Supplementary variable method applied to the MAP/G/1 queueing system

被引：13

作者：

Choi, BD

Hwang, GU

Han, DH

机构：

[1] Korea Adv Inst Sci & Technol, Ctr Appl Math, Taejon 305701, South Korea

[2] Korea Adv Inst Sci & Technol, Dept Math, Taejon 305701, South Korea

[3] Sun Moon Univ, Dept Math, Chungnam 337840, South Korea

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES B-APPLIED MATHEMATICS | 1998年 / 40卷

关键词：

D O I：

10.1017/S033427000001239X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider the MAP/G/1 queueing system with infinite capacity. In analysis, we use the supplementary variable method to derive the double transform of the queue length and the remaining service time of the customer in service (if any) in the steady state. As will be shown in this paper, our method is very simple and elegant. As a one-dimensional marginal transform. of the double transform, we obtain the generating function of the queue Length in the system for the MAP/G/1 queue, which is consistent with the known result.

引用

页码：86 / 96

页数：11

共 17 条

[1]

Bellman R., 1970, INTRO MATRIX ANAL

[2]

David Lucantoni M., 1991, Commun. Stat. Stoch. Models, V7, P1, DOI DOI 10.1080/15326349108807174

[3]

HOKSTAD BT, 1976, SCAND J STAT, V2, P95

[4]

Karlin S, 1975, A First Course in Stochastic Process

[5]

Lucantoni D.M., 1994, STOCH MODELS, V10, P145, DOI DOI 10.1080/15326349408807291

[6] A SINGLE-SERVER QUEUE WITH SERVER VACATIONS AND A CLASS OF NONRENEWAL ARRIVAL PROCESSES [J].

LUCANTONI, DM ;

MEIERHELLSTERN, KS ;

NEUTS, MF .

ADVANCES IN APPLIED PROBABILITY, 1990, 22 (03) :676-705

[7] SIMPLER PROOFS OF SOME PROPERTIES OF THE FUNDAMENTAL PERIOD OF THE MAP/G/1 QUEUE [J].

LUCANTONI, DM ;

NEUTS, MF .

JOURNAL OF APPLIED PROBABILITY, 1994, 31 (01) :235-243

[8]

MINC H., 1988, Nonnegative Matrices

[9]

Neuts M.F., 1989, Structured stochastic matrices of M/G/1 type and their applications

[10]

Neuts M.F., 1981, Matrix-Geometric Solutions in Stochastic Models: an Algorithmic Approach

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