A simple analysis of customer impatience in multi-server queues

In reneging literature, the reneging distribution is often assumed to be deterministic or random. In case of random reneging, it is assumed that the distribution is state independent so that customers have the same reneging rate irrespective of their position in the system. However, one can commonly observe many queuing systems where customers are aware of their system state. In such systems, the reneging rate of customers standing at a distance from the service facility is higher than those placed near the service facility. The reneging rate is not constant but is a function of system state. This paper is an attempt to model such a reneging phenomenon along with balking in a multi-server queuing scenario. Closed form expressions of a number of performance measures are presented. A numerical example is discussed to demonstrate the results in the paper.