Abstract
We consider an infinite-server system with as input process a non-homogeneous Poisson process with rate function Λ(t) = a⊺ X(t). Here {X(t): t ≥ 0} is a generalized multivariate shot-noise process fed by a Lévy subordi-nator rather than by just a compound Poisson process. We study the transient behavior of the model, analyzing the joint distribution of the number of cus-tomers in the queueing system jointly with the multivariate shot-noise process. We also provide a recursive procedure that explicitly identifies transient as well as stationary moments and correlations. Various heavy-tail and heavy-traffic asymptotic results are also derived, and numerical results are presented to provide further insight into the model behavior.
| Original language | English |
|---|---|
| Pages (from-to) | 757-778 |
| Number of pages | 22 |
| Journal | Markov Processes and Related Fields |
| Volume | 26 |
| Issue number | 4 |
| Publication status | Published - 2020 |
Bibliographical note
Publisher Copyright:© Polymat, Moscow 2020.
Funding
The authors gratefully acknowledge useful discussions with Sem Borst and Offer Kella. The research for this paper is partly funded by the NWO Gravitation Project NETWORKS, Grant Number 024.002.003 (Boxma, Mandjes) and an NWO Top Grant, Grant Number 613.001.352 (Boxma, Mandjes, Saxena).
Keywords
- infinite-server queue
- Lévy subordinator
- modulated shot-noise process
- non-homogeneous Poisson process