An explicit expression for time-dependent system size probabilities is obtained for the general state-dependent discrete-time queue with system disaster. Using generating function for the nth state transient probabilities, the underlying difference equation of system size probabilities are transformed into three-term recurrence relation which is then expressed as a continued fraction. The continued fractions are converted into formal power series which yield the time-dependent system size probabilities in closed form. Further, the busy period distribution is obtained for the considered model. As a special case, the system size probabilities and busy period distribution of Geo/Geo/1 queue are deduced. Finally, numerical illustrations are presented to visualize the system effect for various values of the parameters.
As the world's major economies and technologies have matured, they are dominated by service-focused approach leading to study and analysis of service models for improved understanding and efficiency. Research in this direction has been done on various parameters of the finite queues using different approaches. The study discussed in this paper deals with the stationary behavior of two - stage queuing system with infinite capacity where any arriving customer is serviced in two stages in a mutually exclusion fashion. The steady state system size probabilities for the infinite capacity queueing system with two stages of service are obtained in closed form. Further, numerical interpretations are presented to depict the system behavior for values of the parameters.
A catastrophic single server queue with time-dependent arrival and service rates is considered in this paper. The empty system size probability P 0 (t) is obtained through Voltra integral equation. Further, a busy period distribution is discussed for the catastrophic time-dependent queues.
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