Average Cost Semi-Markov Decision Processes and the Control of Queueing Systems

Linn I. Sennott

74 citations0/0 files storedProbability in the Engineering and Informational Sciences

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Advanced Queuing Theory Analysis Probability and Risk Models Optimization and Search Problems

Abstract

Semi-Markov decision processes underlie the control of many queueing systems. In this paper, we deal with infinite state semi-Markov decision processes with nonnegative, unbounded costs and finite action sets. Axioms for the existence of an expected average cost optimal stationary policy are presented. These conditions generalize the work in Sennott [22] for Markov decision processes. Verifiable conditions for the axioms to hold are obtained. The theory is applied to control of the M/G/l queue with variable service parameter, with on-off server, and with batch processing, and to control of the G/M/m queue with variable arrival parameter and customer rejection. It is applied to a timesharing network of queues with a single server and finally to optimal routing of Poisson arrivals to parallel exponential servers. The final section extends the existence result to compact action spaces.

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References

1975Time-Sharing Service Systems. I 1987Optimal control of service rates in networks of queues 1973Optimal control of batch service queues 1978Socially and Individually Optimal Control of Arrivals to a GI/M/1 Queue 1984M/M/1 Queueing Decision Processes with Monotone Hysteretic Optimal Policies

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2004Optimal dynamic assignment of a flexible worker on an open production line with specialists 1991Constrained Discounted Markov Decision Chains 1999M/M/1 Queues with Switching Costs and Hysteretic Optimal Control 2013Dynamic service rate control for a single-server queue with Markov-modulated arrivals 2001A note on optimality conditions for continuous-time Markov decision processes with average cost criterion 1991Value iteration in countable state average cost Markov decision processes with unbounded costs 1993Optimal control of the M/G/1 queue with repeated vacations of the server

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