The stability of two-station multitype fluid networks
成果类型：
Article
署名作者：
Dai, JG; Vande Vate, JH
署名单位：
University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.48.5.721.12408
发表日期：
2000
页码：
721-744
关键词：
摘要：
This paper studies the fluid models of two-station multiclass queueing networks with deterministic routing. A fluid model is globally stable if the fluid network eventually empties under each nonidling dispatch policy. We explicitly characterize the global stability region in terms of the arrival and service rates. We show that the global stability region is defined by the nominal workload conditions and the virtual workload conditions, and we introduce two intuitively appealing phenomena-virtual stations and push starts-that explain the virtual workload conditions. When any of the workload conditions is violated, we construct a fluid solution that cycles to infinity, showing that the fluid network is unstable. When an the workload conditions are satisfied, we solve a network flow problem to find the coefficients of a piecewise linear Lyapunov function. The Lyapunov function decreases to zero, proving that the fluid level eventually reaches zero under any nonidling dispatch policy. Under certain assumptions on the interarrival and service time distributions, a queueing network is stable or positive Harris recurrent if the corresponding fluid network is stable. Thus, the workload conditions are sufficient to ensure the global stability of two-station multiclass queueing networks with deterministic routing.