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February 2017 A new stochastic model and its diffusion approximation
Shai Covo, Amir Elalouf
Braz. J. Probab. Stat. 31(1): 62-86 (February 2017). DOI: 10.1214/15-BJPS303

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.

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Shai Covo. Amir Elalouf. "A new stochastic model and its diffusion approximation." Braz. J. Probab. Stat. 31 (1) 62 - 86, February 2017. https://doi.org/10.1214/15-BJPS303

Information

Received: 1 January 2015; Accepted: 1 October 2015; Published: February 2017
First available in Project Euclid: 25 January 2017

zbMATH: 1380.60085
MathSciNet: MR3601661
Digital Object Identifier: 10.1214/15-BJPS303

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

Rights: Copyright © 2017 Brazilian Statistical Association

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Vol.31 • No. 1 • February 2017
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