A new stochastic model and its diffusion approximation

Shai Covo, Amir Elalouf

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)62-86
Number of pages25
JournalBrazilian Journal of Probability and Statistics
Volume31
Issue number1
DOIs
StatePublished - Feb 2017

Bibliographical note

Publisher Copyright:
© Brazilian Statistical Association, 2017.

Keywords

  • Biconvex covariance function
  • Brownian bridge
  • Diffusion approximation
  • Gaussian process
  • Infinite server queue
  • Inhomogeneous brownian sheet
  • Nonpositively correlated increments

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