Finite capacity single-server queue with Poisson input, general service and delayed renovation

Abstract

This paper is devoted to the performance evaluation of the finite–capacity single-server queue with Poisson input and general service times, which is equipped with the novel queue-control mechanism — called renovation with delay. Renovation implies that each customer, when leaving the system upon its service completion, may also remove customers waiting in the queue. The number of customers to be removed is selected each time independently of the previous decisions and probabilistically based on the given probability distribution. The renovation with the delay considered in this paper means that the system must accumulate the (known) fixed number of service completions before the next renovation can be triggered. First in the literature numerical evidence is given, that the long-run performance of the system with such delayed renovation mechanism can be similar to that of the systems with the well-known active queue management mechanisms such as random early detection, at least in its basic version. The key stationary performance characteristics reported are the loss probability and the mean number of customers in the system. The unified analytical framework for the computation of the key performance characteristics, which is of independent interest, is also developed.