Author:
Miyazawa Masakiyo,Zhao Yiqiang Q.
Abstract
We consider the asymptotic behaviour of the stationary tail probabilities in the discrete-time GI/G/1-type queue with countable background state space. These probabilities are presented in matrix form with respect to the background state space, and shown to be the solution of a Markov renewal equation. Using this fact, we consider their decay rates. Applying the Markov renewal theorem, it is shown that certain reasonable conditions lead to the geometric decay of the tail probabilities as the level goes to infinity. We exemplify this result using a discrete-time priority queue with a single server and two types of customer.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Reference30 articles.
1. Non-negative Matrices and Markov Chains
2. A Markov Renewal Approach to M/G/1 Type Queues with Countably Many Background States
3. Li Q. and Zhao Y. Q. (2002). Light-tailed asymptotics of stationary probability vector of Markov chains of GI/G/1-type. Submitted.
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