Convexity Results for Queueing System with Variable Service Rate

摘要

In this paper we consider a single server queueing system with variable service rate. If the number of customers in system is less than a threshold, the service rate is set in a low value and it also can be switched to a high value once the number reaches to the threshold. We study five performance measures: the probability that the system is empty, the expected number in system and in queue, as well as the expected sojourn time in system and waiting time in queue. And we primarily show that these performance measures have the monotonicity or convexity with respect to the traffic intensity. These results are useful to the optimization problem in queueing system.