the diret mapping, where every new struture requires redesign of the Odessa National Aademy of Teleommuniation, Ukraine, tishtri@rambler.ru

2 model, the offered parametri model orresponds to an arbitrary network struture; the network struture is represented by the marking of definite plaes. The basi idea of the parametri model onstrution onsists in the following: when the flow struture of a network is examined, two basi onnetions are seleted: router to router and router to terminal network. In aordane with it the parametri model ontains the omponents of router and terminal network in one opy. Stream traffi is reated by the model of terminal subsriber) network in the parametri form, whih desription is presented in the next setion. A network is onsidered as a set of routers, onneted with eah other and with terminal networks by point-to-point lines. Definite IP-subnets are assigned to terminal networks. The interfaes of routers do not have home IP-addresses, that orresponds most to the often applied «unnumbered» interfaes of CISCO routers. The main page of the model is represented in Fig.. [#n #t x))=# to)] aout tpx) Transmit `tp{t={n=# to),p=# to)},pk=#pk x)}) rin Customer Terminal `,,~),)`,,,)`,,,) `tp{t={n=# to),p=# to)},pk=#pk x)}) `,,~),)`,,7,)`,,,)`,,,) to `,,,)`,,,)`,,5,)`,,~),) `,,,)`,,6,)`,,5,)`,,,) [#n #t x))=# to),#p #t x))=# to),# to)>0] `5,,,)`5,,,)`5,,6,)`5,,~),) `6,,7,)`6,,~5),)`6,,5,)`6,,,) to `7,,,)`7,,~6),)`7,,6,) Topology CrossTransmit `~),,,) `~),,,) topo `~),,,) `~),,5,) `~5),,6,) `~6),,7,) to tpx) Router R ain `tp{t={n=# to),p=# to)},pk=#pk x)}) Transmit [#n #t x))=# to),#p #t x))=# to),# to)<0] tpx) rout Fig.. The main page of the model The basi omponents of the network model are routers Router and terminal networks Customer. Information about the onnetion of devies to ports is defined by the topology Topology, the topology of a network is a model parameter. The desription of the network topology ontains: ) onnetions between routers, ) onnetions between routers and terminal networks; the number of router and the number of port is speified for eah of two ends of flow line. The reord `6,,7,) means that router number 6 through the port number is onneted to the third port of router 7. The reord `~),,5,) means that terminal network number the number of terminal network is marked by the sign «~») through the first port is onneted to the fourth port of router number 5; it is assumed that all the terminal networks are onneted to the routers through their first port. Ports of routers Router are presented by the plaes rin, rout, ports of terminal network Customer are presented by the plaes аin, аout; ports work in the fullduplex mode, the states of input and output ports are therefore onsidered. In eah plae a paket an be either present or absent; for more preise modeling it is neessary to use the speial mark of the nnel availability avail [7]. A terminal network periodially generates pakets with random soure and destination addresses. From the output port аout the paket is extrated by the transition Transmit and passed to the input port rin of a router, the number of router and port are defined by the values of the above desribed topology in the plae Topology. A router redirets paket to the output port rout in aordane with its routing table. Further the paket is extrated either by the transition Transmit and passed to the input port аin of

3 terminal network or by the transition Cross Transmit and passed to the input port rin of the next router, in aordane with the topology of the network. The loation of a paket in the network is ompletely defined by the number of router and the number of port, both for the pakets being transmitted in nnels and for the pakets being proessed into routers. It should be noted that paket, whih is transmitted in a nnel an have double numeration in aordane with the two ends of the onnetion line. Thus, paket is supplied with a tag, ontaining the number of router and the number of port, is self-identified, that allows to transmit it within the parametri model, onsisting of the unique opy of terminal network and unique opy of router. The reentrany of the mentioned omponents is provided adding the same tags to all the interior data: to the routing table reords, the lists of IP-addresses, the reords of buffers et etera. In Fig. the struture flowrts of the Novosibirsk regional network and a fragment of the European Internet bakbone [] are shown. T R T T a) European Internet bakbone R R R7 R R T T R R5 R7 R R6 R8 T6 T5 R6 T T R T R5 T5 b) Novosibirsk regional network T6 Fig.. Examples of network struture flowrts

