Optimizing Service Rate and the Capacity of an M/M/1/N Queuing System with Retention of Reneged Customers

Abstract

In this paper, we present analysis of a single-server finite capacity Markovian queuing system with reneging and retention of impatient customers. It is assumed that arriving customers renege according to an exponential distribution and the reneged customers may be retained with some probability. The cost model of the system is made. The optimal values of service rate and the system capacity are obtained by using search and classical optimization algorithms. Further, the expected system size is compared with and without the optimization of the system. Some important comparisons are done to show the impact of optimization of parameters like system capacity, mean service rate, and the probability of retaining the reneged customers.