Heavy-traffic asymptotics for stationary GI/G/1-type Markov chains

被引:3
作者
Kimura, Tatsuaki [1 ]
Masuyama, Hiroyuki [2 ]
Takahashi, Yutaka [2 ]
机构
[1] NTT Corp, NTT Serv Integrat Labs, Tokyo 1808585, Japan
[2] Kyoto Univ, Grad Sch Informat, Dept Syst Sci, Kyoto 6068501, Japan
基金
日本学术振兴会;
关键词
Queueing; Heavy-traffic limit; GI/G/1-type Markov chain; Characteristic function; STRUCTURED TRANSITION MATRICES;
D O I
10.1016/j.orl.2012.01.001
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
Asmussen (1987) proved a heavy-traffic limit theorem for the GI/G/1-type Markov chain. As a corollary, the theorem shows that in the heavy-traffic limit, the stationary distribution of the properly scaled level variable is geometric and independent of the phase variable. In this paper, the heavy-traffic asymptotics of the stationary distribution is proved under a weaker condition than Asmussen's, by the characteristic function approach. (C) 2012 Elsevier B.V. All rights reserved.
引用
收藏
页码:185 / 189
页数:5
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