Optimal Idle and Inspection Periods for M/G/1 Queues

摘要

We consider an M/G/1 queue that operates under a (T,N)-policy: whenever the system becomes empty, the server is idle for a time T and then it inspects the queue continuously without serving customers until there are N customers waiting - thereupon the server is activated for service and serves customers continuously until the system becomes empty. This idle-inspection-service cycle is repeated indefinitely. There are costs for inspecting the queue, activating and running the server, and holding customers in the system. We present a computational procedure for determining the design parameters (T,N) that minimizes the average cost.