State-dependent stochastic networks. Part I: Approximations and applications with continuous diffusion limits

• 成果类型: Article
• 署名作者: Mandelbaum, A; Pats, G
• 署名单位: Technion Israel Institute of Technology; Tel Aviv University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 1998
• 页码: 569-646
• 关键词: regulated brownian-motion; heavy-traffic limits; data-handling system; differential-equations; transient-behavior; nonsmooth domains; queues; models; buffers

摘要

In a state-dependent queueing network, arrival and service rates, as well as routing probabilities, depend on the vector of queue lengths. For properly normalized such networks, we derive functional laws of large numbers (FLLNs) and functional central limit theorems (FCLTS). The former support fluid approximations and the latter support diffusion refinements. The fluid limit in FLLN is the unique solution to a multidimensional autonomous ordinary differential equation with state-dependent reflection. The diffusion limit in FCLT is the unique strong solution to a stochastic differential equation with time-dependent reflection. Examples are provided that demonstrate how such approximations facilitate the design, analysis and optimization of various manufacturing, service, communication and other systems.