Approximating and stabilizing dynamic rate jackson networks with abandonment

Jamol Pender, William A. Massey

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

In this paper, we generalize the Gaussian Variance Approximation (GVA), developed by Massey and Pender [16], to Jackson networks with abandonment. We approximate the queue length process with a multivariate Gaussian distribution and thus, we are able to estimate the mean and covariance matrix of the entire network with more accuracy than the associated fluid and diffusion limits of Mandelbaum, Massey, and Reiman [14]. We also show how the GVA method can be used to construct staffing schedules that approximately stabilize salient performance measures such as the probability of delay and the abandonment probabilities for the entire network. Unlike the work of Feldman et al. [5] which uses Monte Carlo simulation to stabilize the delay probabilities, our method does not require simulation and only requires the numerical integration of differential equations for an N-dimensional network, which is more computationally efficient. Lastly, to confirm our approximations are accurate, we perform several numerical experiments for a wide range of parameter settings.

Original languageEnglish (US)
Pages (from-to)1-42
Number of pages42
JournalProbability in the Engineering and Informational Sciences
Volume31
Issue number1
DOIs
StatePublished - Jan 1 2017

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering

Keywords

  • Applied Probability
  • Computational Probability
  • Probabilistic Networks
  • Queueing Theory
  • Simulation
  • Stochastic Modeling

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