Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-23T11:25:25.341Z Has data issue: false hasContentIssue false

A product-form ‘loss network' with a form of queueing

Published online by Cambridge University Press:  14 July 2016

S. A. Berezner*
Affiliation:
University of Natal
A. E. Krzesinski*
Affiliation:
University of Stellenbosch
P. G. Taylor*
Affiliation:
University of Adelaide
*
Postal address: Department of Statistics, University of Natal, 4001 Durban, South Africa. e-mail: [email protected]
∗∗Postal address: Department of Computer Science, University of Stellenbosch, 7600 Stellenbosch, South Africa. e-mail: [email protected]
∗∗∗Postal address: Department of Applied Mathematics, University of Adelaide, South Australia 5005, Australia. e-mail:[email protected]

Abstract

We show that a form of queueing can be introduced into the standard fixed-routing loss network model while retaining a product-form invariant measure.

Keywords

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1997 

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] Bean, N. G. and Taylor, P. G. (1995) Maximal profit dimensioning and tariffing of loss networks. Prob. Eng. Inf. Sci. 9, 323340.CrossRefGoogle Scholar
[2] Berezner, S. A., Inggs, A. M. and Krzesinski, A. E. (1996) Two queueing schemes for multi-service switched networks. Proc Aust. Telecommunication Networks and Applications Conference, Melbourne. pp 267272.Google Scholar
[3] Berezner, S. A. and Krzesinski, A. E. (1995) Order independent loss networks. Proc. Aust. Telecommunications Networks and Applications Conference , Sydney. pp. 381386.Google Scholar
[4] Burman, D., Lehoczky, J. P. and Lim, Y. (1984) Insensitivity of blocking probabilities in a circuit-switched network. J. Appl. Prob. 21, 850859.Google Scholar
[5] Dziong, Z. and Roberts, J. W. (1987) Congestion probabilities in a circuit-switched integrated services network. Perf. Eval. 7, 267284.Google Scholar
[6] Girard, A. (1990) Routing and Dimensioning in Circuit-Switched Networks. Addison-Wesley, New York.Google Scholar
[7] Kaufman, J. S. (1981) Blocking in a shared resource environment. IEEE Trans. Commun. COM-29, 14741481.CrossRefGoogle Scholar
[8] Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, London.Google Scholar
[9] Kelly, F. P. (1988) Adaptive routing in circuit-switched networks. Adv. Appl. Prob. 18, 473505.Google Scholar
[10] Kelly, F. P. (1991) Loss networks. Ann. Appl. Prob. 1, 319378.Google Scholar
[11] Pollett, P. K. and Taylor, P. G. (1993) On the problem of establishing the existence of stationary distributions for continuous-time Markov chains. Prob. Eng. Inf. Sci. 7, 529543.CrossRefGoogle Scholar
[12] Roberts, J. W. (1981) A service system with heterogeneous user requirements. In Performance of Data Communications Systems and their Applications. ed. Pujolle, G. North Holland, Amsterdam. pp. 423431.Google Scholar
[13] Ross, K. W. (1995) Multiservice Loss Models for Broadband Telecommunication Networks. Springer, Berlin.Google Scholar