Calculation of the Characteristics of the Multichannel Queueing System with Pure Losses and Feedback

摘要

A mathematical model of the multichannel queueing system with pure losses and feedback is proposed. Here feedback is characterized by instant returning a part of calls to get a repeated service. Three schemes of returning calls which have already been serviced are studied. In the first scheme the probability of return depends on a number of primary calls in channels; in the second scheme this probability depends on the number of repeated calls in channels; in the third scheme this probability depends on the total number of calls in channels. Both exact and approximate methods to calculate characteristics of the system are developed. The exact method is based on the system of balance equations for the probabilities of system states and the approximate method uses the principles of space merging of two dimensional Markov chains. Results of numerical experiments are given.