A note on the GI/M/1 queue with Poisson negative arrivals

The equilibriumM/M/1 queue with negative arrivals (Harrison and Pitel (1993)) has simple solutions for queue length and sojourn time distributions, but the generalization to M/G/1 (Harrison and Pitel (1996)) is surprisingly complex. In this note, we demonstrate that the generalization toGI/M/1 is much simpler because the embeddedMarkov chain method works easily, in contrast to the M/G/1 case. The crucial difference is as follows: