Classification of Markov processes of M/G/1 type with a tree structure and its applications to queueing models

被引：8

作者：

He, QM ^{[1
]}

机构：

[1] Dalhousie Univ, Dept Ind Engn, DALTECH, Halifax, NS B3J 2X4, Canada

来源：

OPERATIONS RESEARCH LETTERS | 2000年 / 26卷 / 02期

关键词：

Markov process; queueing theory; tree structure; positive recurrence; null recurrence; transience; Lyapunov function; mean drift method;

D O I：

10.1016/S0167-6377(99)00057-7

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

This paper studies the classification problem of Markov processes of M/G/1 type with a tree structure. It is shown that the classification of positive recurrence, null recurrence, and transience of the Markov processes of interest is determined completely by the Perron-Frobenius eigenvalue of a nonnegative matrix. The results are used to find classification criteria for a number of discrete time or continuous time queueing systems with multiple types of customers. (C) 2000 Elsevier Science B.V. All rights reserved.

引用

页码：67 / 80

页数：14

共 50 条

[41] State-dependent M/G/1 type queueing analysis for congestion control in data networks
Altman, Eitan
Avrachenkov, Kostya
Barakat, Chadi
Núez-Queija, Rudesindo
Computer Networks, 2002, 39 (06) : 789 - 808
[42] State-dependent M/G/1 type queueing analysis for congestion control in data networks
Altman, E
Avrachenkov, K
Barakat, C
Núñez-Queija, R
COMPUTER NETWORKS-THE INTERNATIONAL JOURNAL OF COMPUTER AND TELECOMMUNICATIONS NETWORKING, 2002, 39 (06): : 789 - 808
[43] Subexponential asymptotics of the stationary distributions of M/G/1-type Markov chains
Masuyama, Hiroyuki
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 2011, 213 (03) : 509 - 516
[44] A note on the subexponential asymptotics of the stationary distribution of M/G/1 type Markov chains
Kim, Bara
Kim, Jeongsim
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 2012, 220 (01) : 132 - 134
[45] LINEAR INDEPENDENCE OF ROOT EQUATIONS FOR M/G/1 TYPE MARKOV-CHAINS
GAIL, HR
HANTLER, SL
SIDI, M
TAYLOR, BA
QUEUEING SYSTEMS, 1995, 20 (3-4) : 321 - 339
[46] Logarithmic Asymptotics for the GI/G/1-type Markov Chains and their Applications to the BMAP/G/1 Queue with Vacations
Tai, Yongming
He, Qi-Ming
INFOR, 2013, 51 (02) : 92 - 102
[47] Universally consistent conditionalU-statistics for absolutely regular processes and its applications for hidden Markov models
Michel Harel
Madan L. Puri
Annals of the Institute of Statistical Mathematics, 2004, 56 : 819 - 832
[48] Combined M/G/1-G/M/1 type structured chains: A simple algorithmic solution and applications
Jafari, R
Sohraby, K
IEEE INFOCOM 2001: THE CONFERENCE ON COMPUTER COMMUNICATIONS, VOLS 1-3, PROCEEDINGS: TWENTY YEARS INTO THE COMMUNICATIONS ODYSSEY, 2001, : 1065 - 1074
[49] Relaxed functional iteration techniques for the numerical solution of M/G/1 type Markov chains
Paola Favati
Beatrice Meini
BIT Numerical Mathematics, 1998, 38 : 510 - 526
[50] Shift techniques and canonical factorizations in the solution of M/G/1-type Markov chains
Bini, DA
Meini, B
Spitkovsky, IM
STOCHASTIC MODELS, 2005, 21 (2-3) : 279 - 302

← 1 2 3 4 5 →