Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-24T13:39:38.897Z Has data issue: false hasContentIssue false
  • English
  • Français

A heterogeneous blocking system in a random environment

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

G. Falin
G. Falin*
Affiliation:
Moscow State University
*
∗Postal address: Department of Probability, Mechanics and Mathematics Faculty, Moscow State University, Moscow 119899, Russia, e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We obtain a necessary and sufficient condition for the interaction between a service system and an external environment under which the stationary joint distribution of the set of busy channels and the state of the external environment is given by a product-form formula.

Keywords

DECOMPOSITIONINSENSITIVITYLOSS MODELRANDOM ENVIRONMENT

MSC classification

Primary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 1 , March 1996 , pp. 211 - 216
Copyright
Copyright © Applied Probability Trust 1996 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Borovkov, A. A. (1976) Stochastic Processes in Queueing Theory. Springer, New York.Google Scholar
[2] Burman, D. Y. (1981) Insensitivity in queueing systems. Adv. Appl. Prob. 13, 846–859.Google Scholar
[3] Chang, C.-S. and Nelson, R. (1993) Perturbation analysis of the M/M/1 queue in a Markovian environment via the matrix-geometric method. Commun. Statist. Stoch. Models. 9, 233–246.Google Scholar
[4] Chryssaphinou, O. and Papastavridis, S. (1990) Reliability of a consecutive-k-out-of-n system in a random environment. J. Appl. Prob. 27, 452–458.Google Scholar
[5] Cornez, R. (1987) Birth and death processes in random environments with feed-back. J. Appl. Prob. 24, 25–34.Google Scholar
[6] Fakinos, D. (1982) The generalized M/G/k blocking system with heterogeneous servers. J. Operat. Res. Soc. 31, 919–927.Google Scholar
[7] Gaver, D. P., Jacobs, P. A. and Latouche, G. (1984) Finite birth-and-death models in randomly changing environments. Adv. Appl. Prob. 16, 715–731.Google Scholar
[8] Gupta, P. L. and Gupta, R. D. (1990) A bivariate random environmental stress model. Adv. Appl. Prob. 22, 501–503.Google Scholar
[9] Hambly, B. (1992) On the limiting distribution of a supercritical branching process in a random environment. J. Appl. Prob. 29, 499–518.Google Scholar
[10] Kelly, F. (1979) Reversibility and Stochastic Networks. Wiley, New York.Google Scholar
[11] Lefevre, C. and Michaletzky, G. (1990) Interparticle dependence in a linear death process subjected to a random environment. J. Appl. Prob. 27, 491–498.Google Scholar
[12] Lefevre, C. and Milhaud, X. (1990) On the association of the lifelengths of components subjected to a stochastic environment. Adv. Appl. Prob. 22, 961–964.Google Scholar
[13] Posner, M. J. M. and Zuckerman, D. (1990) Optimal R&D programs in a random environment. J. Appl. Prob. 27, 343–350.Google Scholar
[14] Rao, B. M. and Posner, M. J. M. (1984) On the output process of an M/M/1 queue with randomly varying system parameters. Operat. Res. Lett. 3, 191–197.CrossRefGoogle Scholar
[15] Sztrik, J. (1987) On the heterogeneous M/G/n blocking system in a random environment. J. Operat. Res. Soc. 38, 57–63.Google Scholar