FLUID AND DIFFUSION APPROXIMATIONS OF A 2-STATION MIXED QUEUING NETWORK

• 成果类型: Article
• 署名作者: NGUYEN, V
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.20.2.321
• 发表日期: 1995
• 页码: 321-354
• 关键词: orthant

摘要

The subject of this paper is a two-station mixed queueing network with two customer types: ''Open'' customers enter the network at station I and depart the system after receiving service. Meanwhile, a fixed number of ''closed'' customers circulate between stations 1 and 2. Such a mixed queueing network model can represent a single-stage production system that services both make-to-order and make-to-stock customers. We present fluid and diffusion limits for this network under the first-in-first-out service discipline. We find that the heavy traffic limit of the workload process at station 1 is a reflected Brownian motion (RBM) on a finite interval. This result is in contrast to the behavior of the original mixed network model, in which the workload at station 1 need not be bounded.