A Stochastic Model of Message Interchange on a Channel With Transmission Delay

This paper describes a technique for analyzing the statistical behavior of a two-way communication system with transmission delay
(D)
. Messages are transmitted and received by means of servers located at the terminal stations. If
D > 0
, each server is uncertain of the present state of the other, and may initiate transmission when the other has already begun to transmit, thus causing message interference. Interference is measured as the amount of one server's transmission which arrives at the other server when it is already transmitting. The relationship between the size of the delay and the amount of interference is studied here, as well as other quantities that describe the system behavior. The exact solution is available only for
D = 0
, but an approximate solution is found for very small
D
with respect to the lengths of idle periods of the servers, and the asymptotic solution is obtainable for very long
D
. The particular communication system analyzed is a very simple one, but the mathematical technique of handling the delay can be applied to more elaborate systems.