NONERGODICITY OF MATHEMATIC MODEL OF A RANDOM ACCESS NETWORK


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We have considered a random access communication network with conflicts of requests, which mean that the arriving
request and request under service are sent to a retrial pool. For a process of system states changing the embedded
Markov chain is built up. The theorem on non-ergodicity of Markov chain, which proves the instability of functioning of
the computer communication network managed by a random multiple access, is formulated.

参考

  1. Artalejo J. R., Dudin A. N., Klimenok V. I. Stationary analysis of a retrial queue with preemptive repeated attempts // Operations Research Letters. 2001. № 28(4). P. 173-180.
  2. Kernane T. Conditions for stability and instability of retrial queueing systems with general retrial times // Statistics and Probability Letters. 2008. № 78. P. 3244-3248.
  3. Sennot L. I., Humblet P. A., Tweedie R. L. Mean drifts and the non-ergodicity of Markov chains // Operations research. 1983. № 31(4). P. 783-789.
  4. Назаров А. А., Терпугов А. Ф. Теория массового обслуживания : учеб. пособие. Томск : Изд-во науч.- тех. лит., 2004.

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