Institute for Systems Research Technical Reports

Permanent URI for this collectionhttp://hdl.handle.net/1903/4376

This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.

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1995 - 19963

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Author: search.filters.author.Parulekar, M.Subject: search.filters.subject.queueing networks

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    M|G|Input Processes: A versatile class of models for network traffic
    (1996) Parulekar, M.; Makowski, Armand M.; ISR
    We suggest the M|G|input process as a viable model for network traffic due to its versatility and tractability. To gauge its performance, we study the large buffer asymptotics of a multiplexer driven by an M|G|input process. We identify the process as short or long-range dependent by means of simple tests. The decay rate of the tail probabilities for the buffer content (in steady-state) at the multiplexer is investigated using large deviation techniques suggested by Duffield and O'Connell. The appropriate large deviations scaling is found to be related to the forward recurrence time for the service time distribution, and a closed-form expression is derived for the corresponding generalized limiting log-moment generating function associated with the input process. Two very different regimes are identified. We apply our results to cases where the service time distribution in the M|G|input model is (i) Rayleigh (ii) Gamma (iii) Geometric (iv) Weibull (v) Log-Normal and (vi) Pareto - cases (v) and (vi) have recently been found adequate for modeling packet traffic streams in certain networking applications. Finally, we comment on the insufficiency of the short or long- range dependence in the process in clearly describing buffer dynamics.
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    Tail Probabilities for M|G|input Processes (I): Preliminary Asymptotics
    (1996) Parulekar, M.; Makowski, Armand M.; ISR
    The infinite server model of Cox with arbitrary service time distribution appears to provide a very large class of traffic models - Pareto and log-normal distributions have already been reported in the literature for several applications. Here we begin the analysis of the large buffer asymptotics for a multiplexer driven by this class of inputs. Top do so we rely on recent results by Duffield and O'Connel on overflow probabilities for the general single server queue. In this paper we focus on the key step in this approach which is based on large deviations: The appropriate large deviations scaling is shown to be related to the forward recurrence time for the service time distribution, and a closed form expression is derived for the corresponding generalized limiting log-moment generating function associated with the input process. Tow very different regime are identified. In a companion paper we apply these results to obtain the large buffer asymptotics under a variety of service time distributions.
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    Buffer Overflow Probabilities for a Multiplexer with Self- Similar Traffic
    (1995) Parulekar, M.; Makowski, Armand M.; ISR; CSHCN
    We study the large buffer asymptotics of a multiplexer under two different self-similar traffic inputs, namely the so-called M G  model of Cox and the fractional Gaussian noise input model. In the former case we show that the tail probabilities for the buffer content (in steady-state) decay at most hyperbolically. This is contrasted with the situation where the input traffic is fractional Gaussian noise, in which case the tail probabilities display a Weibullian character. Therefore, for a given input rate rin and Hurst parameter H, these dissimilar asymptotics would result in vastly differing buffer engineering practices, which points somewhat to the inadequacy of using H as the sole parameter to characterize long-range dependence.