Mean Waiting Time for a Network with Two Stations under Token Passing Access

This paper presents an analysis of mean waiting times of messages for two stations under token passing access. In each station, messages arrive at waiting buffer of the station with Poisson process and they are transmitted under one- limited discipline. For the system, probabilities for the number of waiting messages, mean number of waiting messages at token´s arrival at a station and mean waiting times of messages are derived. For mean number of waiting messages, which is required to derive mean waiting time, only one equation between mean number of waiting messages at a station and that at the other station is obtained by using a root of the denominator of generating function. Therefore, assuming the other equation with an unknown variable, the mean number of waiting messages at each station is obtained, and then the unknown variable is estimated from comparison with the exact equation in the special cases. Some numerical examples of mean waiting time are illustrated, and our equation of mean waiting time is almost equal to the simulation value. From this result, there is a possibility that our equation may be exact.