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Routing in circuit-switched networks: optimization, shadow prices and decentralization

Published online by Cambridge University Press:  01 July 2016

F. P. Kelly
F. P. Kelly*
Affiliation:
University of Cambridge
*
∗Postal address: Statistical Laboratory, 16 Mill Lane, Cambridge CB2 1SB, UK.
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Abstract

How should calls be routed or capacity allocated in a circuit-switched communication network so as to optimize the performance of the network? This paper considers the question, using a simplified analytical model of a circuit-switched network. We show that there exist implicit shadow prices associated with each route and with each link of the network, and that the equations defining these prices have a local or decentralized character. We illustrate how these results can be used as the basis for a decentralized adaptive routing scheme, responsive to changes in the demands placed on the network.

Keywords

NETWORK FLOWADAPTIVE ROUTINGDECENTRALIZATION
Type
Research Article
Information
Advances in Applied Probability , Volume 20 , Issue 1 , March 1988 , pp. 112 - 144
Copyright
Copyright © Applied Probability Trust 1988 

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References

[1] Baudet, G. M. (1978) Asynchronous iterative methods for multiprocessors. J. Assoc. Comp. Mach. 25, 226–244.CrossRefGoogle Scholar
[2] Benes, V. E. (1966) Programming and control problems arising from optimal routing in telephone networks. Bell Syst. Tech. J. 9, 1373–1438.CrossRefGoogle Scholar
[3] Brockmeyer, E., Halstrom, H. L. and Jensen, A. (1948) The Life and Works of A. K. Erlang. Academy of Technical Sciences, Copenhagen.Google Scholar
[4] Burley, D. M. (1972) Closed form approximations for lattice systems. In Phase Transitions and Critical Phenomena, Vol. 2, ed. Domb, C. and Green, M. S. Academic Press, London, 329–374.Google Scholar
[5] Cooper, R. B. and Katz, S. S. (1964) Analysis of alternate routing networks with account taken of the nonrandomness of overflow traffic. Bell Laboratories.Google Scholar
[6] Cope, G. A. and Kelly, F. P. (1986) The use of implied costs for dimensioning and routing. Report prepared by Stochastic Networks Group, Cambridge, for British Telecom Research Laboratories.Google Scholar
[7] Gallager, R. G. (1977) A minimum delay routing algorithm using distributed computation. IEEE Trans. Comm. 25, 73–85.CrossRefGoogle Scholar
[8] Gibbens, R. J. and Kelly, F. P. (1986) Dynamic routing in fully connected networks.Google Scholar
[9] Harris, R. J. (1973) Concepts of optimality in alternate routing networks. 7th Int. Teletraffic Cong.Google Scholar
[10] Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, Chichester.Google Scholar
[11] Kelly, F. P. (1985) Stochastic models of computer communication systems. J. R. Statist. Soc. B47, 379–395.Google Scholar
[12] Kelly, F. P. (1986) Blocking probabilities in large circuit-switched networks. Adv. Appl. Prob. 18, 473–505.CrossRefGoogle Scholar
[13] Kelly, F. P. (1986) Blocking and routing in circuit-switched networks. In Teletraffic Analysis and Computer Performance Evaluation, ed. Boxma, O. J., Cohen, J. W. and Tijms, H. C., Elsevier, Amsterdam, 37–45.Google Scholar
[14] Kelly, F. P. (1986) Instability in a communications network. In Fundamental Problems in Communication and Computation, ed. Cover, T. and Gopinath, B. Springer-Verlag, Berlin.Google Scholar
[15] Kelly, F. P. (1987) One-dimensional circuit-switched networks. Ann. Prob. 15, 1166–1179.CrossRefGoogle Scholar
[16] Kung, H. T. (1976) Synchronized and asynchronous parallel algorithms for multiprocessors. In Algorithms and Complexity, ed. Traub, J. F., Academic Press, New York, 153–200.Google Scholar
