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Optimal Admission Controls for Erlang's Loss System with Phase-Type Arrivals

Published online by Cambridge University Press:  27 July 2009

Ilze Ziedins
Ilze Ziedins
Affiliation:
Department of Statistics, University of Auckland, Private Bag 92019, Auckland, New Zealand
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Abstract

It is known that a threshold policy (or trunk reservation policy) is optimal for Erlang's loss system under certain assumptions. This paper examines the robustness of this policy under departures from the standard assumption of Poisson arrivals and shows that the optimal policy has a generalized trunk reservation form.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 10 , Issue 3 , July 1996 , pp. 397 - 414
Copyright
Copyright © Cambridge University Press 1996

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References

1.Bean, N.G., Gibbens, R.J., & Zachary, S. (1995). Asymptotic analysis of single resource loss systems in heavy traffic, with applications to integrated networks. Advances in Applied Probability 27: 273–292.Google Scholar
2.Cox, D.R. (1955). A use of complex probabilities in the theory of stochastic processes. Proceedings of the Cambridge Philosophical Society 51: 313–319.CrossRefGoogle Scholar
3.Hordijk, A. & Spieksma, F. (1989). Constrained admission control to a queueing system. Advances in Applied Probability 21: 409–431.CrossRefGoogle Scholar
4.Hunt, P.J. & Laws, C.N. (1991). Asymptotically optimal loss network control. Mathematics of Operations Research 18: 880–900.CrossRefGoogle Scholar
5.Hunt, P.J. & Laws, C.N. (1995). Optimization via trunk reservation in single resource loss systems under heavy traffic. Preprint, University of Cambridge and University of Oxford.Google Scholar
6.Jo, K.Y. & Stidham, S. (1983). Optimal service-rate control of M|G|1 queueing systems using phase methods. Advances in Applied Probability 15: 616–637.Google Scholar
7.Johansen, S.G. & Stidham, S. (1980). Optimal control of arrivals to a stochastic input-output system. Advances in Applied Probability 12: 972–999.CrossRefGoogle Scholar
8.Kelly, F.P. (1990). Routing and capacity allocation in networks with trunk reservation. Mathematics of Operations Research 15: 771–793.CrossRefGoogle Scholar
9.Kelly, F.P. (1991). Loss networks. Annals of Applied Probability 1: 319–378.CrossRefGoogle Scholar
10.Key, P.B. (1990). Optimal control and trunk reservation in loss networks. Probability in the Engineering and Informational Sciences 4: 203–242.Google Scholar
11.Key, P.B. (1994). Some control issues in telecommunications networks. In Kelly, F.P. (ed.), Probability, statistics and optimization: A tribute to Peter Whittle. Chichester: Wiley, pp. 383–395.Google Scholar
12.Langen, H.-J. (1982). Applying the method of phases in the optimization of queueing systems. Advances in Applied Probability 14: 122–142.Google Scholar
13.Lippman, S.A. (1975). Applying a new device in the optimization of exponential queueing systems. Operations Research 23: 687–710.Google Scholar
14.MacPhee, I.M. & Ziedins, I. (1996). Admission controls for networks with diverse routing. In Kelly, F., Zachery, S., & Ziedins, L. (eds.), Stochastic networks: Theory and applications. London: Oxford University Press.Google Scholar
15.Moretta, B. (1995). Behaviour and control of single and two resource loss networks. Ph.D. thesis, Heriot-Watt University.Google Scholar
16.Nguyen, V. (1991). On the optimality of trunk reservation in overflow processes. Probability in the Engineering and Informational Sciences 5: 369–390.Google Scholar
17.Reiman, M.I. (1991). Optimal trunk reservation for a critically loaded network. In Proceedings of the 13th International Teletraffic Congress. Amsterdam: North-Holland.Google Scholar
18.Ross, S.M. (1983). Introduction to stochastic dynamic programming. New York: Academic Press.Google Scholar
19.Stidham, S. Jr, (1985). Optimal control of admission to a queueing system. IEEE Transactions on Automatic Control 30: 705–713.Google Scholar
20.Stidham, S. & Prabhu, N.U. (1974). Optimal control of queueing systems. In Clarke, A.B. (ed.), Mathematical methods in queueing. Lecture Notes in Economics and Mathematical Systems 98. New York: Springer-Verlag, pp. 263–294.CrossRefGoogle Scholar
21.Ziedins, I. (1995). Optimal admission controls for Erlang's loss system with unequal mean holding times (in preparation).Google Scholar