The Geo/G/1 Queue with Negative Customers and Disasters

Abstract

The arrival of a negative customer to a queueing system causes one positive customer to be removed if any is present. On the other hand, the arrival of a disaster removes all the customers in the system. The discrete-time Geo/Geo/1 queue, which has either negative customers or disasters, has recently appeared in the literature[ 3 , 4 ]. We extend this Geo/Geo/1 queue to the Geo/G/1 queue. In so doing, we present both models' probability generating function of the stationary queue length and sojourn time, respectively. We also provide some numerical examples to illustrate the effect of the parameters on these queueing models.