On monotonicity conditions for optimal policies for controlling queueing systems (Q1883805)

Finding an optimal control policy for a controllable queueing system is facilitated if the optimal policy is known to possess certain structural properties. The present paper establishes sufficient conditions for an optimal policy to be monotone in a certain sense. The result is applied to the M/M/K/N queueing system with heterogeneous servers, where the task of the controller is to queue the customers or send them to one of the idle servers, with the aim of minimizing the mean number of customers in the system. The optimal policy has the property that for each set of occupied servers \(S\) there exists a number \(q_S,\) such that a new server with the largest possible service rate must be activitated as soon as the queue length reaches level \(q_S.\)