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Performance analysis approximation in a queueing system of type M/G/1

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  • Louiza Bouallouche-Medjkoune
  • Djamil Aissani

Abstract

In this work, we apply the strong stability method to obtain an estimate for the proximity of the performance measures in the M/G/1 queueing system to the same performance measures in the M/M/1 system under the assumption that the distributions of the service time are close and the arrival flows coincide. In addition to the proof of the stability fact for the perturbed M/M/1 queueing system, we obtain the inequalities of the stability. These results give with precision the error, on the queue size stationary distribution, due to the approximation. For this, we elaborate from the obtained theoretical results, the STR-STAB algorithm which we execute for a determined queueing system: M/Coxian − 2/1. The accuracy of the approach is evaluated by comparison with simulation results. Copyright Springer-Verlag 2006

Suggested Citation

  • Louiza Bouallouche-Medjkoune & Djamil Aissani, 2006. "Performance analysis approximation in a queueing system of type M/G/1," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(2), pages 341-356, May.
    • Handle: RePEc:spr:mathme:v:63:y:2006:i:2:p:341-356
    DOI: 10.1007/s00186-005-0022-8
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    Cited by:

    1. Bernd Heidergott & Arie Hordijk & Haralambie Leahu, 2009. "Strong bounds on perturbations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(1), pages 99-127, August.
    2. Henry Lam, 2016. "Robust Sensitivity Analysis for Stochastic Systems," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1248-1275, November.
    3. KM Rashmi & S. K. Samanta, 2024. "Analysis of Two-Way Communication in $$M_1^X, M_2/G_1,G_2/1$$ M 1 X , M 2 / G 1 , G 2 / 1 Retrial Queue Under the Constant Retrial Policy," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-32, December.

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