V. Rykov, Dmitry Efrosinin, Vladimir Vishnevskiy,
"On sensitivity of reliability models to the shape of life and repair time distributions"
: Proccedings of the International Conference on Availability, Reliability and Security ARES 2014, Seite(n) 430-437, 2014
On sensitivity of reliability models to the shape of life and repair time distributions
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Proccedings of the International Conference on Availability, Reliability and Security ARES 2014
The sensitivity analysis of systems' characteristics to the shape of distributions is a very important task of reliability engineering of stochastic systems and networks. One of the earliest result concerning insensitivity of systems' characteristics to the shape of service time distribution was obtained in case of Erlang's formulas for loss queues with Poisson arrival stream, where steady-state distribution depends only on the mean service times.
The paper deals with simple finite-source queueing models which completely fail if a source area becomes empty. The inter-arrival or service times are assumed to be generally distributed. It is shown that the steady-state probabilities of the systems with a buffer or with generally distributed inter-arrival times are sensitive to the shape of distributions but simultaneously the waiting time distributions have a weak sensitivity. It was observed that the sensitivity vanishes if the complete failure becomes a rare event.
The results are compared with loss queues.