Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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TRANSIENT DISTRIBUTIONS OF LEVEL DEPENDENT QUASI-BIRTH-DEATH PROCESSES WITH LINEAR TRANSITION RATES

  • Shin, Yang-Woo (Department of Statistics Changwon National University)
  • Published : 2000.01.01

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Abstract

Many queueing systems such as M/M/s/K retrial queue with impatient customers, MAP/PH/1 retrial queue, retrial queue with two types of customers and MAP/M/$\infty$ queue can be modeled by a level dependent quasi-birth-death(LDQBD) process with linear transition rates of the form ${\lambda}_k$={\alpga}{+}{\beta}k$ at each level $\kappa$. 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 uniformization technique introduced by van Moorsel and Sanders [11]. We apply the algorithm to some retrial queues and present numerical results.

Keywords

References

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