4 European Internet bakbone Fig. a) ontains seven routers R-R7 and six terminal networks T-T6. The Novosibirsk regional network Fig. b) onsists of eight routers R-R8 and six terminal networks T-T6. In Fig. the examples of topology are represented for networks, shown in Fig.. Eah line desribes the onnetion of a definite router with neighbor routers and terminal networks. Two last lines desribe onnetions between terminal networks and routers. For example, first line of the Novosibirsk regional network Fig. a), «`,,~),)`,,7,)» desribes onnetions of router R with the terminal network T through the first port and the router R7 through the seond port. Expression is the onneting identifier of the desribed onnetions. `,,~),)`,,7,) `,,~),)`,,,)`,,7,) `,,,)`,,,)`,,8,) `,,~),)`,,7,) `5,,~5),)`5,,8,) `6,,~6),)`6,,8,) `7,,,)`7,,,)`7,,8,)`7,,,) `8,,7,)`8,,,)`8,,6,)`8,,5,) `~),,,)`~),,,)`~),,,) `~),,,)`~5),,5,)`~6),,6,) а) European Internet bakbone b) Novosibirsk regional network `,,~),)`,,,)`,,,) `,,~),)`,,7,)`,,,)`,,,) `,,,)`,,,)`,,5,)`,,~),) `,,,)`,,6,)`,,5,)`,,,) `5,,,)`5,,,)`5,,6,)`5,,~),) `6,,7,)`6,,~5),)`6,,5,)`6,,,) `7,,,)`7,,~6),)`7,,6,) `~),,,)`~),,,)`~),,,) `~),,5,)`~5),,6,)`~6),,7,) Fig.. Network topology desription Let us onsider an example of the paket path traing on the main page of the model. Passing of paket within the model from the sender to the reipient is represented in Fig. and onsists of eight steps. On the first step Step) a paket is formed by the terminal network with the number, IP-address of the sender is , the destination IP-address is The paket is put into the output port plae аout. For the advanement of paket in a network it is neessary to rediret the paket to the input port of router represented by the plae rin, aording to the defined topology. In the example the onnetion between the first terminal network and router is presented by the reord `~),,,), whih means that terminal network with the number through the first port is onneted with the first port of the first router. The transition Transmit extrats the paket from the output port аout and passes it to the router input port rin, the number of router and port is determined by the values of the above desribed topology in the plae Topology. The got result is presented on Step, the values of the tag were nged in the transmitted paket t=n=,p=), the number of router beame equal to, number of port equal to. A router is proessing the paket in aordane with its routing table and redirets the paket to the output port rout. On Step in plae rout the paket is presented with the new values of the tag t=n=,p=), the number of router remained equal to, the number of port beame equal to. Further the paket is extrated by the transition CrossTransmit and passed to the input port rin of the next router, in aordane with the reord `,,,) in the topology of network. In the plae rin on Step the paket is presented with the new values of the tag t=n=,p=), the number of the next router is equal to, the number of port is equal.

5 Fig.. The trae of a paket

6 On Step5 in the plae rout the paket is presented with the new values of tag t=n=,p=), the number of router remained equal to, the number of port beame equal to. On Step6 the number and port of the next router is determined, the paket is extrated by the transition CrossTransmit and passed to the router input port rin, the values of the tag have nged t=n=5,p=), the number of router is equal to 5, number of port is equal to. On Step7 router proesses the paket in aordane with its routing table and redirets it to the output port rout, the paket is represented with the new values of the tag t=n=5,p=), number of router - 5, number of port -. The transition Transmit extrats the paket from the router output port аout and passes it to the input port ain of terminal network. The number and the port of terminal network is determined by the values of the earlier desribed topology in the plae Topology. The got result is presented on Step8, the values of the tag were nged in the transmitted paket t=n=~),p=), the number of terminal network is equal to, number of port is equal to. The terminal network proesses the paket, aumulating statistial information about the amount of all of the delivered pakets within the network. Model of IP-router In [] the model of port of IP-router is presented, the model of router is assembled by loning of the port model in a neessary quantity of opies. For simplifiation of the router and network model onstrution, the model of IP-router is built in the parametri form. Presented in Fig. 5 omponent models the work of all the routers, in fat it is the parametri model of the router port, whih desribes the work of all the ports of all the routers. Transmitting pakets and loal information are supplied with tags, whih define definite loation within the network that allows the modeling of all the devies simultaneously. The routing of a paket in the parametri model of router is taken to swithing the paket tag in aordane with its routing table. RT rtr r [#n #t x))=#n r),samenw#ipdst #pk x),# #nw r),# #nw r))] In IN tpx) get `{t={n=#n #t x)),p=#p r)},pk=#pk Buf OUT Out tpx) put x Fig. 5. Model of IP-router port

