On the stationary distribution of queue lengths in a multi-class priority queueing system with customer transfers

Authors:
Jingui Xie;Qi-Ming He;Xiaobo Zhao
Affiliations:
Department of Industrial Engineering, Tsinghua University, Beijing, People's Republic of China 100084;Department of Industrial Engineering, Dalhousie University, Halifax, Canada B3J 2X4;Department of Industrial Engineering, Tsinghua University, Beijing, People's Republic of China 100084
Venue:
Queueing Systems: Theory and Applications
Year:
2009

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Abstract

This paper deals with a multi-class priority queueing system with customer transfers that occur only from lower priority queues to higher priority queues. Conditions for the queueing system to be stable/unstable are obtained. An auxiliary queueing system is introduced, for which an explicit product-form solution is found for the stationary distribution of queue lengths. Sample path relationships between the queue lengths in the original queueing system and the auxiliary queueing system are obtained, which lead to bounds on the stationary distribution of the queue lengths in the original queueing system. Using matrix-analytic methods, it is shown that the tail asymptotics of the stationary distribution is exact geometric, if the queue with the highest priority is overloaded.