Geometric tail of queue length of low-priority customers in a nonpreemptive priority MAP/PH/1 queue

Authors:
Jungong Xue;Attahiru S. Alfa
Affiliations:
School of Mathematical Science, Fudan University, Shanghai, China 200433;Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, Canada R3T 5V6
Venue:
Queueing Systems: Theory and Applications
Year:
2011

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Abstract

We consider a MAP/PH/1 queue with two priority classes and nonpreemptive discipline, focusing on the asymptotic behavior of the tail probability of queue length of low-priority customers. A sufficient condition under which this tail probability decays asymptotically geometrically is derived. Numerical methods are presented to verify this sufficient condition and to compute the decay rate of the tail probability.