Performance analysis of a fluid flow system modulated by a single server queue prone to catastrophic failures and repairs

Abstract

<p style='text-indent:20px;'>This article deals with a new class of fluid flow queue regulated by an <inline-formula><tex-math id="M1">\begin{document}$ M/M/1 $\end{document}</tex-math></inline-formula> queueing system in the presence of active catastrophic failures and subsequent repairs of the server. The distribution of the stationary buffer-content is determined in terms of modified Bessel function of first kind. Besides, an explicit closed-form analytical expression for the probability density function of the fluid level in the stationary regime is derived in an elegant manner. Some important and essential performance measures are obtained. Finally, numerical results are provided to illustrate the behaviour of the buffer content distribution and the performance measures for the proposed fluid flow queueing model.</p>