[17] Liggett, T. M. (1985) Interacting Particle Systems. Springer-Verlag, New York.CrossRefGoogle Scholar
[18] 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
[19] Lottin, J. and Forestier, J. P. (1980) A decentralized control scheme for large telephone networks. Proc. IFAC Symp. on Large Scale Systems Theory and Applications, Toulouse, France.CrossRefGoogle Scholar
[20] Louth, G. M. (1986) Phase transition in a circuit-switched network.Google Scholar
[21] Lubachevsky, B. and Mitra, D. (1986) A chaotic, asynchronous algorithm for computing the fixed point of a nonnegative matrix of unit spectral radius. J. Assoc. Comp. Mach. 33, 130–150.CrossRefGoogle Scholar
[22] Lundy, M. and Mees, A. (1986) Convergence of the annealing algorithm. Math. Programming 34, 111–124.CrossRefGoogle Scholar
[23] Malinvaud, E. (1972) Lectures on Microeconomic Theory. North-Holland, Amsterdam.Google Scholar
[24] Mason, L. G. (1985) Equilibrium flows, routing patterns and algorithms for store-and-forward networks. Large Scale Systems 8.Google Scholar
[25] Mitra, D. (1987) Asymptotic analysis and computational methods for a class of simple circuit-switched networks with blocking. Adv. Appl. Prob. 19, 219–239.CrossRefGoogle Scholar
[26] Mitra, D., Romeo, F. and Sangiovanni-Vincentelli, A. (1986) Convergence and finite-time behaviour of simulated annealing. Adv. Appl. Prob. 18, 747–771.CrossRefGoogle Scholar
[27] Nakagome, Y. and Mori, H. (1973) Flexible routing in the global communication network. 7th Int. Teletraffic Cong. Google Scholar
[28] Narendra, K. S., Wright, E. A. and Mason, L. G. (1977) Applications of learning automata to telephone traffic routing and control. IEEE Trans. Syst., Man Cybernet. 7, 785–792.CrossRefGoogle Scholar
[29] Narendra, K. S. and Mars, P. (1983) The use of learning algorithms in telephone traffic routing–a methodology. Automatica 19, 495–502.CrossRefGoogle Scholar
[30] Ott, T. J. and Krishnan, K. R. (1985) State dependent routing of telephone traffic and the use of separable routing schemes. 11th Int. Teletraffic Cong. (ed. Akiyama, M.), Elsevier, Amsterdam.Google Scholar
[31] Pioro, M. and Wallstrom, B. (1985) Multihour optimization of non-hierarchical circuit-switched communication networks with sequential routing. 11th Int. Teletraffic Cong. (ed. Akiyama, M.), Elsevier, Amsterdam.Google Scholar
[32] Sevcik, K. C. and Mitrani, I. (1981) The distribution of queueing network states at input and output instants. J. Assoc. Comput. Mach. 28, 358–371.CrossRefGoogle Scholar
[33] Spivak, M. (1965) Calculus on Manifolds. Benjamin, New York.Google Scholar
[34] Stidham, S. (1984) Optimal control of admission, routing, and service in queues and networks of queues: a tutorial review. In Analytical and Computational Issues in Logistics R&D, U.S. Army Research Office, 330–377.Google Scholar
[35] Stidham, S. (1985) Optimal control of admission to a queueing system. IEEE Trans. Autom. Congr. 30, 705–713.CrossRefGoogle Scholar
[36] Syski, R. (1960) Introduction to Congestion Theory in Telephone Systems. Oliver and Boyd, London.Google Scholar
[37] Whitt, W. (1985) Blocking when service is required from several facilities simultaneously. A.T. & T. Tech. J. 64, 1807–1856.Google Scholar
[38] Young, H. P. (1985) Cost allocation. In Proc. Symp. Appl. Math. 33, Amer. Math. Soc., 69–94.CrossRefGoogle Scholar
[39] Ziedins, I. (1985) Blocking in Queueing and Loss Systems. Knight Prize Essay, University of Cambridge.Google Scholar
[40] Ziedins, I. (1987) Quasi-stationary distributions and one-dimensional circuit-switched networks. J. Appl. Prob. 24, 965–977.CrossRefGoogle Scholar