Closed Queueing Networks in Heavy Traffic: Fluid Limits and Efficiency
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We address the behavior of stochastic Markovian closed queueing networks in heavy traffic, i.e., when the population trapped in the network increases to infinity. All service time distributions are assumed to be exponential. We show that the fluid limits of the network can be used to study the asymptotic throughput in the infinite population limit. As applications of this technique, we show the efficiency of all policies in the class of Fluctuation Smoothing Policies for Mean Cycle Time (FSMCT), including in particular the Last Buffer First Serve (LBFS) policy for all reentrant lines, and the Harrison-Wein balanced policy for two station reentrant lines. By efficiency we mean that they attain bottleneck throughput in the infinite population limit.