Steady-State Analysis for Multiserver Queues Under Size Interval Task Assignment in the Quality-Driven Regime

• 成果类型: Article
• 署名作者: Zhang, Bo; Zwart, Bert
• 署名单位: International Business Machines (IBM); IBM USA
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1120.0571
• 发表日期: 2013
• 页码: 504-525
• 关键词: server; asymptotics; systems

摘要

We study the steady-state behavior of multiserver queues with general job size distributions under size interval task assignment (SITA) policies. Assuming Poisson arrivals and the existence of the alpha th moment of the job size distribution for some alpha > 1, we show that if the job arrival rate and the number of servers increase to infinity with the traffic intensity held fixed, the SITA policy parameterized by alpha minimizes in a large deviation sense the steady-state probability that the total number of jobs in the system is greater than or equal to the number of servers. The optimal large deviation decay rate can be arbitrarily close to the one for the corresponding probability in an infinite-server queue, which only depends on the system traffic intensity but not on any higher moments of the job size distribution. This supports in a many-server asymptotic framework the common wisdom that separating large jobs from small jobs protects system performance against job size variability.