STOCHASTIC DISCRETE FLOW NETWORKS - DIFFUSION APPROXIMATIONS AND BOTTLENECKS

• 成果类型: Article
• 署名作者: HONG, C; MANDELBAUM, A
• 署名单位: Stanford University; New Jersey Institute of Technology; Technion Israel Institute of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1991
• 页码: 1463-1519
• 关键词: reflected brownian-motion; LIMIT-THEOREMS; queues

摘要

Diffusion approximations for stochastic congested networks, both open and closed, are described in terms of the networks' bottlenecks. The approximations arise as limits of functional central limit theorems. The limits are driven by reflected Brownian motions on the nonnegative orthant (for open networks) and on the simplex (for closed ones). The results provide, in particular, invariance principles for Jackson's open queueing networks, Gordon and Newell's closed networks and some of Spitzer's finite particle systems with zero-range interaction.