Fluid Limits of G/G/1+G Queues Under the Nonpreemptive Earliest-Deadline-First Discipline

• 成果类型: Article
• 署名作者: Atar, Rami; Biswas, Anup; Kaspi, Haya
• 署名单位: Technion Israel Institute of Technology; Technion Israel Institute of Technology
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2014.0690
• 发表日期: 2015
• 页码: 683-702
• 关键词: many-server queues; diffusion

摘要

A single-server queueing model is considered with customers that have deadlines. If a customer's deadline elapses before service is offered, the customer abandons the system (customers do not abandon while being served). When the server becomes available, it offers service to the customer having the earliest deadline among those that are in the queue. We obtain a fluid limit of the queue length and abandonment processes and for the occupation measure of deadlines, in the form of measure-valued processes. We characterize the limit by means of a Skorohod problem in a time-varying domain that has an explicit solution. The fluid limits also describe a certain process called the frontier that is well known to play a key role in systems operating under this scheduling policy.