Article: Uncertainty propagation in M/G/1/K queue modelled by parametric p-box using Taylor series expansion approach Journal: International Journal of Mathematics in Operational Research (IJMOR) 2026 Vol.34 No.3 pp.328 - 353 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. Inderscience Publishers - linking academia, business and industry through research

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

Authors: Zina Hamoudi; Sofiane Ouazine; Karim Abbas; Kamel Haouam

Addresses: LAMIS Laboratory, Department of Mathematics and Informatics, Faculty of the Exact Sciences, Natural and Life Sciences, University of Tebessa, 12000 Tebessa, Algeria; Department of Technology, Faculty of Technology, University of Bejaia, 06000 Bejaia, Algeria ' Applied Mathematics Laboratory LMA, Department of Mathematics, Faculty of the Exact Sciences, University of Bejaia, 06000 Bejaia, Algeria ' Research Unit LaMOS, Department of Operational Research, Faculty of the Exact Sciences, University of Bejaia, 06000 Bejaia, Algeria ' LAMIS Laboratory, Department of Mathematics and Informatics, Faculty of the Exact Sciences, Natural and Life Sciences, University of Tebessa, 12000 Tebessa, Algeria

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.

Keywords: M/G/1/K queue; probability-boxes; epistemic uncertainty; multivariate Taylor-series expansions; risk analysis; Monte Carlo simulation.

DOI: 10.1504/IJMOR.2026.155540

International Journal of Mathematics in Operational Research, 2026 Vol.34 No.3, pp.328 - 353

Received: 28 Jun 2024
Accepted: 07 Aug 2024
Published online: 05 Aug 2026 *

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

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