Queues with Negative Arrivals

E. Gelenbe, P. W. Glynn, and K. Sigman

Journal of Applied Probability, Vol. 28, 245-250 (1991)

We study single-server queueing models where in addition to regular arriving customers, there are negative arrivals. A negative arrival has the effect of removing a customer from the queue. The way in which this removal is specified gives rise to several different models. Unlike the standard FIFO GI/GI/1 model, the stability conditions for these new models may depend upon more than just the arrival and service rates; the entire distributions of interarrival and service times may be involved.