Queueing Systems

, Volume 49, Issue 2, pp 187–213 | Cite as

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

  • Valentina Klimenok
  • Che Soong Kim
  • Dmitry Orlovsky
  • Alexander Dudin


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.


BMAP/PH/N/0 queueing model stationary state distribution Erlang loss model invariant property 


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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Valentina Klimenok
    • 1
  • Che Soong Kim
    • 2
  • Dmitry Orlovsky
    • 3
  • Alexander Dudin
    • 3
  1. 1.Department of Applied Mathematics and Computer ScienceBelarusian State UniversityMinskBelarus
  2. 2.Department of Industrial EngineeringSangji UniversityWonju, KangwonKorea
  3. 3.Department of Applied Mathematics and Computer ScienceBelarusian State UniversityMinskBelarus

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