A general result for deriving product-form solutions in Markovian models

WOSP/SIPEW'10 - Proceedings of the 1st Joint WOSP/SIPEW International Conference on Performance Engineering

Volumn , Issue , 2010, Pages 165-176

  Marin, Andrea ^a   Vigliotti, Maria Grazia ^b  

^a CA' FOSCARI UNIVERSITY OF VENICE   (Italy)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Product form solutions; Queueing theory

Indexed keywords

ANALYSIS TOOLS; BALANCE EQUATIONS; COMPLEX SOFTWARE; COMPOUND AGENTS; GENERAL METHOD; HARDWARE ARCHITECTURE; MARKOVIAN MODEL; PERFORMANCE EVALUATION; PRODUCT FORM SOLUTIONS; PRODUCT FORMS; PRODUCT-FORM;

GAME THEORY; MARKOV PROCESSES; OPERATIONS RESEARCH; STOCHASTIC MODELS; THEOREM PROVING;

QUEUEING THEORY;

EID: 77950496445     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1712605.1712632     Document Type: Conference Paper

References (29)

1. P. V. Afshari, S. C. Bruell, and R. Y. Kain. Modeling a new technique for accessing shared buses. In Proc. of the Computer Network Performance Symp., pages 4-13, New York, NY, USA, 1982. ACM Press.
2. C. Baier and H. Hermanns. Model-Checking Algorithms for Continuous-Time Markov Chains. IEEE Trans. Softw. Eng., 29(6):524-541, 2003.
3. G. Balbo, S. C. Bruell, and M. Sereno. Product form solution for Generalized Stochastic Petri Nets. IEEE Trans. on Software Eng., 28:915-932, 2002.
4. G. Balbo, S. C. Bruell, and M. Sereno. On the relations between BCMP Queueing Networks and Product Form Solution Stochastic Petri Nets. Proc. of 10th Int. Workshop on Petri Nets and Performance Models, 2003., pages 103-112, 2003.
5. S. Balsamo, R. Mamprin, and M. Marzolla. Performance evaluation of software architectures with Queueing Network Models. In Carmen Bobenau, editor, Proc. of the European Simulation and Modeling Conf. (ESMc'04), pages 206-213, UNESCO, Paris, France, 2004.
6. S. Balsamo and M. Marzolla. Performance evaluation of UML software architectures with multiclass Queueing Network models. In WOSP '05: Proc. of the 5th int. workshop on Soft. and Perf., pages 37-42, Palma, Illes Balears, Spain, 2005. ACM.
7. F. Baskett, K. M. Chandy, R. R. Muntz, and F. G. Palacios. Open, closed, and mixed networks of queues with different classes of customers. J. ACM, 22(2):248-260, 1975.
8. R. J. Boucherie. A characterisation of independence for competing Markov chains with applications to stochastic Petri nets. IEEE Tran. on Software Eng., 20(7):536-544, 1994.
9. G. Clark. Techniques for the Construction and Analysis of Algebraic Performance Models. PhD thesis, The University of Edinburgh, 2000.
10. J. L. Coleman, W. Henderson, and P. G. Taylor. Product form equilibrium distributions and a convolution algorithm for Stochastic Petri nets. Perform. Eval., Elsevier, 26:159-180, 1996.
11. N.J. Dingle, P.G. Harrison, and W.J. Knottenbelt. Uniformization and hypergraph partitioning for the distributed computation of response time densities in very large Markov models. Journal of Parallel and Distributed Computing, 64(8):908-920, August 2004.
12. E. Gelenbe. Product form networks with negative and positive customers. Journal of Applied Prob., 28(3):656-663, 1991.
13. P. Harrison and J. Hillston. Exploiting quasi-reversible structures in Markovian process algebra models. The Computer Journal, 38(7):510-520, 1995.
14. P. G. Harrison. Turning back time in Markovian process algebra. Theoretical Computer Science, 290(3):1947-1986, January 2003.
15. P. G. Harrison. Compositional reversed Markov processes, with applications to G-networks. Perform. Eval., Elsevier, 57(3):379-408, 2004.
16. P. G. Harrison. Reversed processes, product forms and a non-product form. Linear Algebra and Its Applications, 386:359-381, July 2004.
17. Peter G. Harrison and Maria G. Vigliotti. Algebraic product-forms do not need balance equations. Submitted to Computer Journal, 2009.
18. Peter G. Harrison and Maria G. Vigliotti. Perturbation of a non-product-form network into a new product-form: equilibrium state probabilities and response time density. In Proc. of Fourth Int. Conf. on Perform. Eval. Methodologies and Tools (VALUETOOLS'09), October 2009.
19. J. Hillston. A Compositional Approach to Performance Modelling. PhD thesis, Department of Computer Science, University of Edinburgh, 1994.
20. J. Hillston and N. Thomas. Product form solution for a class of PEPA models. Perform. Eval., Elsevier, 35(3-4):171-192, 1999.
21. J. R. Jackson. Jobshop-like queueing systems. Management Science, 10:131-142, 1963.
22. K. Kant. Introduction to Computer System Performance Evaluation. McGraw-Hill, 1992.
23. F. Kelly. Reversibility and stochastic networks. Wiley, New York, 1979.
24. J. Kramer and J. Magee. Concurrency: State Models Java Programs, 2nd Edition. Worldwide Series in Computer Science. John Wiley Sons, April 2006.
25. J. Y. Le Boudec. A BCMP extension to multiserver stations with concurrent classes of customers. In SIGMETRICS '86/PERFORMANCE '86: Proc. of the 1986 ACM SIGMETRICS Int. Conf. on Computer perf. modelling, measurement and eval., pages 78-91, New York, NY, 1986. ACM Press.
26. A. Marin and S. Rota Bul̀o. A general algorithm to compute the steady-state solution of cooperating markov chains. In proc. of 17th Annual Meeting of the IEEE Int. Symp. on Modelling, Analysis and Simulation of Computer and Telecommunication System, MASCOTS 09, pages 515-524, London, UK, 2009.
27. R. R. Muntz. Poisson departure processes and queueing networks. Technical Report IBM Research Report RC4145, Yorktown Heights, New York, 1972.
28. M. Sereno. Towards a product form solution for stochastic process algebras. The Computer Journal, 38(7):622-632, December 1995.
29. Connie U. Smith and Lloyd G. Williams. Five steps to establish software performance engineering. In Int. CMG Conference, pages 507-516, Reno, Nevada, USA, 2006.