Waiting Times in Token Rings with Helical Window and Window-Gated Service

Abstract

We extend our recent analysis of symmetric token rings to include a more practical window-based access rule. Instead of constant-size “helical” windows (which sometimes require the idle token to be artificially delayed), we now handle variable-size “gated” windows, defined as the minimum of a design parameter, w, and the lag of the algorithm when the token arrives. For suitable values of w, we can give exact closed-form expressions for the mean, variance and moment generating function for the system time, assuming Poisson traffic at rate G/N at each of N stations, arbitrarily spaced around the ring, and a general independent service time distribution common to all stations. These restrictions on w ensure that the lag induced by each packet transmission requires the idle token to make an integral number of tours of the ring. Suitable values for w are quite easy to find when the walk time is much smaller than the mean service time, but may not exist when the walk time is much larger. Nevertheless, we show via simulation that the analytical solution can still be a very good approximation even when the conditions for exact results are not met. Window-gated service also has significant performance advantages over more traditional service disciplines, especially when the walk time is small or the variance of the packet length distribution is large.