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The authors propose a computationally simple approximate expression for the equivalent capacity or bandwidth requirement of both individual and multiplexed connections, based on their statistical characteristics and the desired... more

The authors propose a computationally simple approximate expression for the equivalent capacity or bandwidth requirement of both individual and multiplexed connections, based on their statistical characteristics and the desired grade-of-service (GOS). The purpose of such an expression is to provide a unified metric to represent the effective bandwidth used by connections and the corresponding effective load of network links. These link metrics can then be used for efficient bandwidth management, routing, and call control procedures aimed at optimizing network usage. While the methodology proposed can provide an exact approach to the computation of the equivalent capacity, the associated complexity makes it infeasible for real-time network traffic control applications. Hence, an approximation is required. The validity of the approximation developed is verified by comparison to both exact computations and simulation results

We describe a new algorithm for Gaussian Elimination suitable for general (unsymmetric and possibly singular) sparse matrices, of any entry type, which has a natural parallel and distributed-memory formulation but degrades gracefully to... more

We describe a new algorithm for Gaussian Elimination suitable for general (unsymmetric and possibly singular) sparse matrices, of any entry type, which has a natural parallel and distributed-memory formulation but degrades gracefully to sequential execution. We present a sample MPI implementation of a program computing the rank of a sparse integer matrix using the proposed algorithm. Some preliminary performance measurements are presented and discussed, and the performance of the algorithm is compared to corresponding state-of-the-art algorithms for floating-point and integer matrices.

Some methods being used to speed up floating-point computation in Maple are described. Specifically, we discuss the evaluation of the elementary functions square root and logarithm. We also describe the correct rounding of these... more

Some methods being used to speed up floating-point computation in Maple are described. Specifically, we discuss the evaluation of the elementary functions square root and logarithm. We also describe the correct rounding of these evaluations. The key eciency improvement is called progressive precision increase. 1 High precision computations in Maple One of the advantages of computer-algebra systems for scientific computation is the easy way in which traditional approximate numerical computation can be combined with symbolic computation and with high-precision approximate numerical computation. Developments in this field have been given a further stimulus by the realization that many sets of equations coming from engineering or science are not exact, but contain coecients that are known only approximately. Even if a system of equations is known exactly, there are enormous speed-ups possible if the analysis of the system can be shifted to the approximate numerical domain. As a result o...

In this paper, we study the strong stability in the M=G=1 queueing system with breakdowns and repairs after perturbation of the breakdown's parameter. Using the approximation conditions in the classical M=G=1 system, we obtain... more

In this paper, we study the strong stability in the M=G=1 queueing system with breakdowns and repairs after perturbation of the breakdown's parameter. Using the approximation conditions in the classical M=G=1 system, we obtain stability inequalities with exact computation of the constants. Thus, we can approximate the characteristics of the M=G=1 queueing system with breakdowns and repairs by the classical M=G=1 corresponding ones.

Abstract. Given a Cylindrical Algebraic Decomposition of an implicit algebraic curve, visualizing distinct curve arcs is not as easy as it stands because, despite the absence of singularities in the interior, the arcs can pass arbitrary... more

Abstract. Given a Cylindrical Algebraic Decomposition of an implicit algebraic curve, visualizing distinct curve arcs is not as easy as it stands because, despite the absence of singularities in the interior, the arcs can pass arbitrary close to each other. We present an algorithm to visualize distinct connected arcs of an algebraic curve efficiently and precise (at a given resolution), irrespective of how close to each other they actually pass. Our hybrid method inherits the ideas of subdivision and curve-tracking methods. With an adaptive mixed-precision model we can render the majority of algebraic curves using floating-point arithmetic without sacrificing the exactness of the final result. The correctness and applicability of our algorithm is borne out by the success of our webdemo 1 presented in [10].

In this paper we consider the problem of finding a near-optimal policy in a continuous space, discounted Markovian Decision Problem (MDP) by employing value-function-based methods when only a single trajectory of a fixed policy is... more

In this paper we consider the problem of finding a near-optimal policy in a continuous space, discounted Markovian Decision Problem (MDP) by employing value-function-based methods when only a single trajectory of a fixed policy is available as the input. We study a policy-iteration algorithm where the iterates are obtained via empirical risk minimization with a risk function that penalizes high magnitudes of the Bellman-residual. Our main result is a finite-sample, high-probability bound on the performance of the computed policy that depends on the mixing rate of the trajectory, the capacity of the function set as measured by a novel capacity concept (the VC-crossing dimension), the approximation power of the function set and the controllability properties of the MDP. Moreover, we prove that when a linear parameterization is used the new algorithm is equivalent to Least-Squares Policy Iteration. To the best of our knowledge this is the first theoretical result for off-policy control learning over continuous state-spaces using a single trajectory.

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