Ergodicity of the BMAP/PH/ s/ s+K Retrial Queue w ith PH-Retrial Times

Define the traffic intensity as the ratio of the arrival rate to the service rate. This paper s hows that t he BMAP/PH/s/s+K retrial queue with PH-retrial times is ergodic if and only if its traffic intensity is less than one. The result implies that t he BMAP/PH/s/s+K retrial queue with PH-retrial times and the c orresponding BMAP/PH/s queue have the same c ondition for ergodicity, a fact which has been believed for a long time without rigorous proof. This paper also s hows that t he same c ondition is necessary and sufficient for two modified retrial queueing s ystems to be ergodic. In addition, conditions for ergodicity of two BMAP/PH/s/s+K retrial queues with PH-retrial times and impatient customers are obtained.