The Effect of Self-similar Traffic On The Performance of PLAYTHROUGH Ring Networks
Wantou Siantou, Stephane Joseph
Silio, Charles B
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PLAYTHROUGH ring performance is studied with self-similar traffic patterns. Measurements made by others on local networks connected to the Internet have shown that TCP traffic is self-similar. Self-similar traffic can be generated using heavy-tailed distributions. In particular, others have shown that the Weibull distribution provides a good fit for TCP connection interarrival times. The Weibull distribution, with specific parameters measured in real networks, is used to simulate the operation of the PLAYTHROUGH ring under self-similar traffic. Simulation results reveal that the mean waiting time performance of the PLAYTHROUGH ring under self-similar traffic is markedly worse than that of hitherto assumed traffic patterns using the exponentially distributed interarrival times and geometrically distributed message lengths. Furthemore, it appears that, in general, mean waiting times are significantly greater for PLAYTHROUGH ring under exponential interarrival times and Weibull-distributed message lengths than in the case when message interarrival times and message lengths are assumed to be Weibull-distributed and geometrically distributed, respectively. An analytical model is derived for various PLAYTHROUGH ring performance metrics under the assumption of exponential interarrivals and Weibull-distributed message lengths, including the moments of the number of minipackets, control frame round trip time, transmission time, service time, blocking duration, and waiting time. When Weibull interarrival times are assumed, finding an analytical model for waiting times is a seemingly intractable problem because the Laplace transform of the Weibull distribution does not have a closed form. However, it is shown that, under heavy loads, mean waiting times under the assumption of exponentially distributed interarrival times and geometrically distributed message lengths are, in general, a lower bound on mean waiting times under the assumption of Weibull interarrivals and geometrically distributed message lengths. Moreover, under heavy loads, mean waiting times under the assumption of exponentially distributed interarrival times and Weibull message lengths are, in general, upper bounds on mean waiting times under the assumption of Weibull interarrivals and geometrically distributed message lengths. This work provides the first analytical approxiamtion that predicts the performance of PLAYTHROUGH ring under self-similar traffic. In fact, no prior analytical model exists for any ring network under self-similar traffic, including TOKEN ring.