Ergodicity of the BMAP/PH}/s/s+K retrial queue with PH-retrial times

Define the traffic intensity as the ratio of the arrival rate to the service rate. This paper shows that the 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 the BMAP/PH/s/s+K retrial queue with PH-retrial times and the corresponding BMAP/PH/s queue have the same condition for ergodicity, a fact which has been believed for a long time without rigorous proof. This paper also shows that the same condition is necessary and sufficient for two modified retrial queueing systems 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. Key words: Retrial queue, ergodicity, sample path method, mean-drift method, matrix analytic methods, batch Markov arrival process (BMAP), PH-distribution, and impatient customer, Lyapunov function.

• Type: Journal
• Year: 2000
• Where: QUESTA
• Authors: Qi-Ming He, Hui Li, Yiqiang Q. Zhao
• Keywords: PH-retrial Times, QUESTA 2000, Retrial Queue, Traffic Intensity