SPDE LIMITS OF MANY-SERVER QUEUES

• 成果类型: Article
• 署名作者: Kaspi, Haya; Ramanan, Kavita
• 署名单位: Technion Israel Institute of Technology; Brown University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/11-AAP821
• 发表日期: 2013
• 页码: 145-229
• 关键词: heavy-traffic limits

摘要

This paper studies a queueing system in which customers with independent and identically distributed service times arrive to a queue with many servers and enter service in the order of arrival. The state of the system is represented by a process that describes the total number of customers in the system, and a measure-valued process that keeps track of the ages of customers in service, leading to a Markovian description of the dynamics. Under suitable assumptions, a functional central limit theorem is established for the sequence of (centered and scaled) state processes as the number of servers goes to infinity. The limit process describing the total number in system is shown to be an Ito diffusion with a constant diffusion coefficient that is insensitive to the service distribution beyond its mean. In addition, the limit of the sequence of (centered and scaled) age processes is shown to be a diffusion taking values in a Hilbert space and is characterized as the unique solution of a stochastic partial differential equation that is coupled with the Ito diffusion describing the limiting number in system. Furthermore, the limit processes are shown to be semimartingales and to possess a strong Markov property.