Analysis of a batch arrival retrial queue with impatient customers subject to the server disasters

Abstract

<p style='text-indent:20px;'>We consider an <inline-formula><tex-math id="M1">\begin{document}$ M^X/G/1 $\end{document}</tex-math></inline-formula> retrial queue with impatient customers subject to disastrous failures at which times all customers in the system are lost. When the server finishes serving a customer and finds the orbit empty, the server becomes dormant until <inline-formula><tex-math id="M2">\begin{document}$ N $\end{document}</tex-math></inline-formula> or more customers accumulate. If a coming batch of customers finds the server idle, one of the arriving customers begins his service immediately and the rest join the orbit to repeat their request later. Otherwise, if the server is dormant or busy or down, all customers of the coming batch enter the orbit. When the server is under repair, customers in the orbit can become impatient after waiting a random amount of time and leave the system. By using the characteristic method for partial differential equations, the steady-state distributions of the server state and the number of customers in the orbit are obtained along with various performance measures. In addition, the reliability of the system is analyzed detailed. Finally, an application to telecommunication networks is provided and the effects of various parameters on the system performance are demonstrated numerically.