Abstract
In this paper a class of closed queueing network is modelled in the Markovian process algebra PEPA and solved using the classical Mean Value Analysis (MVA). This approach is attractive as it negates the need to derive the entire state space, and so certain metrics from large models can be obtained with little computational effort. The class of model considered includes models which are not obviously classical closed queueing models. The approach is illustrated with three examples.
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Keywords
- Average Response Time
- Queue Size
- Continuous Time Markov Chain
- Average Queue Length
- Underlying Markov Chain
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Clark, G., Gilmore, S., Hillston, J., Thomas, N.: Experiences with the PEPA Performance Modelling Tools. IEE Proceedings–Software 146(1), 11–19 (1999)
Haverkort, B.: Performance of Computer Communication Systems: A Model-based Approach. Wiley, Chichester (1998)
Hillston, J.: A Compositional Approach to Performance Modelling. Cambridge University Press, Cambridge (1996)
Hillston, J.: Exploiting Structure in Solution: Decomposing Compositional Models. In: Brinksma, E., Hermanns, H., Katoen, J.-P. (eds.) EEF School 2000 and FMPA 2000, vol. 2090, p. 278. Springer, Heidelberg (2001)
Hillston, J.: Fluid-flow approximation of PEPA models. In: Proceedings of QEST 2005, pp. 33–43. IEEE Computer Society Press, Los Alamitos (2005)
Mitrani, I.: Probabilistic Modelling. Cambridge University Press, Cambridge (1998)
Lavenberg, S., Reiser, M.: Stationary state space probabilities at arrival instants for closed queueing networks with multiple types of customers. Journal of Applied Probability 17(4), 1048–1061 (1980)
Reiser, M., Lavenberg, S.: Mean value analysis of closed multichain queueing networks. JACM 22(4), 313–322 (1980)
Sevcik, K., Mitrani, I.: The distribution of queueing network states at input and output instants. JACM 28(2), 358–371 (1981)
Stallings, W.: Cryptography and Network Security: Principles and Practice. Prentice-Hall, Englewood Cliffs (1999)
Thomas, N.: Mean value analysis for a class of PEPA models, Technical Report CS-TR-1128, School of Computing Science, Newcastle University (2008)
Thomas, N.: Using ODEs from PEPA models to derive asymptotic solutions for a class of closed queueing networks, Technical Report CS-TR-1129, School of Computing Science, Newcastle University (2008)
Thomas, N., Zhao, Y.: Fluid flow analysis of a model of a secure key distribution centre. In: Proceedings 24th Annual UK Performance Engineering Workshop, Imperial College London (2008)
Zhao, Y., Thomas, N.: Approximate solution of a PEPA model of a key distribution centre. In: Kounev, S., Gorton, I., Sachs, K. (eds.) SIPEW 2008. LNCS, vol. 5119, pp. 44–57. Springer, Heidelberg (2008)
Zhou, J., Gollmann, D.: An efficient non-repudiation protocol. In: Proceedings of the l0th Computer Security Foundations Workshop (CSFW 1997). IEEE Computer Society Press, Los Alamitos (1997)
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Thomas, N., Zhao, Y. (2009). Mean Value Analysis for a Class of PEPA Models. In: Bradley, J.T. (eds) Computer Performance Engineering. EPEW 2009. Lecture Notes in Computer Science, vol 5652. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02924-0_5
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DOI: https://doi.org/10.1007/978-3-642-02924-0_5
Publisher Name: Springer, Berlin, Heidelberg
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