The discrete-time Geo/Geo/1 queue with negative customers and disasters

The arrival of a negative customer to a queueing system causes one ordinary customer to be removed (or killed) if any is present. The arrival of a disaster, on the other hand, kills all the customers in the system if any. In this paper, we extend the queueing theory on negative arrivals and disasters to the discrete-time Geo/Geo/1 queueing system. Specifically, we find the ergodicity condition and give explicit formulae for the stationary distribution. We also provide some numerical results to illustrate the effect of the parameters on several performance characteristics.