A queueing model with feedback applied to a communication problem with interference-caused retransmissions

Abstract

A queueing model with feedback is proposed as a mathematical representation of a communication system with interference-caused retransmissions. A satellite receives messages of constant length from ground stations. New messages arrive in a Poisson pattern with constant rate. A finite number of channels is available for transmission and channel selection is random among all channels. All messages with overlapping transmission times on the same channel have to be retransmitted. The arrival rate of messages is a composition of the constant arrival rate of the basic Poisson process and the arrival rate of the feedback from retransmissions. The arrival rate is approximated in discrete time steps. A necessary and sufficient condition for a finite limiting point of the resulting sequence of arrival rates is derived. Numerical results for finite limiting points, rate of convergence, and expected number of transmissions have been computed. Examples for sequences of arrival rates have been tabulated.