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For given external arrival process and given service-time distributions, the object is to determine the order of infinite-capacity single-server queues in series that minimizes the long-run average sojourn time per customer. We gain additional insight into this queueing design problem, and congestion in non-Markov open queueing networks more generally, by performing simulations for the case of two queues. For this design problem, we conclude that the key issue is variability: The order tends to matter more when the service-time distributions have significantly different variability, and less otherwise. Arranging the queues in order of increasing service-time variability, using the squared coefficient of variation as a partial characterization of variability, seems to be an effective simple design heuristic. Parametric-decomposition approximations seem to provide relatively good quantitative estimates of how much the order matters.queueing networks, tandem queues, departure processes, queueing system design, simulation, approximations, parametric-decomposition approximations

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In this article, we are concerned with scheduling stochastic jobs in a flowshop with rn machines and zero intermediate storage. We assume that there are n -2 identically distributed and 2 fast stochastic jobs. Roughly, the main result states that the makespan is stochastically minimized by placing one of the fast jobs first and the other last.