On the self-similar nature of Ethernet traffic (extended version)
IEEE/ACM Transactions on Networking (TON)
Theoretical Computer Science - Special issue on dynamic and on-line algorithms
Self-similarity in World Wide Web traffic: evidence and possible causes
Proceedings of the 1996 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Estimating the heavy tail index from scaling properties
Methodology and Computing in Applied Probability
Traffic aided opportunistic scheduling for wireless networks: algorithms and performance bounds
Computer Networks: The International Journal of Computer and Telecommunications Networking
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In this paper we present a new scheduler, the α scheduler, which performs better on heavy tailed traffic than the Foreground-Background (FB) scheduler which is known to be optimal in scheduling traffic which has unknown characteristics. The α -scheduler is able to provide a closer approximation to the Shortest Remaining Processing Time (SRPT) scheduler which is known to provide optimal scheduling in the case when the length of the packets to be scheduled is known. We are able to improve our α -scheduler SRPT approximation by basing our expected remaining processing time on an estimate of the shape parameter, α, from the standard heavy tailed Pareto complementary probability distribution function, P[X t] = ctα. We review various methods of estimating α based on linear regression methods on the standard Log-Log Complement Distribution plot first proposed by Crovella in [5] and studied in more detail in [4]. We show that even using the standard sliding window least mean square estimator our scheduler exhibits improved performance over the FB scheduler. The particular scheduling problem we investigate in detail concerns the servicing of a number of ingress flows being fed by heavy tailed distributions. The egress channel is a bottleneck link, for example a shared wireless TDMA domain. Each flow is characterized as having a distinct shape parameter which may change (slowly) over time. While the scheduling is real time, the {αi} estimation does not need to be. For example, the traffic pattern associated with a particular link might change when the user upgrades a software package which employs a new data communication model. We report on numerical experiments in which we schedule generated samples with the perfect knowledge of {αi} and experiments in which we attempt to use our Pareto shape parameter estimation methods. We show that the scheduling QoS metrics introduced in [1], stochastically bound slowdown and response time, are improved with our scheduler versus the Foreground-Background scheduler reported on in [1].