Nigel G Bean, David A Green and Peter G Taylor,
Department of Applied Mathematics,
University of Adelaide,
5005, Australia.
In a recent paper, Olivier and Walrand claimed that the departure process of an MMPP/M/1 queue is not a MAP unless the queue is a stationary M/M/1 queue . They also conjectured that the departure process of a MAP/PH/1 queue is not a MAP 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 a MAP .
AMS Classifications: Primary 60 K25, Secondary 60 J10