Transient Analysis of a Multi-server Queuing Model with Discouraged Arrivals and Retention of Reneging Customers

摘要

In this paper, we study a finite capacity Markovian multi-server queuing system with discouraged arrivals, reneging, and retention of reneging customers. The transient state probabilities of the queuing system are obtained by using a computational technique based on the 4th order Runge-Kutta method. With the help of the transient state probabilities, we develop some important measures of performance of the system, such as time-dependent expected system size, time-dependent expected reneging rate, and time-dependent expected retention rate. The transient behavior of the system size probabilities and the expected system size is also studied. Further, the variations in the expected system size, the expected reneging rate, and the expected retention rate with respect to the probability of retaining a reneging customer are also studied. Finally, the effect of discouraged arrivals in the same model is analyzed.