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On the Nash equilibria for the FCFS queueing system with load-increasing service rate

Part of: Game theory Operations research and management science Distribution theory - Probability

Published online by Cambridge University Press:  01 July 2016

A. C. Brooms
A. C. Brooms*
Affiliation:
Birkbeck College
*
∗ Postal address: School of Economics, Mathematics and Statistics, Birkbeck College, Malet Street, London WC1E 7HX, UK. Email address: [email protected]
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Abstract

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We consider a service system (QS) that operates according to the first-come-first-served (FCFS) discipline, and in which the service rate is an increasing function of the queue length. Customers arrive sequentially at the system, and decide whether or not to join using decision rules based upon the queue length on arrival. Each customer is interested in selecting a rule that meets a certain optimality criterion with regard to their expected sojourn time in the system; as a consequence, the decision rules of other customers must be taken into account. Within a particular class of decision rules for an associated infinite-player game, the structure of the Nash equilibrium routeing policies is characterized. We prove that, within this class, there exist a finite number of Nash equilibria, and that at least one of these is nonrandomized. Finally, with the aid of simulation experiments, we explore the extent to which the Nash equilibria are characteristic of customer joining behaviour under a learning rule based on system-wide data.

Keywords

Queuestate-dependent service ratenoncooperative gameNash equilibriumsimulation

MSC classification

Primary: 90B22: Queues and service 91A10: Noncooperative games
Secondary: 60E15: Inequalities; stochastic orderings 91A13: Games with infinitely many players
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 37 , Issue 2 , June 2005 , pp. 461 - 481
Copyright
Copyright © Applied Probability Trust 2005 

References

Altman, E. and Shimkin, N. (1996). Learning and equilibrium in processor sharing systems. Res. Rep. EE-1113, Department of Electrical Engineering, Technion.Google Scholar
Altman, E. and Shimkin, N. (1998). Individual equilibrium and learning in processor sharing systems. Operat. Res. 46, 776–784.Google Scholar
Ben-Shahar, I., Orda, A. and Shimkin, N. (2000). Dynamic service sharing with heterogeneous preferences. Queueing Systems 35, 83–103.Google Scholar
Brooms, A. C. (2000). Individual equilibrium dynamic routing in a multiple server retrial queue. Prob. Eng. Inf. Sci. 14, 9–26.CrossRefGoogle Scholar
Brooms, A. C. (2003). Assessing the performance of a shared resource: simulation vs. the Nash equilibrium. In Keynote Papers, YOR13 (Bath, UK, 2003), ed. Taylor, J., The Operational Research Society, Birmingham, pp. 3–19.Google Scholar
Buche, R. and Kushner, H. J. (2000). Stochastic approximation and user adaptation in a competitive resource sharing system. IEEE Trans. Automatic Control 45, 844–853.Google Scholar
Lippman, S. (1975). Applying a new device in the optimization of exponential queuing systems. Operat. Res. 23, 687–709.Google Scholar
Lippman, S. A. and Stidham, S. (1977). Individual versus social optimisation in exponential congestion systems. Operat. Res. 25, 233–247.Google Scholar
Naor, P. (1969). The regulation of queue size by levying tolls. Econometrica 37, 15–24.CrossRefGoogle Scholar
Yechiali, U. (1971). On optimal balking rules for the GI/M/1 queueing process. Operat. Res. 19, 349–370.Google Scholar