The busy period analysis of a queue with heterogeneous servers and threshold service policy

Abstract

In the present paper we consider a queueing system with heterogeneous exponential servers. The service policy is a threshold-based control one, i.e. the fastest server must be switched on whenever it is free and at least one customer is in the system, while the slower ones must be activated when the number of customers in a queue reaches some threshold level specified for a certain server. We investigate algorithmically the busy period distribution by deriving expressions for the Laplace transforms and perform recursive calculation of the corresponding moments and the number of customers served during busy period, The optimal threshold levels for the mean busy period minimization are calculated.