Fluid Limits for Many-Server Systems with Reneging Under a Priority Policy

Abstract

A multiclass many-server system is considered, in which customers are served according to a nonpreemptive priority policy and may renege while waiting to enter service. The service and reneging time distributions satisfy mild conditions. Building on an approach developed by Kaspi and Ramanan, the law-of-large-numbers many-server asymptotics are characterized as the unique solution to a set of differential equations in a measure space, regarded as fluid model equations. In stationarity, convergence to the explicitly solved invariant state of the fluid-model equations is established. An immediate consequence of the results in the case of exponential reneging is the asymptotic optimality of an index policy, called the cμ/θ rule, for the problem of minimizing linear queue-length and reneging costs. A certain Skorohod map plays an important role in obtaining both uniqueness of solutions to the fluid-model equations and convergence.

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