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.