Queueing networks with path-dependent arrival processes

Kerry Fendick () and Ward Whitt ()
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Kerry Fendick: Johns Hopkins University Applied Physics Laboratory
Ward Whitt: Columbia University

Queueing Systems: Theory and Applications, 2023, vol. 105, issue 1, No 3, 17-46

Abstract: 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.

Keywords: Path-dependent stochastic processes; Generalized Polya process; Gaussian Markov process; Diffusion approximations; Queues; Heavy-traffic limit; 60F17; 60G15; 90B22 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11134-023-09885-9

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