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Uncertainty propagation in M/G/1/K queue modelled by parametric p-box using Taylor series expansion approach

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  • Zina Hamoudi
  • Sofiane Ouazine
  • Karim Abbas
  • Kamel Haouam

Abstract

The main purpose of the current paper is to use the multivariate Taylor series expansion for analysis of the M/G/1/K queue, and give a new formula of the closed-form expressions for the higher-order sensitivity of discrete-time Markov chain stationary distribution with respect to multiple parameters using a fundamental matrix. We also include the probability boxes, and assume that all parameters have a uniform distribution. In addition, we use the Markov's inequality to estimate the risk incurred by working with uncertain performances of the M/G/1/K queue. Several numerical examples are also presented and the obtained results are compared to the corresponding Monte Carlo simulation.

Suggested Citation

  • Zina Hamoudi & Sofiane Ouazine & Karim Abbas & Kamel Haouam, 2026. "Uncertainty propagation in M/G/1/K queue modelled by parametric p-box using Taylor series expansion approach," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 34(3), pages 328-353.
    • Handle: RePEc:ids:ijmore:v:34:y:2026:i:3:p:328-353
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