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Lack of Invariant Property of the Erlang Loss Model in Case of MAP Input

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Abstract

The BMAP/PH/N/0 model with three different disciplines of admission (partial admission, complete rejection, complete admission) is investigated. Loss probability is calculated. Impact of the admission discipline, variation and correlation coefficients of inter-arrival times distribution, and variation of service times distribution on loss probability is analyzed numerically. As by-product, it is shown by means of numerical results that the invariant property of the famous Erlang M/G/N/0 system, which was proven by B. A. Sevastjanov, is absent in case of the MAP input.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Belarusian State University, 4 F. Skorina Ave., 220050, Minsk, Belarus

    Valentina Klimenok

  2. Department of Industrial Engineering, Sangji University, Wonju, Kangwon, Korea, 220-702

    Che Soong Kim

  3. Department of Applied Mathematics and Computer Science, Belarusian State University, 4 F. Skorina Ave., 220050, Minsk, Belarus

    Dmitry Orlovsky & Alexander Dudin

Authors
  1. Valentina Klimenok
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  2. Che Soong Kim
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  3. Dmitry Orlovsky
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  4. Alexander Dudin
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Corresponding author

Correspondence to Valentina Klimenok.

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AMS subject classification: Primary 60K25, 60K20

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Klimenok, V., Kim, C.S., Orlovsky, D. et al. Lack of Invariant Property of the Erlang Loss Model in Case of MAP Input. Queueing Syst 49, 187–213 (2005). https://doi.org/10.1007/s11134-005-6481-z

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  • DOI: https://doi.org/10.1007/s11134-005-6481-z

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