Queues in Series via Interacting Particle Systems
本文研究了一个由大量单服务器队列串联而成的网络，利用相互作用粒子系统的结果推导其流体力学极限，从而描述网络的瞬态行为。
In this paper, we consider a serial network with very large (infinite) number of single server queues. Initially, the network is empty. The input process to the network is Poisson with rate less than one (unsaturated case) or one (saturated case) and the service times at each queue is exponential with mean one. We exploit results for interacting particle systems, in particular, the zero-range and simple-exclusion processes to investigate the approach to equilibrium of this network. We derive the hydrodynamic limit of this queueing network which dramatically describes the transient behavior of this network.