Admission control for finite capacity queueing model with general retrial times and state-dependent rates

Abstract

The finite state dependent queueing model with $ F $-policy is investigated by considering the general retrial attempts. On arrival in the system, if the job finds the server engaged, it is forced to enter into the retrial orbit. After a random period of time, the job from the retrial orbit re-attempts for the service. According to $ F $-policy, as the system attains its full capacity, the arrivals are restricted to join the system until the number of jobs comes down to the prefixed threshold value '$ F $'. The supplementary variable corresponding to the remaining retrial time is used to frame the governing equations which are solved by using Laplace-Stieltjes transform and then applying the recursive method. Special models for machine repair and time-sharing queue are deduced by setting the state dependent rates. Several system indices are obtained explicitly which are further used to facilitate the sensitivity analysis by considering a numerical illustration. A cost function is constructed and minimized for evaluating the optimal threshold parameter and optimal service rate.

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