Optimality results for a simple flow control problem

This paper presents a problem of optimal flow control for discrete-time M|M|1 queues, where the decision-maker seeks to maximize the throughput subject to a bound on the average queue size. The problem is cast as a constrained Markov decision process and solved via Lagrangian arguments. The optimal...

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Bibliographic Details
Published in26th IEEE Conference on Decision and Control Vol. 26; pp. 1852 - 1857
Main Authors Ma, Dye-jyun, Makowski, Armand M.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.12.1987
Subjects
Communication system control
Control systems
Dynamic programming
Educational institutions
Lagrangian functions
Optimal control
Size control
Stochastic processes
Throughput
Transmitters
Online AccessGet full text
DOI10.1109/CDC.1987.272833

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Summary:This paper presents a problem of optimal flow control for discrete-time M|M|1 queues, where the decision-maker seeks to maximize the throughput subject to a bound on the average queue size. The problem is cast as a constrained Markov decision process and solved via Lagrangian arguments. The optimal strategy is shown to be a threshold policy which saturates the constraint. The method of analysis proceeds through the discounted version of the Lagrangian problems whose value functions are shown to be integer-concave. Dynamic Programming and stochastic comparison ideas constitute the main ingredients of the solution.
DOI:10.1109/CDC.1987.272833