Distribution of the busy period in a controllable <i>M/M</i>/2 queue operating under the triadic (0, <i>K, N, M</i>) policy

Abstract

We consider an M/M/ 2 queueing system with removable service stations operating under steady-state conditions. We assume that the number of operating service stations can be adjusted at customers' arrival or service completion epochs depending on the number of customers in the system. The objective of this paper is to obtain the distribution of the busy period using the theory of the gambler's ruin problem. As special cases, the distributions of the busy periods for the ordinary M/M/ 2 queueing system, the M/M/ 1 queueing system operating under the N policy and the ordinary M/M/ 1 queueing system are obtained.