7 The initial marking of the routing table RT ontains the amount of reords equal to the produt of routers quantity in the network and the quantity of subnets, for the probed network 7*=68. In Fig. 6 the routing table is represented in the form of the plae RT marking for the router R. The stati routing is onsidered, the presented model of router uses the omplete speifiations of hosts and networks IP-addresses. The proessing of IP-addresses required the reation of additional funtions for the determination of IP-address belonging to some subnet listed in the routing table, the mentioned funtions were presented in []. Eah reord in the routing table ontains the tag onsisting of the router number; moreover it ontains IP-address of terminal subnet and the port number, whih the terminal subnet is reable through. For example the reord `{n=,nw=8,99,0,0),8),p=} means that at the first router through the seond port the subnet with the IP-address 8,99,0,0),8) is reable. `{n=,nw=,5,8,0),7),p=} `{n=,nw=9,79,8,0),9),p=} `{n=,nw=9,98,0,0),9),p=} `{n=,nw=7,,8,0),0),p=} `{n=,nw=6,0,60,0),9),p=} `{n=,nw=8,8,6,0),9),p=} `{n=,nw=95,00,0,0),6),p=} `{n=,nw=8,99,0,0),8),p=} `{n=,nw=85,55,0,0),6),p=} `{n=,nw=,7,,0),9),p=} `{n=,nw=8,,0,0),6),p=} `{n=,nw=80,8,96,0),0),p=} `{n=,nw=6,7,0,0),9),p=} `{n=,nw=8,9,0,0),9),p=} `{n=,nw=,60,9,0),8),p=} `{n=,nw=7,6,,0),0),p=} `{n=,nw=8,07,0,0),7),p=} `{n=,nw=95,5,0,0),9),p=} `{n=,nw=6,6,0,0),9),p=} `{n=,nw=,,6,0),8),p=} `{n=,nw=95,,,0),9),p=} `{n=,nw=85,,0,0),6),p=} `{n=,nw=8,,0,0),6),p=} `{n=,nw=6,7,0,0),6),p=} Fig. 6. The marking of plae RT Ports of the router work in the full-duplex mode. From the input nnel of port IN a paket is extrated by the transition get and put to the internal buffer Buf of router. The variable tpx) on the onneting ar ontains the tag number of router and number of port) and the paket sender address, destination address, ontent). The funtion samenw determines the belonging of destination IP-address in aordane with the routing table presented by the plae RT. The transition put extrats a paket from the buffer and puts it into the plae OUT, modeling the output nnel of port. Three basi types of tokens are used in the model: the type desribes pakets transmitting within the network, the type rtr - reords of routing table, the type tagpkt - the routed pakets. The funtion samenw determines the belonging of IPaddress to a subnet. Delarations of types and variables are represented in Fig. 7. olset ip=produt INT*INT*INT*INT; olset nip=produt INT*ip; var i,,k:int; val TN=6; olset mask=int; olset nwt=produt ip*mask; olset nwa=reord n:int*nw:nwt; var srnw, dstnw: nwa; val TN=6; olset tq=int with..tn timed; fun powx,0)= powx,y)=powx,y-)*x; olset b=int timed; var d:b; olset pkt=reord ipsr:ip*ipdst:ip*data:b timed; olset tag=reord n:int*p:int; olset tagpkt=reord t:tag*pk:pkt timed; olset =union tp:tagpkt+avail timed; var x:tagpkt; olset topo=produt INT*INT*INT*INT; var to:topo; olset rtr=reord n:int*nw:nwt *p:int; var r:rtr; var sr,dst:nip; Fig. 7. Delarations of basi data types and variables

8 The proesses of pakets loss are not modeled, as far as the orret work of stati routing tables is assumed. The simple model of router with the obligatory buffering is presented; model elements for the usage of rout ahe and diret transmission between ports an be added. Model of terminal networks A model of realisti traffi is an important onstituent, to providing general adequay of the built models to real-life proesses; the traffi model, offered in [], is used in the present work. A terminal network periodially generates pakets with random soure and destination addresses, the soure address is in the range of addresses of own subnets, and the destination address in the range of addresses of all the subnets of the modeled fragment of the Internet bakbone. The model of terminal network Terminal is presented in Fig. 8. The generating of pakets is based on the use of the plae allnw, ontaining IP-addresses and masks of all the subnets of the modeled fragment of bakbone. The reord of eah IP-address ontains the tag, indiating the number of terminal network whih it belongs to. Addresses are extrated into the plaes ipsr soure address) and ipdst destination address. The most diffiult ation is the generating of random IP-address on given network address and mask. For these aims the funtion genip, presented in [] is used, the ontent of paket is modeled pointing its length. In the present model all the IP-subnets of eah terminal network generate pakets to all the IP-subnets of all the other terminal networks. The intensity of traffi is defined by a random funtion, in our ase uniform distribution, but there an be modeled the speialized traffi of Erlang, Poisson. Creation of matrix traffi, defining the intensity between the pairs of subnet is possible. tpx) In Counter In k+ k `0 TraffiIN INT sr `tp{t={n=~),p=}, pk={ipsr=# sr),ipdst=# Out Out [=# sr),=# dst)] i+ i dst `0 TraffiOUT tq INT tq.all) tq [#n srnw=],genip#nw srnw))) ipsr IpGenerate nip srnw@+delay) srnw `6 d allnw Data nwa INT tq dstnw dstnw@+delay) [#n dstnw<>],genip#nw dstnw))) ipdst IpGenerate nip `{n=,nw=,5,8,0),7)} `{n=,nw=9,79,8,0),9)} `{n=,nw=9,98,0,0),9)} `{n=,nw=7,,8,0),0)} `{n=,nw=6,0,60,0),9)} `{n=,nw=8,8,6,0),9)} `{n=,nw=95,00,0,0),6)} `{n=,nw=8,99,0,0),8)} `{n=,nw=85,55,0,0),6)} `{n=,nw=,7,,0),9)} `{n=,nw=8,,0,0),6)} `{n=,nw=80,8,96,0),0)} `{n=,nw=6,7,0,0),9)} `{n=,nw=8,9,0,0),9)} `{n=,nw=,60,9,0),8)} `{n=,nw=7,6,,0),0)} `{n=5,nw=8,07,0,0),7)} `{n=5,nw=95,5,0,0),9)} `{n=5,nw=6,6,0,0),9)} `{n=5,nw=,,6,0),8)} `{n=6,nw=95,,,0),9)} `{n=6,nw=85,,0,0),6)} `{n=6,nw=8,,0,0),6)} `{n=6,nw=6,7,0,0),6)} Fig. 8. Model of terminal networks Output pakets are put into the plae OUT. The plae TRAFFICOUT serves for the alulation of generated pakets quantity, the plae Data models the ontent of pakets. An output paket assembly is implemented by the transition via the assoiation of soure and destination addresses, and also the ontent, while the transition delay sets the periodiity of the generating. A yli reiteration of ations forms pakets, provided irulation of token in the sequene of plaes,,.

