Transient solution of the M/M/c queue with balking and reneging

This paper presents an analysis for the M/M/c queue with balking and reneging. It is assumed that arriving customers balk with a fixed probability and renege according to a negative exponential distribution. The generating function technique will be used to obtain the transient solution of system which results in a simple differential equation. Based on the properties of Bessel functions in the solution of this differential equation the probabilities can be extracted in a direct way.