Finite capacity M/M/r queueing system with queue-dependent servers

In this paper, we investigate finite multiserver queueing system with queue dependent heterogeneous servers; the number of servers changes depending on the queue length. Recursive method is employed to solve the steady state equations governing the model. The expression for the average number of customers in the system is obtained, which is further used to establish cost function. In order to gain maximum net profit, the threshold values of queue length at which servers are made available one by one, are determined. Some special cases are deduced, which match with earlier exiting results. We examine the effect of number of servers and input rate on average queue lengths by looking at a numerical illustration. The optimal threshold parameters and corresponding net profit are also tabulated.