Abstract
This paper considers a kind of queueing problem with a Poisson number of customers or, more generally, objects which may arrive in groups of random size. The focus is on the total quantity over time, called system size. The main result is that the process representing the system size, properly normalized, converges in finite-dimensional distributions to a centered Gaussian process (the diffusion approximation) with several attractive properties. Comparison with existing works (where the number of objects is assumed nonrandom) highlights the contribution of the present paper.
| Original language | English |
|---|---|
| Pages (from-to) | 62-86 |
| Number of pages | 25 |
| Journal | Brazilian Journal of Probability and Statistics |
| Volume | 31 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 2017 |
Bibliographical note
Publisher Copyright:© Brazilian Statistical Association, 2017.
Funding
This research was supported by the Cathedra of the Department of Management, Bar Ilan University, Israel. Thanks to the referee for many valuable suggestions to improve the presentation of the paper.
| Funders |
|---|
| Department of Management, Bar Ilan University, Israel |
Keywords
- Biconvex covariance function
- Brownian bridge
- Diffusion approximation
- Gaussian process
- Infinite server queue
- Inhomogeneous brownian sheet
- Nonpositively correlated increments
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