Transient analysis of an M/M/c queuing system with retention of reneging customers

摘要

In this paper, we study the transient behaviour of an M/M/c queuing system with reneging and retention of reneging customers. The probability generating function technique along with Bessel function properties is used to derive the time-dependent state probabilities explicitly. The transient behaviour of system size probabilities, the expected system size, the average reneging rate, and the average retention rate is studied with the help of a numerical example.