Large deviation analysis of subexponential waiting times in a processor-sharing queue

• 成果类型: Article
• 署名作者: Jelenkovic, P; Momcilovic, P
• 署名单位: Columbia University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.28.3.587.16396
• 发表日期: 2003
• 页码: 587-608
• 关键词: reduced-load equivalence; integral limit-theorems; cramers condition; distributions; asymptotics; account; sums

摘要

We investigate the distribution of the waiting time V in a stable M/G/1 processor-sharing queue with traffic intensity p < 1. When the distribution of a customer service request B belongs to a large class of subexponential distributions with tails heavier than e(-rootx), it is shown that P[V > x] = P[B > (1 - p)x](1 + o(1)) as x --> infinity. Furthermore, we demonstrate that the preceding relationship does not hold if the service distribution has a lighter tail than e(-rootx).