The output process of an MMPP/M/1 queue

Abstract

Olivier andWalrand (1994) claimed that the departure process of an MMPP/M/1 queue is not anMAP unless the queue is a stationary M/M/1 queue. They also conjectured that the departure process of an MAP/PH/1 queue is not anMAP unless the queue is a stationary M/M/1 queue. We show that their proof of the first result has an algebraic error, which leaves open the above question of whether the departure process of an MMPP/M/1 can be an MAP. © 1998 Applied Probability Trust.