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Computation of the Variance of the Waiting Time for Token Rings

The main new result in this paper is a simple expression for the variance of the waiting time for a token ring with an infinite number of stations, nonsymmetric Poisson traffic, deterministic ring delays, and virtually identical service distributions. These results can be considered as an approximation to the large ring where no individual station dominates the traffic. In the process, the exact equations for obtaining the variance of the waiting time for arbitrary traffics and service densities are found. In general, if there are n nonsymmetric stations, about n3equations need to be solved.