Control of M|M|1|N queue parameters under constraints

Abstract

An optimal control of the MM1N queue is considered on the basis of the minimum criterion for the expected service time if constraints on the average number of rejected demands and average energy expenditure are present. Two variants of an input flow are studied: with the separation of demands according to priorities and without such a separation. A dual optimization method and a Lagrange multiplier rule are used to synthesize a constrained optimal control. Two iteration procedures, the effectiveness of which is analyzed on the basis of the numerical simulation results, are presented in order to solve numerically a dual problem.