NOVEL HEAVY-TRAFFIC REGIMES FOR LARGE-SCALE SERVICE SYSTEMS

被引：7

作者：

Janssen, A. J. E. M. ^{[1
]}

Van Leeuwaarden, J. S. H. ^{[1
]}

Mathijsen, B. W. J. ^{[1
]}

机构：

[1] Eindhoven Univ Technol, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 2015年 / 75卷 / 02期

关键词：

heavy-traffic approximation; heavy-traffic regimes; large service systems; queueing theory; asymptotic analysis; saddle point method; Riemann zeta function; QUEUES; LIMITS; TIME; CUMULANTS; MAXIMUM;

D O I：

10.1137/140960815

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a family of heavy-traffic regimes for large-scale service systems, presenting a range of scalings that include both moderate and extreme heavy traffic, as compared to classical heavy traffic. The heavy-traffic regimes can be translated into capacity sizing rules that lead to economies-of-scales, so that the system utilization approaches 100% while congestion remains limited. We obtain heavy-traffic approximations for stationary performance measures in terms of asymptotic expansions, using a nonstandard saddle point method, tailored to the specific form of integral expressions for the performance measures, in combination with the heavy-traffic regimes.

引用

页码：787 / 812

页数：26

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