An Absorbing Markov Chain Approach to GI/M/1 Queues with Generalized Vacations

Kyung Chul Chae ； Sang Min Lee

《Asia Pacific Management Review》 10卷3期 (2005/06) Pp. 163-167

https://doi.org/10.6126/APMR.2005.10.3.01

並列摘要

Stationary probabilities of the embedded Markov chains of a class of GI/M/1 queues can be obtained by a simple multiplication y(I-Q)^(-1), where the j th entry of the row vector y is the probability that the system state seen by the first arrival during a busy period is j and (I-Q)^(-1) is the fundamental matrix associated with the standard GI/M/1 queue. In this paper, we present the entries of (I-Q)^(-1) explicitly. Also, we illustrate how to find y by examples such as the N-policy GI/M/1 queue with or without exponential multiple vacations.

並列關鍵字

Queues ； GI/M/1 ； N-policy ； Multiple vacations ； Fundamental matrix

參考文獻

Chae, K.C.,Lee, S.M.,Kim, N.K.,Kim, J.D.,Lee, H.W(2004).A trial solution approach to GI/M/1 queues with N-policy and exponential vacations.Journal of the Korean Statistical Society.33(3),283-298.

Choi, B.D.,Han, D.H(1994).G/M(superscript a, b) /1 queues with server vacations.Journal of Operation Research Society Japan.37,171-181.

Choi, B.D.,Park, K.K(1991).A G/M/1 vacation model with exhaustiveserver.Communications of Korean Mathematical Society.6,267-281.

Neuts, M.F(1994).Matrix-geometric Solutions in Stochastic Models.New York:Dover Publications.

Ross, S.M(2004).Introduction to Probability Models, 8th ed.San Diego:Academic Press.