Optimal design of a bulk service queue

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.