9 Input pakets, delivered to a terminal network, are put into the input port plae IN, further proessed by the transition Counter. The result of input pakets proessing is the aumulation of statistial information, in the plae TRAFFICIN the ount of amount of all the pakets delivered within the network is implemented. 5 Comparison of parametri model and model with diret mapping It is shown in the series of omputational experiments, that the evaluations of rateristis traffi and paket delivery time), got by the parametri model and by the traditional method [], are idential. Thus, for the evaluation of interngeability equivalene) let us onsider advantages and laks of the offered models. The laks of parametri models is above all things ompliation of pereption and weak vividness. Advantages onsist in the model does not require rebuilding at the nge of network struture, onsequently onveniently to use the offered models for networks design, onstruted models an be applied in the model-driven development of networks, network hardware and software; small number of Petri net elements, omparative desription is presented in Table ; the lead-time of the parametri model is diminished onsiderably. Network Table Comparison of model elements quantity Novosibirsk regional network European Internet bakbone Parametri model Main page omponents nodes Router omponents 8 7 nodes Terminal network omponents 6 6 nodes Total omponents 5 nodes Conlusions The model of IP-networks is presented in the parametri form. The topology of a network whih is the parameter of the model is desribed, on the example of the Novosibirsk regional network and European Internet bakbone. The built parametri model redues the time of model onstrution for a given network; model adequay is onfirmed omparing to the earlier got results and the measuring of real-life networks rateristis. The maim diretion for future work is the modeling of dynami routing protools to fill up routing tables automatially.

10 Referenes [] Jensen K. Colored Petri Nets - Basi Conepts, Analysis Methods and Pratial Use. / K. Jensen Springer-Verlag, 997. Vol p. [] Beaudouin-Lafon M. CPN Tools: A Tool for Editing and Simulating Coloured Petri Nets / M. Beaudouin-Lafon, W.E. Makay, M. Jensen et al. // LNCS: Tools and Algorithms for the Constrution and Analysis of Systems. 00. Vol. 0. P [] Zaitsev D.A. Swithed Ethernet Response Time Evaluation via Colored Petri Net Model / D.A. Zaitsev, T.R. Shmeleva // Proeedings of International Middle Eastern Multionferene on Simulation and Modelling, August 8-0, 006. Alexandria Egypt) P [] Sakun A.L., Zaitsev D.A. An Evaluation of MPLS Effiay using Colored Petri Net Models, Pro. Of International Middle Eastern Multionferene on Simulation and Modelling MESM'008), Amman Jordan), August 6-8, 008, P -6. [5] Bereznyuk M.V., Gupta K.K., Zaitsev D.A. Effetiveness of Bluetooth Address Spae Usage, Proeedings of 0 th International Conferene, Software & Systems Engineering and their Appliations ICSSEA 007), Paris -6 Deember 007. [6] Zaitsev D.A., Shmeleva T.R. Priniples of parametri Petri Net models onstrution for swithed networks // Simulation and Computer Graphis: Proeedings of -st International Sientifi-Tehni Conferene, Otober , Donetsk, DonNTU, 005, p In Russ. [7] Zaitsev D.A., Shmeleva T.R. Evaluation of Ethernet networks rateristis using parametri Petri nets // Zviazok Communiations), no., p In Russ.