A POLLACZEK-KHINTCHINE FORMULA FOR M G/1 QUEUES WITH DISASTERS/

A disaster occurs in a queue when a negative arrival causes all the wo rk (and therefore customers) to leave the system instantaneously. Rece nt papers have addressed several issues pertaining to queueing network s with negative arrivals under the i.i.d. exponential service times as sumption. Here we relax this assumption and derive a Pollaczek-Khintch ine-like formula for M/G/1 queues with disasters by making use of the preemptive LIFO discipline. As a byproduct, the stationary distributio n of the remaining service time process is obtained for queues operati ng under this discipline. Finally, as an application, we obtain the La place transform of the stationary remaining service time of the custom er in service for unstable preemptive LIFO M/G/1 queues.