Messaoud Bounkhel
King Saud University College of Science, Department of Mathematics

Lotfi Tadj
American University in Dubai, School of Business Administration, Department of Management and e-business

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.