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On the asymptotic expression of the time-dependent solution of an M/G/1 queueing model

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  • Geni Gupur

    (Xinjiang University)

Abstract

We study asymptotic expression of the time-dependent solution of the M/G/1 queueing model with additional optional service and no waiting capacity, which is described by finite partial differential equations with integral boundary conditions. We prove that the underlying operator, which corresponds to the M/G/1 queueing model with additional optional service and no waiting capacity, has finitely many eigenvalues at most in a strip region on the left half complex plane, all eigenvalues are real, algebraic multiplicity of each eigenvalue is one and 0 is its strictly dominant eigenvalue, thus we give asymptotic expression of the time-dependent solution of the M/G/1 queueing model with additional optional service and no waiting capacity.

Suggested Citation

  • Geni Gupur, 2022. "On the asymptotic expression of the time-dependent solution of an M/G/1 queueing model," Partial Differential Equations and Applications, Springer, vol. 3(2), pages 1-16, April.
    • Handle: RePEc:spr:pardea:v:3:y:2022:i:2:d:10.1007_s42985-022-00157-4
    DOI: 10.1007/s42985-022-00157-4
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    References listed on IDEAS

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    1. Muthukrishnan Senthil Kumar & Aresh Dadlani & Kiseon Kim, 2020. "Performance analysis of an unreliable M/G/1 retrial queue with two-way communication," Operational Research, Springer, vol. 20(4), pages 2267-2280, December.
    2. Madhu Jain & Sandeep Kaur & Parminder Singh, 2021. "Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)," Operational Research, Springer, vol. 21(4), pages 2203-2246, December.
    3. B. R. K. Kashyap, 1966. "The Double-Ended Queue with Bulk Service and Limited Waiting Space," Operations Research, INFORMS, vol. 14(5), pages 822-834, October.
    4. Samira Taleb & Amar Aissani, 2016. "Preventive maintenance in an unreliable M/G/1 retrial queue with persistent and impatient customers," Annals of Operations Research, Springer, vol. 247(1), pages 291-317, December.
    5. Muthukrishnan Senthil Kumar & Aresh Dadlani & Kiseon Kim, 2020. "Correction to: Performance analysis of an unreliable M/G/1 retrial queue with two-way communication," Operational Research, Springer, vol. 20(4), pages 2281-2281, December.
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