Abstract
A discrete-time Geo/Geo/1 queue with system disaster is considered in this paper. The time-dependent and steady state probabilities of number of customers present in the system are obtained in terms of ballot numbers by solving the underlying system of difference equations using the generating function and continued fractions. Further, the busy period distribution is derived in terms of Catalan numbers. For special cases, time-dependent system size probabilities and busy period distribution are verified with the existing results in the literature. Numerical illustrations are provided for different parameter values to see their effect on performance measures and to get more insight of the model behavior.
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