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

Authors:
Valentina Klimenok;Che Soong Kim;Dmitry Orlovsky;Alexander Dudin
Affiliations:
Department of Applied Mathematics and Computer Science, Belarusian State University, Minsk, Belarus 220050;Department of Industrial Engineering, Sangji University, Wonju, Kangwon, Korea 220-702;Department of Applied Mathematics and Computer Science, Belarusian State University, Minsk, Belarus 220050;Department of Applied Mathematics and Computer Science, Belarusian State University, Minsk, Belarus 220050
Venue:
Queueing Systems: Theory and Applications
Year:
2005

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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.