Messaoud Bounkhel ^†

Lotfi Tadj ^‡

^† King Saud University

College of Science, Department of Mathematics,

P.O. Box 2455, Riyadh 11451, Saudi Arabia

bounkhel@ksu.edu.sa

School of Business Administration, Department of Management and e-business

P.O. Box 28282, Dubai, United Arab Emirates

ltadj@aud.edu

Abstract

This paper uses a control-theoretic approach, the so-called predictive control, for the optimal design of a single-server, finite capacity, bulk-service queueing system. The problem is presented as an optimal control problem with one state vector variable and one control variable.  The optimal service rate is obtained explicitly under a general quadratic cost function.  Illustrative numerical examples are presented and the effect of the initial state distribution on the shape of the optimal solution is demonstrated.

Keywords: Queue, optimal control, predictive control, optimal design

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