The choice of the AN-net order mainly depends on how accurately the proposed model behaves with respect to the original system. This behavior is performed in a way that allows the preservation of the logical operation of both the MN net and the AN net. The main function of the AN net is to provide the MN net with tokens through the logical interface AMI net.

The MAI-net interface acts as an outlet for the MN-net tokens. The behavior of the MAI net is achieved by controlling the flow of tokens from OPMN and OTMN to the places of the AN net. The behavior of the AMI net is achieved by controlling the flow of tokens from the kAN sites of the AN net to IPMN and ITMN.

The lack of tokens in the AN-net network can cause the operation of the entire system to stop. The first form connects the kAN of the AN-net site to each IPMN site. Similarly, another design connects the kAN sites of the AN network to each ITMN pass through the PAMI sites.

Since the EM model consists of the MN network and the AN network, the matrix Q of the MRP representing the EM model will be of dimension nMNu nAN (see equation 2.7).

## Application and Numerical Simulations

In step 4, only the AN-net, AMI-net, MAI-net, and CN-net gateway rates need to be updated, while the MN-net gateway rates are net, MAI-net , and CN-net is requested, while MN-net transition rates remain unchanged. In order to obtain any performance measure, we need to know the values of the transition rates of the developed model. To use practical parameter values as presented in [32], the explicit Runge Kutta (which we used in steps 2 and 3 of the algorithm in Section 3) can be replaced by the implicit Runge Kutta [31].

The size of the matrix Q is of large dimensions; therefore, it is difficult to use the complete model in fig. The behavior of the labeled client module is known so that the corresponding SRN model can be built. Since the SRN model of the tagged client module represents the MN network, the locations: pMN,1, pMN,2, pMN,3, and pMN,4 can replace the locations: PTI, PTA, PTS, and PSP, respectively.

In other words, the input of the MN net is from the locations pMN,1 and pMN,2 and its output is taken from the transitions tMN,2 and tMN,4. 1 , we estimate (based on the algorithm described in Section 3) the other required performance measures of the MN net ( ( ;2d d5. The main function of MAI net is to provide feedback from the MN net to the rest of the model.

Another advantage of the MAI net is to control the flow of tokens from the MN net transitions: tMN,2, and tMN,3 to the AN net, thereby ensuring non-binding of PN tokens in the AN net to avoid 3.e, the CN-net consists of the transitions: tCN,1 and tCN,2, one of them is connected to the AN-net places: pAN,1, pAN,2 and pAN,3 by inhibiting arcs. Are weights for the variable arcs of the equivalent model of the sign ring-based system Arc location Arc Variable arc weight function (arc multiple) From MN net.

During the identification process, the MN network transition rates are therefore kept constant, while the transition rates for the AN network, the AMI network, the MAI network and the CN network are continuously changed. This result makes sense because the main task of the AN network is to generate tokens, while the AMI network and the MAI network are responsible for controlling the flow into and out of the MN network. As shown in Table 4, the difference (%Dj; 1d j d 5) between the measures obtained from the EM model and those of the complete model (Fig. 2b) is approximately 10.

The RS of the full model contains 1880 states, while the RS of the equivalent model contains only 101 states. Transition rates of the equivalent model before and after identification using the algorithm in section (3.1).

## Conclusion

Since some of the transition rates of the proposed model are unknown, we have used the algorithm proposed in Section 3 to determine these unknown rates. From these results, we conclude that the proposed modeling technique is much easier to handle due to the following facts. The use of the proposed model greatly reduces the number of RS states.

The RS of the complete SRN model contains 1880 states, while those of the proposed model are only 101 states. The size of the matrix Q of the proposed model is much smaller than that of the complete SRN model. It is important to note that the application of the proposed modeling technique does not depend on whether the desired system has homogeneous or heterogeneous behavior, but on the interaction between the proposed networks that make up the modeled systems.

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DrawNet++: Model objects to support performance analysis and simulation of complex systems." Proceedings of the 12th. International Conference on Modeling Tools and Techniques for Computer and Communication System Performance Evaluation (TOOLS 2002), London, UK. Towards an Adequate framework for the specification and validation of runtime evolving complex discrete-event systems." Proceedings of the 1st Workshop on Modeling Object Components and Agents, Aarhus Unversity, Denmark, DAIMI PB.

