Transient analysis of a discrete-time infinite server queue with system disaster (Q2204570)

Summary: This paper studies a discrete-time infinite server queue subject to system disaster. The exact time-dependent probabilities of the number of customers present in the system are obtained using generating functions, continued fractions and confluent hypergeometric functions. Further, the results are extended to obtain closed form expression for busy period distribution and steady state system size probabilities. Numerical illustrations are provided to visualise the effect of system size probabilities, both in steady state and transient state, and busy period distribution for different parameter values.