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Optimal routeing in two-queue polling systems

Published online by Cambridge University Press:  16 November 2018

I. J. B. F. Adan
Affiliation:
Eindhoven University of Technology
V. G. Kulkarni
Affiliation:
University of North Carolina
N. Lee
Affiliation:
University of North Carolina
E. Lefeber
Affiliation:
Eindhoven University of Technology
Corresponding
E-mail address:

Abstract

We consider a polling system with two queues, exhaustive service, no switchover times, and exponential service times with rate µ in each queue. The waiting cost depends on the position of the queue relative to the server: it costs a customer c per time unit to wait in the busy queue (where the server is) and d per time unit in the idle queue (where there is no server). Customers arrive according to a Poisson process with rate λ. We study the control problem of how arrivals should be routed to the two queues in order to minimize the expected waiting costs and characterize individually and socially optimal routeing policies under three scenarios of available information at decision epochs: no, partial, and complete information. In the complete information case, we develop a new iterative algorithm to determine individually optimal policies (which are symmetric Nash equilibria), and show that such policies can be described by a switching curve. We use Markov decision processes to compute the socially optimal policies. We observe numerically that the socially optimal policy is well approximated by a linear switching curve. We prove that the control policy described by this linear switching curve is indeed optimal for the fluid version of the two-queue polling system.

MSC classification

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2018 

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