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.
| Original language | American English |
|---|---|
| Pages (from-to) | 233-255 |
| Number of pages | 23 |
| Journal | Queueing Systems |
| Volume | 92 |
| Issue number | 3-4 |
| DOIs | |
| State | Published - 14 Aug 2019 |
Bibliographical note
Funding Information:Acknowledgements OK’s work has been supported by Israel Science Foundation (Grant Number 1647/17) and the Vigevani Chair in Statistics. The research of OB and MM is partly funded by the NWO Gravitation Programme Networks (Grant Number 024.002.003) and an NWO Top Grant (Grant Number 613.001.352).
Funding Information:
OK?s work has been supported by Israel Science Foundation (Grant Number 1647/17) and the Vigevani Chair in Statistics. The research of OB and MM is partly funded by the NWO Gravitation Programme Networks (Grant Number 024.002.003) and an NWO Top Grant (Grant Number 613.001.352).
Publisher Copyright:
© 2019, The Author(s).
Keywords
- Coxian process
- M/G/∞
- Multivariate shot-noise process
- Subordinator