Brazilian Journal of Probability and Statistics

A new stochastic model and its diffusion approximation

Shai Covo and Amir Elalouf

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1485334825

Digital Object Identifier
doi:10.1214/15-BJPS303

Mathematical Reviews number (MathSciNet)
MR3601661

Zentralblatt MATH identifier
1380.60085

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

Citation

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. https://projecteuclid.org/euclid.bjps/1485334825


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