ASYMPTOTIC BEHAVIOR FOR MArP/PH/2 QUEUE WITH JOIN THE SHORTEST QUEUE DISCIPLINE

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This paper considers a parallel queueing model with two servers, where arriving customers join the shortest queue. In [14], we studied a similar queueing model, and obtained the tail decay rate of the stationary distribution by using the matrix analytic approach. The main objectives of this paper are to extend the result in [14] to a more general model, and to clarify difficulty when we apply similar techniques as in [14]. In this paper, we study an MArP/PH/2 queue with join the shortest queue discipline, and show that the geometric tail asymptotics of the stationary distribution is obtained under a certain condition on the service time distribution.

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