Abstract
Performance engineering has become a central plank in the design of complex, time-critical systems. It is supported by stochastic modelling, a brief history of which is given, going back to Erlang as long ago as 1909. This in turn developed according to successive new generations of communication and computer architectures and other operational systems. Its evolution through queues and networks is reviewed, culminating in the unification of many specification and solution techniques in a common formalism, stochastic process algebra. Recent results are given on the automatic computation of separable solutions for the equilibrium state probabilities in systems specified in such a formalism. A performance engineering support environment is proposed to integrate these methods with others such as response time analysis and fluid models, which are better suited to large scale aggregation of similar components in a continuous space.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Basharin, G.P., Langville, A.N., Naumov, V.A.: The life and work of A.A. Markov. J. Linear Algebra and its Applications 386, 3–26 (2004)
Baskett, F., Chandy, K.M., Muntz, R.R., Palacios, F.: Open, Closed and Mixed Networks of Queues with Different classes of Customers. J. ACM 22(2), 248–260 (1975)
Bennett, A.J., Field, A.J., Woodside, C.M.: Experimental Evaluation of the UML Profile for Schedulability, Performance and Time. In: Baar, T., Strohmeier, A., Moreira, A., Mellor, S.J. (eds.) UML 2004. LNCS, vol. 3273, pp. 143–157. Springer, Heidelberg (2004)
Bernardo, M., Donatiello, L., Gorrieri, R.: Integrating performance and functional analysis of concurrent systems with EMPA. In: Proc. of the 1st Workshop on Distributed Systems: Algorithms, Architectures and Languages, Levico (Italy), June 1996, pp. 5–6 (1996)
Boucherie, R.J.: A Characterisation of Independence for Competing Markov Chains with Applications to Stochastic Petri Nets. IEEE Transactions on Software Engineering 20(7), 536–544 (1994)
Brockmeyer, E., Halstrom, H.L., Jensen, A.: The life and works of A.K. Erlang. The Copenhagen Telephone Company (1948)
Chao, X., Miyazawa, M., Pinedo, M.: Queueing networks: customers, signals and product form solutions. Wiley, Chichester (1999)
Erlang, A.K.: The Theory of Probabilities and Telephone Conversations. Nyt Tidsskrift for Matematik BÂ 20 (1909)
Erlang, A.K.: Solution of some Problems in the Theory of Probabilities of Significance in Automatic Telephone Exchanges. Elektrotkeknikeren 13 (1917)
Gelenbe, E.: Random neural networks with positive and negative signals and product form solution. Neural Computation 1(4), 502–510 (1989)
Gelenbe, E.: G-networks with triggered customer movement. Journal of Applied Probability 30, 742–748 (1993)
Gelenbe, E.: The first decade of G-networks. European Journal of Operational Research 126(2), 231–232 (2000)
Gelenbe, E., Fourneau, J.-M.: G-networks with resets. In: Performance 2002. Performance Evaluation, vol. 49, pp. 179–191 (2002)
Gelenbe, E., Schassberger, R.: Stability of product form G-networks. Probability in the Engineering and Informational Sciences 6, 271–276 (1992)
Gordon, W.J., Newell, G.F.: Closed Queueing Systems with Exponential Servers. Operations Research 15(2), 254–265 (1967)
Harrison, P.G.: Turning Back Time in Markovian Process Algebra. Theoretical Computer Science 290(3), 1947–1986 (2003)
Harrison, P.G.: Separable equilibrium state probabilities via time reversal in Markovian process algebra. Theoretical Computer Science (2005) (under review)
Harrison, P.G.: Compositional reversed Markov processes, with applications to G-networks. Performance Evaluation 57(3), 379–408 (2004)
Harrison, P.G.: Reversed processes, product forms and a non-product form. J. Linear Algebra and its Applications 386, 359–382 (2004)
Hermanns, H., Rettelbach, M., Wei, T.: Formal Characterisation of Immediate Actions in SPA with Nondeterministic Branching. The Computer Journal 38(7), 530–541 (1995)
Hillston, J.: A Compositional Approach to Performance Modelling. PhD thesis, University of Edinburgh (1994)
Hillston, J., Thomas, N.: Product form solution for a class of PEPA models. Performance Evaluation 35, 171–192 (1999)
Jackson, J.R.: Jobshop-like queueing systems. Management Science 10(1), 131–142 (1963)
Kelly, F.P.: Reversibility and Stochastic Networks. John Wiley Sons Ltd, Chichester (1979)
King, P.J.B., Pooley, R.: Derivation of Petri Net Performance Models from UML Specifications of Communications Software. In: Haverkort, B.R., Bohnenkamp, H.C., Smith, C.U. (eds.) TOOLS 2000. LNCS, vol. 1786, pp. 262–276. Springer, Heidelberg (2000)
Petriu, D.B., Woodside, M.: A Metamodel for Generating Performance Models from UML Designs. In: Baar, T., Strohmeier, A., Moreira, A., Mellor, S.J. (eds.) UML 2004. LNCS, vol. 3273, pp. 143–157. Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Harrison, P. (2005). Performance Engineering and Stochastic Modelling. In: Bravetti, M., Kloul, L., Zavattaro, G. (eds) Formal Techniques for Computer Systems and Business Processes. EPEW WS-FM 2005 2005. Lecture Notes in Computer Science, vol 3670. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11549970_1
Download citation
DOI: https://doi.org/10.1007/11549970_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28701-8
Online ISBN: 978-3-540-31903-0
eBook Packages: Computer ScienceComputer Science (R0)