Evaluating the contribution of nonmonotone trajectories to the failure of a queuing system in a busy period

Authors: Kovalenko, I.1; Kuznetsov, I.2

Source: Cybernetics and Systems Analysis, Volume 47, Number 4, July 2011 , pp. 506-514(9)

Publisher: Springer

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Abstract:

A queuing system with the service time distribution being a mixture of two exponential distributions is considered. A necessary and sufficient condition is established for the probability of failure during a busy period to be equivalent to the probability of monotone failure. Conditions under which nonmonotone failures make the major contribution to the system failure are also obtained. These conditions are compared to the well-known sufficient conditions.

Keywords: Markov transition graph; asymptotic estimate; mixture of exponential distributions; monotone failure; queuing system

Document Type: Research Article

DOI: http://dx.doi.org/10.1007/s10559-011-9333-3

Affiliations: 1: V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine, Email: kovigo@yandex.ru 2: V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine, Email: Nkuznetsov2004@jandex.ru

Publication date: July 1, 2011

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