Optimal open-loop control of vacations, polling and service assignment

We consider in this paper the optimal open-loop control of vacations in que ueing systems. The controller has to take actions without state information . We first consider the case of a single queue, in which the question is wh en should vacations be taken so as to minimize, in some general sense, work loads and waiting times. We then consider the case of several queues, in wh ich service of one queue constitutes a vacation for others. This is the opt imal polling problem. We solve both problems using new techniques from [2,4 ] based on multimodularity.