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Queueing networks with path-dependent arrival processes

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Abstract

This paper develops a Gaussian model for an open network of queues having a path-dependent net-input process, whose evolution depends on its early history, and satisfies a non-ergodic law of large numbers. We show that the Gaussian model arises as the heavy-traffic limit for a sequence of open queueing networks, each with a multivariate generalization of a Polya arrival process. We show that the net-input and queue-length processes for the Gaussian model satisfy non-ergodic laws of large numbers with tractable distributions.

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Authors and Affiliations

  1. Johns Hopkins University Applied Physics Laboratory, Laurel, MD, USA

    Kerry Fendick

  2. Industrial Engineering and Operations Research, Columbia University, New York, USA

    Ward Whitt

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  1. Kerry Fendick
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  2. Ward Whitt
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Correspondence to Ward Whitt.

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Fendick, K., Whitt, W. Queueing networks with path-dependent arrival processes. Queueing Syst 105, 17–46 (2023). https://doi.org/10.1007/s11134-023-09885-9

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