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Monotonicity properties of user equilibrium policies for parallel batch systems

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Abstract

We study a simple network with two parallel batch-service queues, where service at a queue commences when the batch is full and each queue is served by infinitely many servers. A stream of general arrivals observe the current state of the system on arrival and choose which queue to join to minimize their own expected transit time. We show that for each set of parameter values there exists a unique user equilibrium policy and that it possesses various monotonicity properties. User equilibrium policies for probabilistic routing are also discussed and compared with the state-dependent setting.

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  1. Department of Statistics, University of Auckland, Auckland, New Zealand

    Yizheng Chen, Mark Holmes & Ilze Ziedins

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  1. Yizheng Chen
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  2. Mark Holmes
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  3. Ilze Ziedins
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Correspondence to Yizheng Chen.

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Chen, Y., Holmes, M. & Ziedins, I. Monotonicity properties of user equilibrium policies for parallel batch systems. Queueing Syst 70, 81–103 (2012). https://doi.org/10.1007/s11134-011-9264-8

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