Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-09T22:56:10.603Z Has data issue: false hasContentIssue false
  • English
  • Français

Maximal Profit Dimensioning and Tariffing of Loss Networks

Published online by Cambridge University Press:  27 July 2009

N. G. Bean  and
P. G. Taylor
N. G. Bean
Affiliation:
Department of Applied Mathematics, University of Adelaide, S.A. 5005, Australia
P. G. Taylor
Affiliation:
Department of Applied Mathematics, University of Adelaide, S.A. 5005, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we present a unified approach to the optimal dimensioning and tariffing of loss networks. In our formulation the optimum is chosen to maximize the profit for the company operating the loss network. We assume that the operating company has the flexibility to determine tariffs and grade of service — although both of these can possibly be subject to regulatory constraints. The fact that the tariffing may affect demand and, hence, the dimensioning makes it essential that the operating company include the tariff/demand trade-off in determining the optimal way to dimension the loss network. A consequence of our formulation is that the optimal tariff structure has a particularly simple form, with the optimal tariff on a particular route separating into a term related to the tariff/demand trade-off on that route and a term that reflects the cost of the circuits used by the route.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 9 , Issue 3 , July 1995 , pp. 323 - 340
Copyright
Copyright © Cambridge University Press 1995

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.Ash, G.R., Cardwell, R.H. & Murray, R.P. (1981). Design and optimization of networks with dynamic routing. Bell System Technical Journal 60: 1787–1820.CrossRefGoogle Scholar
2.Berry, L.T.M. (1971). A mathematical model for optimizing telephone networks. Ph.D. thesis, University of Adelaide.Google Scholar
3.Burman, D.Y., Lehoczky, J.P. & Lim, Y. (1984). Insensitivity of blocking probabilities in a circuit-switched network. Journal of Applied Probability 21: 850–859.CrossRefGoogle Scholar
4.Chung, S.-P., Kashper, A. & Ross, K.W. (1993). Computing approximate blocking probabilities for large loss networks with state-dependent routing. IEEE/ACM Transaction on Networking 1(1): 105–115.CrossRefGoogle Scholar
5.Girard, A. (1990). Routing and dimensioning in circuit switched networks. Addison-Wesley, 1990.Google Scholar
6.Girard, A. & Liau, B. (1993). Dimensioning of adaptively routed networks. IEEE Transactions on Networking 1: 460–468.CrossRefGoogle Scholar
7.Jagerman, D.L. (1974). Some properties of the Erlang loss function. Bell System Technical Journal 53: 525–551.CrossRefGoogle Scholar
8.Jensen, A. (1950). Moe's principle: An econometric investigation intended as an aid in dimensioning and managing telephone plants. Copenhagen Telephone Company.Google Scholar
9.Katz, S.S. (1971). Trunk engineering of non-hierarchical networks. In Proceedings of the International Teletraffic Congress, ITC 6, Munich, pages 142.1–142.8.Google Scholar
10.Kelly, F.P. (1988). Routing in circuit-switched networks: optimization, shadow prices and decentralization. Advances in Applied Probability 20: 112–144.CrossRefGoogle Scholar
11.Kelly, F.P. (1990). Routing and capacity allocation in networks with trunk reservation. Mathematics of Operations Research 15.CrossRefGoogle Scholar
12.Kelly, F.P. (1991). Loss networks. The Annals of Applied Probability 1: 319–378.CrossRefGoogle Scholar
13.Louth, G.Mitzenmacher, M. & Kelly, F.P. (1993). Computational complexity of loss networks. Research Report No. 93–7, The Statistical Laboratory, University of Cambridge, 16 Mill Lane, Cambridge, CB2 1SB, U.K.Google Scholar
14.Low, S.H. & Varaiya, P.P. (1993). A new approach to service provisioning in ATM networks. IEEE/ACM Transaction on Networking 1(5): 547–553.CrossRefGoogle Scholar
15.Pratt, C.W. (1967). The concept of marginal overflow in alternate routing. Australian Telecommunications Research 1(2): 76–82.Google Scholar
16.Truitt, C.J. (1954). Traffic engineering techniques for determining trunk requirements in alternate routing trunk networks. Bell System Technical Journal 33: 277–302.CrossRefGoogle Scholar