On stationary characteristics of a multiserver exponential queuing system with reordering of requests

Abstract

A queuing system (QS) with several parallel devices and a common storage of limited capacity is considered. The system receives a Poisson flow of requests. A request, that finds all the places in the drive occupied, is lost and does not affect the functioning of the system in the future. The duration of the request service is random, independent of each other and has an exponential distribution. The intensity of maintenance of the devices is different. The request, which has the possibility of selecting a device, selects from all the available devices the one, that has the highest intensity. The functioning of the system is subject to the requirement to maintain the order of withdrawal of requests from it in accordance with their order of receipt. Requests that have violated the order, until it is restored, are contained in the reordering buffer located at the exit of the system. Such QS are known in the literature as systems with reordering of requests [1]–[6]. In [5], an algorithm was developed for calculating the stationary probabilities of the states of the system under consideration. The main task of this work is to obtain analytical expressions for a number of stationary characteristics based on the results of [5].