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A note on extended uniformization for non-exponential stochastic networks

Published online by Cambridge University Press:  14 July 2016

Nico M. Van Dijk*
Affiliation:
Free University, Amsterdam
*
Present address: Department of Econometrics, University of Amsterdam, Jodenbreestraat 23, 1011 NH Amsterdam, The Netherlands.

Abstract

The standard uniformization technique for continuous-time Markov chains is generalized to non-exponential stochastic networks.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1991 

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References

[1] Boucherie, R. and Van Dijk, N. M. (1991) Product forms for queueing networks with state-dependent multiple job transitions. Adv. Appl. Prob. 23, 152187.10.2307/1427516Google Scholar
[2] Gavish, B. and Schweitzer, P. J. (1977) The Markovian queue with bounded waiting time. Management Sci. 23, 13491357.10.1287/mnsc.23.12.1349Google Scholar
[3] Hordijk, A. and Schassberger, R. (1982) Weak convergence of generalized semi-Markov processes. Stoch. Proc. Appl. 12, 271291.10.1016/0304-4149(82)90048-5Google Scholar
[4] Jensen, A. (1953) Markov chains as an aid in the study of Markov processes. Skan. Aktuartidskr. 36, 8791.Google Scholar
[5] Keilson, J. (1963) A gambler's ruin type problem in queueing theory. Operat. Res. 11, 570576.10.1287/opre.11.4.570Google Scholar
[6] Law, A. M. and Kelton, W. D. (1982) Simulation Modeling and Analysis. McGraw-Hill, New York.Google Scholar
[7] Ross, S. M. (1987) Approximating transition probabilities and mean occupation times in continuous-time Markov chains. Prob. Eng. Inf. Sci. 1, 251264.10.1017/S0269964800000036Google Scholar
[8] Ross, S. M. (1985) Introduction to Probability Models. Academic Press, New York.Google Scholar
[9] Tijms, H. C. (1986) Stochastic Modelling and Analysis', A Computational Approach. Wiley, New York.Google Scholar
[10] Tijms, H. C. and Eikeboom, A. M. (1986) A simple technique in Markovian control with applications to resource allocation. Oper. Res. Lett. 1, 2532.10.1016/0167-6377(86)90096-9Google Scholar
[11] Van Dijk, N. M. (1984) Controlled Markov Processes: Time-discretization. CWI Tract 11, Mathematical Center, Amsterdam, The Netherlands.Google Scholar
[12] Van Dijk, N. M. (1991) Approximate uniformization for continuous-time Markov chains with an application to performability analysis. Stoch. Proc. Appl. 10.1016/0304-4149(92)90018-LGoogle Scholar