Assessment of the Probability of System Failure with Maximum Service Accumulation Elements

A.V. Makarichev, Dr Sc. (Phys.-Math.), A.A. Kud Kharkiv National Automobile and Highway University (Yaroslav Mudry St. 25, Kharkiv, 61002, Ukraine, e-mail:,
A.B. Shchukin
N.Ye. Zhukovsky National Aerospace University «Kharkiv  Aviation  Institute» (Chkalov St. 17, Kharkiv, 61070, Ukraine)

Èlektron. model. 2018, 40(5):41-48


A single-line queuing systems is considered. Incoming stream of requirements is the Poisson flow. The requirement service is performed in the order of arrival. The maintenance of the requirements consists of two independent non-negative random variables. In the course of time, distributed as the first of two quantities, there appears another Poisson flow of requirements with independent identically distributed lengths. Of these, the maximum length requirement is chosen. This maximum length is the second term of the service requirement time. The number of requirements in the system as a function of time forms a regenerating process. The moments of the absence of requirements in the system are the moments of regeneration. At the moment of transition of the random process from the state n to the state n + 1, a failure occurs (n = 1, 2, …). Two-way estimates for the probability of failure at the regeneration period are found. Moreover, the upper and lower bounds for ordinary duplication (n = 1) coincide.


the probability of system failure, maximum service accumulation elements.


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