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اﺪﻤﺘﻌﻣ ﺔﺟﺬﻤﻨﻠﻟ ﺪﻳﺪـﺟ ﻚﻴﻨﻜﺗﻠﻋ

ﻰ تﺎﺒﺳﺎﺤﻟا ﺔﻤﻈﻧأ ءادأ ةءﺎﻔﻛ ﻞﻴﻠﺤﺘﻟ يﺮﺘﺑ تﺎﻜﺒﺷ تﺎﻳﺮﻈﻧ

ةﺰﻴﻤﻤﻟا ﺔﻴﻛﺮﺤﻟا تﻻﺎﺤﻟا تاذ

ﻢﻳﺮﻛ دﻮﻤﺤﻣ ﺮﻴﻤـﺳ

ﻲﻨﻴﻠﻴﻜﻟا .س .و و *سﻮﺑد.يأ .ﻲﺗ ، ﺪﻤﺤﻣ

ﺚﺤﺒﻟا ﺺﺨﻠﻣ ﻢﻈﻧ ىﺪﺣﻹ جذﻮﳕ ﻞﻤﻋ ﰲ ﲑﻜﻔﺘﻟا نﺎﻛﺔﻘﺑﺎﺴﻟا ثﻮﺤﺒﻟاو تﺎﺳارﺪﻟا ﻊﻴﲨ ﰲ

ﻟا اﺬﻫ ءاﺰﺟأ ﻦﻣ ءﺰﺟ ﻞﻜﻟ ﻲﻛﺮﳊا كﻮﻠﺴﻟا ﺔﻓﺮﻌﻣ ﺐﻠﻄﺘﻳ ﺔﻴﻌﻗاﻮﻟا ﺔﻴﻠﻤﻌﻟا تﺎﺒﺳﺎﳊا ﻦﻜﻟو .مﺎﻈﻨ

ﺎﻧدرأ اذإ ﺮﻬﻈﺗ ﺔﻴﻘﻴﻘﳊا ﺔﻠﻜﺸﳌاأ

ﻲﻛﺮﳊا كﻮﻠﺴﻟا (ﻂﻘﻓ) ﻪﻨﻣ فﺮﻌﻧ ﻦﳓو مﺎﻈﻨﻟا اﺬﳍ جذﻮﳕ ﻢﻤﺼﻧ ن

ءﺰﳉأ

ﻈﻧ ﺔﻄﺳاﻮﺑ ﺎﻬﺘﺳارد ﻢﺘﻳ ﱂ ﺔﻠﻜﺸﳌا ﻩﺬﻫ نإ ﺎﻧﺪﺟو ﺪﻘﻠﻓ ﺎﻨﺘﻓﺮﻌﻣو اﺬﳍو .ﻪﺟﺬﻤﻨﻠﻟ يﱰﺑ تﺎﻜﺒﺷ تﺎﻳﺮ

اﺪﻤﺘﻌﻣ ﻪﺟﺬﻤﻨﻠﻟ ﺪﻳﺪﺟ ﻚﻴﻨﻜﺗ حﱰﻘﻧ ﺚﺤﺒﻟا اﺬﻫ ﰲ ﺎﻨﻧﺄﻓ ﺐﺒﺴﻟاﻠﻋ

ﻰ يﱰﺑ تﺎﻜﺒﺷ تﺎﻳﺮﻈﻧ دﺎﲢا

ﺄﻓﺎﻜﻣ يﱰﺑ ﺔﻜﺒﺸﻟ جذﻮﳕ ﻢﻴﻤﺼﺗ ﰎ حﱰﻘﳌا ﻚﻴﻨﻜﺘﻟا اﺬﻫ ﰲ .ﺔﻴﺿﺎﻳﺮﻟا ﻢﻜﺤﺘﻟا تﺎﻳﺮﻈﻧ ﻊﻣ ﻪﺟﺬﻤﻨﻠﻟ ﻣ نﻮﻜﺘﻳ جذﻮﻤﻨﻟا اﺬﻫ .ﻪﻟ جذﻮﳕ ﻞﻤﻋ بﻮﻠﻄﳌا مﺎﻈﻨﻠﻟ

بﻮﻠﻄﳌا مﺎﻈﻨﻟا ﻦﻣ مﻮﻠﻌﳌا و مﺎﳍا ءﺰﳉا ﻞﺜﳝ ﺔﻴﺴﻴﺋﺮﻟا جذﺎﻤﻨﻟا ﻩﺬﻫ ىﺪﺣإ .ﲔﺴﻴﺋﺮﻟا ﲔﺟذﻮﻤﻨﻟا ﲔﺑ ﺪﻣ ﺔﻓﺮﻌﳌ .مﺎﻈﻨﻟا اﺬﻫ ءاﺰﺟأ ﻲﻗﺎﺑ ﻞﺜﳝ ﻲﺴﻴﺋﺮﻟا ﺮﺧﻵا جذﻮﻤﻨﻟا .ﻪﻟ جذﻮﳕ ﻞﻤﻋ

ﻚﻴﻨﻜﺘﻟا ةءﺎﻔﻛ

ﻋ ﻪﻘﻴﺒﻄﺗ ﰎ ﺪﻘﻠﻓ حﱰﻘﳌا ﺪﻳﺪﳉاﻠﻰ

ﺔﻴﻌﻗاﻮﻟا ﺔﻴﻠﻤﻌﻟا تﺎﺒﺳﺎﳊا ﻩﺰﻬﺟأ ىﺪﺣإ