Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-09T06:20:38.671Z Has data issue: false hasContentIssue false
  • English
  • Français

Limit theorems for loss networks with diverse routing

Published online by Cambridge University Press:  01 July 2016

I. B. Ziedins  and
F.P. Kelly
I. B. Ziedins*
Affiliation:
Heriot-Watt University
F.P. Kelly*
Affiliation:
University of Cambridge
*
∗Postal address: Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK.
∗∗Postal address: Statistical Laboratory, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, UK.
Get access Rights & Permissions [Opens in a new window]

Abstract

Loss networks have long been of interest to telephone engineers, and are becoming increasingly important as models of computer and information systems. In this paper we present an asymptotic analysis of loss networks exhibiting various forms of symmetry. Our aim is to better understand the behaviour of networks involving very large numbers of links and routes, where an exact analysis is not possible and approximations are required.

Keywords

BLOCKING PROBABILITIESERLANG'S FORMULA
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 4 , December 1989 , pp. 804 - 830
Copyright
Copyright © Applied Probability Trust 1989 

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] Akinpelu, J. M. (1984) The overload performance of engineered networks with nonhierarchical and hierarchical routing. AT & T Tech. J. 63, 1261–1281.Google Scholar
[2] Brockmeyer, E., Halstrom, H. L. and Jensen, A. (1948) The Life and Works of A. K. Erlang. Academy of Technical Sciences, Copenhagen.Google Scholar
[3] Brown, T. C. (1983) Some Poisson approximations using compensators. Ann. Prob. 11, 726–744.Google Scholar
[4] Brown, T. C. and Pollett, P. K. (1982) Some distributional approximations in Markovian queueing networks. Adv. Appl. Prob. 14, 654–671.Google Scholar
[5] Burman, D. Y., Lehoczky, J. P. and Lim, Y. (1984) Insensitivity of blocking probabilities in a circuit switching network. J. Appl. Prob. 21, 850–859.Google Scholar
[6] Heyman, D. P. (1985) Asymptotic marginal independence in large networks of loss systems. Presented at ORSA/TIMS Applied Probability Conference, Williamsburg, Va., January 1985. Bell Communications Research, Holmdel.Google Scholar
[7] Holtzman, J. M. (1971) Analysis of dependence effects in telephone trunking networks. Bell Syst. Tech. J. 50, 2647–2662.Google Scholar
[8] Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, Chichester.Google Scholar
[9] Kelly, F. P. (1985) Stochastic models of computer communication systems. J. R. Statist. Soc. B 47, 379–395.Google Scholar
[10] Kelly, F. P. (1986) Blocking probabilities in large circuit-switched networks. Adv. Appl. Prob. 18, 473–505.Google Scholar
[11] Lin, P. M., Leon, B. J. and Stewart, C. R. (1978) Analysis of circuit-switched networks employing originating-office control with spill-forward. IEEE Trans. Comm. 26, 754–765.Google Scholar
[12] Mitra, D. (1985) Probabilistic models and asymptotic results for concurrent processing with exclusive and non-exclusive locks. SIAM J. Comp. 14, 1030–1051.Google Scholar
[13] Mitra, D. (1987) Asymptotic analysis and computational methods for a class of simple, circuit-switched networks with blocking. Adv. Appl. Prob. 19, 219–239.Google Scholar
[14] Mitra, D. and Weinberger, P. J. (1984) Probabilistic models of database locking: solutions, computational algorithms and asymptotics. J. Assoc. Comp. Mach. 31, 855–878.Google Scholar
[15] Nakagome, Y. and Mori, H. (1973) Flexible routing in the global communication network. Proc. 7th International Teletraffic Congress. Google Scholar
[16] Pinsky, E. and Yemeni, Y. (1984) A statistical mechanics of some interconnection networks. In Performance' 84, ed. Gelenbe, E., Elsevier, Amsterdam.Google Scholar
[17] Pollett, P. K. (1984) Distributional approximations for networks of quasireversible queues. In Stochastic Analysis and Applications, ed. Truman, A. and Williams, D., Lecture Notes in Mathematics 1095, Springer-Verlag, Berlin.Google Scholar
[18] Whitt, W. (1985) Blocking when service is required from several facilities simultaneously. AT & T Tech. J. 64, 1807–1856.Google Scholar
[19] Whittle, P. (1986) Systems in Stochastic Equilibrium. Wiley, Chichester.Google Scholar