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Optimal Control and Trunk Reservation in Loss Networks

Published online by Cambridge University Press:  27 July 2009

Peter B. Key
Affiliation:
Performance Engineering Division British Telecom Research Laboratories Ipswich IP5 7RE, England

Abstract

Consider a stochastic loss network, where calls or customer types arrive and have to find a path through the network to a given destination, and where our aim is to maximize the gain (suitably defined) from the network. In general there will be a number of paths available, and when a call arrives the two questions to answer are first, should the call be accepted, and secondly, if it is accepted which route should it take? The answer to the first question is in some sense harder than the second, and all dynamic routing or control policies have some explicit or implicit mechanism for rejecting calls and so answer the question in some way.

Type
Articles
Copyright
Copyright © Cambridge University Press 1990

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References

Akinpelu, J.M. (1983). The overload performance of engineered networks with non-hierarchical routing. In Proceedings of the 10th international teletraffic congress, Montreal.Google Scholar
Ackerley, R.G. (1987). Hysteresis-type behaviour in networks with extensive overflow. British Telecom Technology Journal 5: No 4.Google Scholar
Kelly, F.P. (1986). Blocking probabilities in large circuit-switched networks. Advances in Applied Probability 18: 473505.CrossRefGoogle Scholar
Burman, D.Y., Lehoczky, J.P. & Lim, Y. (1984). Insensitivity of blocking probabilities in a circuit-switched network. Journal of Applied Probability 21: 850859.CrossRefGoogle Scholar
Kelly, F.P. (1979). Reversibility and Stochastic Networks. Chichester: Wiley.Google Scholar
Key, P.B. (1988). Markov decision processes and optimal control in circuit-switched networks. In Proceedings of the fifth UK teletraffic symposium. IEE publications.Google Scholar
Kelly, F.P. (1985). Stochastic models of computer communication networks. Journal of the Royal Statistical Society Series B 47: 379395.Google Scholar
Zachary, S. (1988). Control of stochastic loss networks, with applications. Journal of the Royal Statistical Society Series B 50: 6173.Google Scholar
Ott, T.J. & Krishnan, K.R. (1985). State dependent routing of telephone traffic and the use of separable routing schemes. In Akiyama, M., ed. Proceedings of the 11th teletraffic congress. Amsterdam: Elsevier.Google Scholar
Lippman, S.A. (1975). Applying a new device in the optimization of exponential queueing systems. Operations Research 23: 687710.CrossRefGoogle Scholar
Lippman, S.A. & Stidham, S. (1977). Individual versus social optimization in exponential congestion systems. Operations Research 35: 233247.CrossRefGoogle Scholar
Stidham, S. (1985). Optimal control of admission to a queueing system. IEEE Transactions on Automatic Control 30: 705713.CrossRefGoogle Scholar
Kelly, F.P. (1988). Routing in circuit-switched networks: optimization, shadow prices, and decentralization. Advances in Applied Probability 20: 112144.CrossRefGoogle Scholar
Kelly, F.P. (1988). Routing and capacity allocation in networks with trunk reservation. Subimitted to Mathematics of Operations Research.Google Scholar
Lin, P.M., Leon, B.J. & Stewart, C.R. (1978). Analysis of circuit-switched networks employing originating-office control with spill-forward. IEEE Transactions on Communications 26: 754767.CrossRefGoogle Scholar
Girard, A. & Ouimet, Y. (1983). End-to-end blocking for circuit-switched networks: polynomial algorithms for some special cases. IEEE Transactions on Communications 31: 12691273.CrossRefGoogle Scholar
Whitt, W. (1985). Blocking when service is required from several facilities simultaneously. A.T. & T. Technical Journal: 18071856.Google Scholar
Ziedins, I. (1986). Stochastic models of traffic in star and line networks. Ph.D. Thesis, University of Cambridge, Cambridge, England.Google Scholar
Gibbens, R.J. (1988). Dynamic routing in circuit-switched networks: The dynamic alternative iouting strategy. Ph.D. Thesis, University of Cambridge, Cambridge, England.Google Scholar
Gibbens, R.J., Kelly, F.P. & Key, P.B. (1988). Dynamic Alternative Routing–Modelling and Behaviour. In Proceedings of the 12th international teletraffic congress. Amsterdam: Elsevier.Google Scholar
Whittle, P. (1988). Approximation in large-scale circuit-switched networks. Probability in the engineering and informational sciences 2: 279291.CrossRefGoogle Scholar
Foschini, G.J., Gopinath, B. & Hayes, J.F. (1981). Optimum allocation of servers to two types of competing customers. IEEE Transactions on Communications 29: 10511055.CrossRefGoogle Scholar
Ross, S.M. (1970). Applied probability models with optimization applications. San Francisco, CA: Holden Day.Google Scholar
Ross, S.M. (1983). Introduction to stochastic dynamic programming. New York: Academic Press.Google Scholar
Serfozo, R.F. (1979). An equivalence between continuous and discrete time Markov decision processes. Operations Research 27: 616620.CrossRefGoogle Scholar
Howard, R.A. (1960). Dynamic programming and Markov processes. Wiley: New York.Google Scholar
Tijms, H.C. (1986). Stochastic modeling and analysis. Chichester: Wiley.Google Scholar
Krishnan, K.R. & Ott, T.J. (1988). Forward-looking routing: A new state-dependent routing scheme. In Proceedings of the 12th international teletraffic congress. Amsterdam: Elsevier.Google Scholar
Girard, A. (1985). Blocking probability of noninteger groups with trunk reservation. IEEE Transactions on Communications 33: 113120.CrossRefGoogle Scholar
Cameron, W.H., Regnier, J., Galloy, P. & Savoie, A.M. (1983). Dynamic Routing for Intercity Telephone Networks. In Proceedings of the 10th international teletraffic congress, Montreal.Google Scholar
Ross, K.W. & Tsang, D.Optimal circuit access policies in an ISDN environment. IEEE Transactions on Communications 37: 934940.CrossRefGoogle Scholar