Networks of ·/G/∞ queues with shot-noise-driven arrival intensities

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...

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Bibliographic Details
Published in:Queueing systems 2017-08, Vol.86 (3-4), p.301-325
Main Authors: Koops, D. T., Boxma, O. J., Mandjes, M. R. H.
Format: Article
Language:English
Subjects:
Business and Management
Central limit theorem
Computer Communication Networks
Control
Decay rate
Infinity
Markov analysis
Noise
Operations Research/Decision Theory
Poisson density functions
Probability Theory and Stochastic Processes
Queues
Queuing theory
Shot noise
Supply Chain Management
Systems Theory
Transient analysis
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Summary: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.
ISSN:0257-0130
1572-9443
DOI:10.1007/s11134-017-9520-7