Modeling Heavy Tails in Traffic Sources for Network Performance Evaluation
Heavy tails in work loads (file sizes, flow lengths, service times, etc.) have significant negative impact on the performance of queues and networks. In the context of the famous Internet file size data of Crovella and some very recent data sets from a wi
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Abstract Heavy tails in work loads (file sizes, flow lengths, service times, etc.) have significant negative impact on the performance of queues and networks. In the context of the famous Internet file size data of Crovella and some very recent data sets from a wireless mobility network, we examine the new class of LogPH distributions introduced by Ramaswami for modeling heavy-tailed random variables. The fits obtained are validated using separate training and test data sets and also in terms of the ability of the model to predict performance measures accurately as compared with a trace-driven simulation using NS-2 of a bottleneck Internet link running a TCP protocol. The use of the LogPH class is motivated by the fact that these distributions have a power law tail and can approximate any distribution arbitrarily closely not just in the tail but in its entire range. In many practical contexts, although the tail exerts significant effect on performance measures, the bulk of the data is in the head of the distribution. Our results based on a comparison of the LogPH fit with other classical model fits such as Pareto, Weibull, LogNormal, and Log-t demonstrate the greater accuracy achievable by the use of LogPH distributions and also confirm the importance of modeling the distribution in its entire range and not just in the tail. Keywords Network performance distribution Markov chain
Heavy tailed random variables
LogPH
V. Ramaswami (&) R. Jana V. Aggarwal Florham Park, New Jersey, USA e-mail: [email protected] K. Jain College Park, Maryland, USA
G. S. S. Krishnan et al. (eds.), Computational Intelligence, Cyber Security and Computational Models, Advances in Intelligent Systems and Computing 246, DOI: 10.1007/978-81-322-1680-3_4, Springer India 2014
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1 Introduction The negative impact of heavy tails in work loads on the performance of systems is well known in the queuing literature. Indeed, many new scheduling strategies came to be invented primarily to avoid these bad effects of very large work loads (even if they be infrequent and from a small set of customers) for systems with schedules such as the First-in-First-Out discipline. Concern about heavy tails nevertheless holds even in the context of modern-day systems such as high-speed and wireless networks. Indeed, the increasing presence of bandwidth-intensive video and streaming audio has heightened the concern particularly in wireless networks as evidenced, for example, by the AT&T experience soon after the introduction of the iPhone. An early work drawing attention to the presence of heavy tails in Internet file sizes is that of Crovella [4]. We use Crovella’s data set and model the distribution as a LogPH distribution and also in terms of classical models such as Pareto, Weibull, LogNormal, and Log-t. The LogPH distribution was proposed by Ramaswami [6] who identified it to have a power law tail and dense (in the weak convergence metric) in the class of all distributions on [1, ?). A LogPH random variable Y is a rand
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