Infinite-server systems with Coxian arrivals

Onno Boxma (), Offer Kella () and Michel Mandjes ()
Additional contact information
Onno Boxma: Eurandom
Offer Kella: The Hebrew University of Jerusalem
Michel Mandjes: University of Amsterdam

Queueing Systems: Theory and Applications, 2019, vol. 92, issue 3, No 2, 233-255

Abstract: Abstract We consider a network of infinite-server queues where the input process is a Cox process of the following form: The arrival rate is a vector-valued linear transform of a multivariate generalized (i.e., being driven by a subordinator rather than a compound Poisson process) shot-noise process. We first derive some distributional properties of the multivariate generalized shot-noise process. Then these are exploited to obtain the joint transform of the numbers of customers, at various time epochs, in a single infinite-server queue fed by the above-mentioned Cox process. We also obtain transforms pertaining to the joint stationary arrival rate and queue length processes (thus facilitating the analysis of the corresponding departure process), as well as their means and covariance structure. Finally, we extend to the setting of a network of infinite-server queues.

Keywords: Coxian process; M/G/ $$\infty $$ ∞; Multivariate shot-noise process; Subordinator; Primary: 60K25; Secondary: 90B15 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s11134-019-09613-2

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