Modelling and Simulation of Queuing Models through the concept of Petri Nets
Abstract In recent years Petri Nets has been in demand due to its visual depiction. Petri Nets are used as an effective method for portraying synchronization, a concurrency between different system activities. In queuing models Petri networks are used to represent distributed modeling of the system and thus evaluate their performance. By specifying suitable stochastic Petri Nets models, the authors concentrate on representing multi-class queuing systems of various queuing disciplines. The key idea is to define SPN models that simulate a given queue discipline 's behavior with some acceptable random choice. Authors have find system queuing with both a single server and multiple servers with load-dependent service rate. Petri networks in the queuing model have enhanced scalability by combining queuing and modeling power expressiveness of 'petri networks.' Examples of application of SPN models to performance evaluation of multiprocessor systems demonstrate the utility and effectiveness of this modeling method. In this paper, authors have made use of Stochastic Petri nets in queuing models to evaluate the performance of the system.
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Basak, A., & Choudhury, A. (2019). Bayesian inference and prediction in single server M/M/1 queuing model based on queue length. Communications in Statistics-Simulation and Computation, 1-13.
Boukredera, D., & Adel-Aissanou, K. (2020). Modeling and Performance Analysis of Cognitive Radio Networks Using Stochastic Timed Colored Petri Nets. Wireless Personal Communications, 1-29.
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Luo, Q., Chen, Y., Chen, L., Luo, X., Xia, H., Zhang, Y., & Chen, L. (2019). Research on situation awareness of airport operation based on Petri nets. IEEE Access, 7, 25438-25451.
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Siddiqui, S., Darbari, M., & Yagyasen, D. (2020). An QPSL Queuing Model for Load Balancing in Cloud Computing. International Journal of e-Collaboration (IJeC), 16(3), 33-48.
Varela, A. M., Ramírez, J. A. R., Gómez, L. H. H., González, Á. M., & Reyes, M. Y. J. (2015). Lean production system model with Petri nets to support for decision making. Ingeniare, 182-195.
Vijayashree, K. V., & Janani, B. (2018). Transient analysis of an M/M/1 queueing system subject to differentiated vacations. Quality Technology & Quantitative Management, 15(6), 730-748.
Wanini Gonçalves de Araújo, K., de Andrade, M. O., Lima, R. M. F., & de Oliveira, C. A. L. (2020). Performance analysis of metropolitan bus rapid transit line via generalized stochastic petri nets. Journal of Urban Planning and Development, 146(1), 05019019.
Corchado, J. M., Bajo, J., De Paz, Y., and Tapia, D. I., 2008. Intelligent environment for monitoring Alzheimer patients, agent technology for health care. Decision Support Systems, 44(2):382–396.
Corchado, J. M., Pavón, J., Corchado, E. S., and Castillo, L. F., 2004. Development of CBR-BDI agents: a tourist guide application. In Advances in case-based reasoning, pages 547–559. Springer.
Zato, C. et al., 2012. PANGEA–Platform for Automatic coNstruction of orGanizations of intElligent Agents. In Distributed Computing and Artificial Intelligence, pages 229–239. Springer.
Ajmone Marsan, M., Conte, G., & Balbo, G. (1984). A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems. ACM Transactions on Computer Systems (TOCS), 2(2), 93-122.
Bakhshandeh, M., Mehrjerdi, Y. Z., & Nasab, H. H. (2019, January). A Proactive Approach to Evaluate Performance of BPEL Workflows by Queuing Theory and Stochastic Petri Net. In 2019 15th Iran International Industrial Engineering Conference (IIIEC) (pp. 52-56). IEEE.
Balsamo, S., & Marin, A. (2007). On representing multiclass M/M/k queues by generalized stochastic Petri nets. In Proc. of ECMS/ASMTA-2007 Conference (pp. 121-128).
Basak, A., & Choudhury, A. (2019). Bayesian inference and prediction in single server M/M/1 queuing model based on queue length. Communications in Statistics-Simulation and Computation, 1-13.
Boukredera, D., & Adel-Aissanou, K. (2020). Modeling and Performance Analysis of Cognitive Radio Networks Using Stochastic Timed Colored Petri Nets. Wireless Personal Communications, 1-29.
Camelo, G. R., Coelho, AS., Borges, RM., & de Souza, RM. (2010). Theory of queues and simulation applied to the shipment of iron ore and manganese at the tip terminal of Madeira. Notebooks of the IME-Série Estatística. 29(2), 1-14.
Khomonenko, A., & Gindin, S. (2016, April). Performance evaluation of cloud computing accounting for expenses on information security. In 2016 18th Conference of Open Innovations Association and Seminar on Information Security and Protection of Information Technology (FRUCT-ISPIT) (pp. 100-105). IEEE.
Koriem, S. M., Dabbous, T. E., & El-Kilani, W. S. (2004). A new Petri net modeling technique for the performance analysis of discrete event dynamic systems. Journal of systems and software, 72(3), 335-348.\
Luo, Q., Chen, Y., Chen, L., Luo, X., Xia, H., Zhang, Y., & Chen, L. (2019). Research on situation awareness of airport operation based on Petri nets. IEEE Access, 7, 25438-25451.
Pauleve, L., Magnin, M., & Roux, O. (2010). Tuning temporal features within the stochastic ?-calculus. IEEE Transactions on Software Engineering, 37(6), 858-871.
Peterson, J. L. (1977). Petri nets. ACM Computing Surveys (CSUR), 9(3), 223-252.
Peterson, J. L. (1981). Petri net theory and the modeling of systems. Prentice Hall PTR.
Siddiqui, S., Darbari, M., & Yagyasen, D. (2020). An QPSL Queuing Model for Load Balancing in Cloud Computing. International Journal of e-Collaboration (IJeC), 16(3), 33-48.
Varela, A. M., Ramírez, J. A. R., Gómez, L. H. H., González, Á. M., & Reyes, M. Y. J. (2015). Lean production system model with Petri nets to support for decision making. Ingeniare, 182-195.
Vijayashree, K. V., & Janani, B. (2018). Transient analysis of an M/M/1 queueing system subject to differentiated vacations. Quality Technology & Quantitative Management, 15(6), 730-748.
Wanini Gonçalves de Araújo, K., de Andrade, M. O., Lima, R. M. F., & de Oliveira, C. A. L. (2020). Performance analysis of metropolitan bus rapid transit line via generalized stochastic petri nets. Journal of Urban Planning and Development, 146(1), 05019019.
Corchado, J. M., Bajo, J., De Paz, Y., and Tapia, D. I., 2008. Intelligent environment for monitoring Alzheimer patients, agent technology for health care. Decision Support Systems, 44(2):382–396.
Corchado, J. M., Pavón, J., Corchado, E. S., and Castillo, L. F., 2004. Development of CBR-BDI agents: a tourist guide application. In Advances in case-based reasoning, pages 547–559. Springer.
Zato, C. et al., 2012. PANGEA–Platform for Automatic coNstruction of orGanizations of intElligent Agents. In Distributed Computing and Artificial Intelligence, pages 229–239. Springer.
Siddiqui, S., Darbari, M., & Yagyasen, D. (2020). Modelling and Simulation of Queuing Models through the concept of Petri Nets. ADCAIJ: Advances in Distributed Computing and Artificial Intelligence Journal, 9(3), 17–28. Retrieved from https://revistas.usal.es/cinco/index.php/2255-2863/article/view/ADCAIJ2020931728
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