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SELF-SIMILARITY AND LONG-RANGE-DEPENDENT TRAFFIC The queueing models and solutions we have presented, developed and applied in this book are very useful and have wide applicability. However, one of the most significant recent findings for the design and performance evaluation of networks has been the discovery of selfsimilarity and long-range dependence (LRD) in a variety of traffic types [17.1]. Why is it significant? Well, the essence of self-similarity is that a time-varying process behaves in a similar way over all time scales. The observations made on a variety of traffic types in different network technologies show bursty behaviour over a wide range. | Introduction to IP and ATM Design Performance With Applications Analysis Software Second Edition. J M Pitts J A Schormans Copyright 2000 John Wiley Sons Ltd ISBNs 0-471-49187-X Hardback 0-470-84166-4 Electronic 17 Self-similar Traffic play it again Sam SELF-SIMILARITY AND LONG-RANGE-DEPENDENT TRAFFIC The queueing models and solutions we have presented developed and applied in this book are very useful and have wide applicability. However one of the most significant recent findings for the design and performance evaluation of networks has been the discovery of selfsimilarity and long-range dependence LRD in a variety of traffic types 17.1 . Why is it significant Well the essence of self-similarity is that a time-varying process behaves in a similar way over all time scales. The observations made on a variety of traffic types in different network technologies show bursty behaviour over a wide range of time scales. And as we have seen in previous chapters bursty behaviour has a much greater impact on finite resources. Let s take a memoryless process first and see how that scales with time. Figure 17.1 shows the results of simulating traffic for 10 000 seconds. The first 100 seconds of the arrival process are shown as a thin grey line and here we see typical variable behaviour around a mean value of about 25 arrivals per second. The thick black line shows the process scaled by 100 i.e. the number of arrivals is averaged every 100 seconds and so the 100 scaled time units cover the full 100 00 seconds of the simulation. This averaging clearly shows a reduction in the variability of the process when viewed on the longer time scale - the mean value of 25 arrivals per second is evident. Figure 17.2 takes a self-similar process and plots it in the same way. In this case we can see the high variability of the process even after scaling. However it is not self-similarity which is the underlying phenomenon but rather it is the presence of many basic communications processes .
