A Single Server Queue With Limited Capacity And A Flexible Service Rate

Abstract

The arrival process of the model under studies in this paper is Poisson with state-dependent parameters, and the service time distribution is negative exponential with state-dependent rate. If there are n customers in the system, then the arrival rate is , and the service rate is . When a customer finds a server free, they enter the service station immediately; if not, they enter a queue of size N (N>0). In the waiting line, the customer follows to the First Come, First Served policy. During the customer's service period, if they are satisfied with the service at any point during the service period, they will either continue with probability  or leave the system with probability 1 - . At this point, the service rate becomes  (0< ).The group transformed inverse of the infinitesimal generator has been used for the analysis of this model, which is defined using the infinitesimal generator matrix. We derive the steady-state probabilities analytically using the group generalized inverses. On the basis of the same, performance metrics are generated. Moreover, a few calculations are given.