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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Author: search.filters.author.Makowski, Armand M.Subject: search.filters.subject.large deviations

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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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    On the Effective Bandwidth of the Output Process of a Single Server Queue
    (1995) Banege, Lionel; Makowski, Armand M.; ISR; CSHCN
    We show that the initial condition of the buffer content in a G/G/1 queue satisfies a Sample Path Large Deviations Principle with convex good rate function, provided it has an exponential decay rate. This result is then used to derive conditions under which the transient and stationary output processes satisfy the same Large Deviations Principle. The relationship between the Large Deviations Principle and the effective bandwidth of a queue is discussed.