An analysis of discrete-time Geo/Geo/1 queue with feedback, repair and disaster

摘要

A discrete-time queue with feedback subject to system disaster, server failures and repair is considered in this paper. The time-dependent system-size probabilities are obtained by using generating functions where the system of difference equations in two parameters namely time epoch (m) and number of customers (n) are transformed into another difference equation in terms of generating functions. The difference equations of generating functions satisfy a three-term recurrence relation which leads to continued fraction. System-size probabilities and some performance measures in steady-state are derived. Further, busy period distribution, reliability and availability are also obtained. Numerical illustrations are provided for different parameter values to see their effect on performance measures and to get more in-sight of the model behaviour.