A method for calculating stationary queue distribution in a queuing system with flows of ordinary and negative claims and a bunker for superseded claims

Abstract

A queuing system with one service unit and Poisson flows of positive and negative claims is considered. There is an infinite buffer for positive claims. A negative claim arriving at the system knocks out a positive claim waiting in the buffer and moves it to another infinite buffer (bunker). The claims from bunker are served with relative priority. If upon arrival of negative claim the buffer is empty, it leaves the system without affecting it. The service times for claims from buffer and bunker have exponential distributions with different parameters. A new method that provides efficient calculation of stationary distribution of the number of customers in buffer and bunker is proposed.