Queue dependent probabilistic additional space heterogeneous queueing problem

Abstract

In this paper we consider the steady state behaviour of a queueing system with probabilistically available queue length dependent additional space. The system operates at two different levels. The arrivals and the departures at these two levels occur at different rates. Whenever the system size reaches a certain length, the system adds an additional space with some probability. Steady state probabilities at both the levels are calculated explicitly. The average number of customers in the system is also obtained. Associating the cost with the rent of the additional space and the waiting of the customers, a criterion to obtain the decision points at which the hiring of additional space will be profitable and that for the size of the additional space to be hired are discussed.