An additional space special service facility heterogeneous queue

Abstract

In this paper we consider steady-state behaviour of a heterogeneous queueing system with instantaneously available special service facility and probabilistically available additional space both of which are queue-length dependent. The system operates at two different levels. The arrivals and the departures at these two levels occur at different rates. Steady-state probabilities at both the levels are calculated explicitly. Average number of customers in the system is also obtained. Associating the various costs, a criterion to obtain the decision points at which the hiring of additional space will be profitable and that for the size of additional space to be hired is discussed.