Brazilian Journal of Probability and Statistics

A new stochastic model and its diffusion approximation

Shai Covo and Amir Elalouf

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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.

Article information

Braz. J. Probab. Stat., Volume 31, Number 1 (2017), 62-86.

Received: January 2015
Accepted: October 2015
First available in Project Euclid: 25 January 2017

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Zentralblatt MATH identifier

Diffusion approximation Gaussian process biconvex covariance function nonpositively correlated increments Brownian bridge inhomogeneous Brownian sheet infinite server queue


Covo, Shai; Elalouf, Amir. A new stochastic model and its diffusion approximation. Braz. J. Probab. Stat. 31 (2017), no. 1, 62--86. doi:10.1214/15-BJPS303.

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