Abstract
Many queueing systems such asM/M/s/K retrial queue with impatient customers, MAP/PH/1 retrial queue, retrial queue with two types of customers andMAP/M/∞ queue can be modeled by a level dependent quasi-birth-death (LDQBD) process with linear transition rates of the form λk = α+ βk at each levelk. The purpose of this paper is to propose an algorithm to find transient distributions for LDQBD processes with linear transition rates based on the adaptive uniformizaton technique introduced by van Moorsel and Sanders [11]. We apply the algorithm to some retrial queues and present numerical results.
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Shin, Y.W. Transient distributions of level dependent quasi-birth-death processes with linear transition rates. Korean J. Comput. & Appl. Math 7, 83–100 (2000). https://doi.org/10.1007/BF03009929
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DOI: https://doi.org/10.1007/BF03009929