Networks of $$\cdot /G/\infty $$ · / G / ∞ queues with shot-noise-driven arrival intensities

D. T. Koops (), O. J. Boxma and M. R. H. Mandjes
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D. T. Koops: University of Amsterdam
O. J. Boxma: Eindhoven University of Technology
M. R. H. Mandjes: University of Amsterdam

Queueing Systems: Theory and Applications, 2017, vol. 86, issue 3, No 6, 325 pages

Abstract: Abstract We study infinite-server queues in which the arrival process is a Cox process (or doubly stochastic Poisson process), of which the arrival rate is given by a shot-noise process. A shot-noise rate emerges naturally in cases where the arrival rate tends to exhibit sudden increases (or shots) at random epochs, after which the rate is inclined to revert to lower values. Exponential decay of the shot noise is assumed, so that the queueing systems are amenable to analysis. In particular, we perform transient analysis on the number of jobs in the queue jointly with the value of the driving shot-noise process. Additionally, we derive heavy-traffic asymptotics for the number of jobs in the system by using a linear scaling of the shot intensity. First we focus on a one-dimensional setting in which there is a single infinite-server queue, which we then extend to a network setting.

Keywords: Infinite-server queue; Stochastic arrival rate; Cox; Doubly stochastic Poisson; Shot noise; Network; Functional central limit theorem; Heavy traffic; 60K25 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s11134-017-9520-7

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