Institute for Systems Research

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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.
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    Risk-Sensitive Control and Dynamic Games for Partially Observed Discrete - Time Nonlinear Systems
    (1992) James, Matthew R.; Baras, John S.; Elliott, Robert J.; ISR
    In this paper we solve a finite-horizon partially observed risk- sensitive stochastic optimal control problem for discrete-time nonlinear systems, and obtain small noise and small risk limits. The small noise limit is interpreted as a deterministic partially observed dynamic game, and new insights into the optimal solution of such game problems are obtained. Both the risk-sensitive stochastic control problem and the deterministic dynamic game problem are solved using information states, dynamic programming, and associated separated policies. A certainty equivalence principle is also discussed. Our results have implications for the nonlinear robust stabilization problem. The small risk limits is a standard partially observed risk neutral stochastic optimal control problem.