zbMATH — the first resource for mathematics

PEPA queues: capturing customer behaviour in queueing networks. (English) Zbl 1279.90043
Aldini, Alessandro (ed.) et al., Proceedings of the fifth workshop on quantitative aspects of programming languages (QAPL 2007), Braga, Portugal, March 24–25, 2007. Amsterdam: Elsevier. Electronic Notes in Theoretical Computer Science 190, No. 3, 3-25 (2007).
Summary: Queueing network formalisms are very good at describing the spatial movement of customers, but typically poor at describing how customers change as they move through the network. We present the PEPA queues formalism, which uses the popular stochastic process algebra PEPA to represent the individual state and behaviour of customers and servers. We offer a formal semantics for PEPA queues, plus a direct translation to PEPA, allowing access to the existing tools for analysing PEPA models. Finally, we use the ipc/DNAmaca tool-chain to provide passage-time analysis of a dual web server example.
For the entire collection see [Zbl 1275.68011].
90B22 Queues and service in operations research
68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
Full Text: DOI
[1] Ajmone Marsan, M.; Conte, G.; Balbo, G., A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems, ACM transactions on computer systems, 2, 93-122, (1984)
[2] Argent-Katwala, A., “A compositional, collaborative performance pipeline,” Ph.D. thesis, Imperial College, London, United Kingdom (2006) · Zbl 1185.68103
[3] Bradley, J. T., N. J. Dingle, S. T. Gilmore and W. J. Knottenbelt, Derivation of passage-time densities in PEPA models using ipc: the Imperial PEPA Compiler, in: G. Kotsis, editor, MASCOTS’03, Proceedings of the 11th IEEE/ACM International Symposium on Modeling, Analysis and Simulation of Computer and Telecommunications Systems (2003), pp. 344-351
[4] Clark, G., “Techniques for the Construction and Analysis of Algebraic Performance Models,” Ph.D. thesis, Department of Computer Science, University of Edinburgh, Edinburgh EH9 3JZ, UK (1994)
[5] Clark, G.; Hillston, J., Product form solution for an insensitive stochastic process algebra structure, Performance evaluation, 50, 129-151, (2002) · Zbl 1159.68514
[6] Clark, G.; Sanders, W., Implementing a stochastic process algebra within the Möbius modeling framework, (), 200-215 · Zbl 1010.68526
[7] Dao-Thi, T.-H.; Mairesse, J., Zero-automatic queues, (), 64-78
[8] Gelenbe, E., Queuing networks with negative and positive customers, Journal of applied probability, 28, 656-663, (1991) · Zbl 0741.60091
[9] Gilmore, S.; Hillston, J., The PEPA workbench: A tool to support a process algebra-based approach to performance modelling, (), 353-368
[10] Gilmore, S.; Hillston, J.; Ribaudo, M., PEPA nets: A structured performance modelling formalism, (), 111-130 · Zbl 1047.68527
[11] Hillston, J., A compositional approach to performance modelling, () · Zbl 1080.68003
[12] Kwiatkowska, M.Z.; Norman, G.; Parker, D., Prism: probabilistic symbolic model checker, () · Zbl 1047.68533
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.