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Queueing networks with path-dependent arrival processes

Author

Listed:
  • Kerry Fendick

    (Johns Hopkins University Applied Physics Laboratory)

  • Ward Whitt

    (Columbia University)

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.

Suggested Citation

  • Kerry Fendick & Ward Whitt, 2023. "Queueing networks with path-dependent arrival processes," Queueing Systems: Theory and Applications, Springer, vol. 105(1), pages 17-46, October.
    • Handle: RePEc:spr:queues:v:105:y:2023:i:1:d:10.1007_s11134-023-09885-9
    DOI: 10.1007/s11134-023-09885-9
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    References listed on IDEAS

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