Heavy loads and heavy tails

被引:0
|
作者
Borst, Sem [1 ]
机构
[1] Eindhoven Univ Technol, Dept Math & Comp Sci, POB 513, NL-5600 MB Eindhoven, Netherlands
来源
INDAGATIONES MATHEMATICAE-NEW SERIES | 2023年 / 34卷 / 05期
关键词
Heavy-tailed distributions; Heavy-traffic limit; Tail asymptotics; FLUID QUEUES; REGULAR VARIATION; RANDOM-WALKS; M/G/1; QUEUE; ASYMPTOTICS;
D O I
10.1016/j.indag.2023.04.003
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The present paper is concerned with the stationary workload of queues with heavy-tailed (regularly varying) characteristics. We adopt a transform perspective to illuminate a close connection between the tail asymptotics and heavy-traffic limit in infinite-variance scenarios. This serves as a tribute to some of the pioneering results of J.W. Cohen in this domain. We specifically demonstrate that reducedload equivalence properties established for the tail asymptotics of the workload naturally extend to the heavy-traffic limit.(c) 2023 The Author(s). Published by Elsevier B.V. on behalf of Royal Dutch Mathematical Society (KWG). This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
引用
收藏
页码:1038 / 1063
页数:26
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