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

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

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Article ID: iaor20013077
Country: Netherlands
Volume: 35
Issue: 1/4
Start Page Number: 317
End Page Number: 348
Publication Date: Jan 2000
Journal: Queueing Systems
Authors: , ,
Abstract:

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.

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