651 research outputs found

    Random permutations and queues

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    Externalities in the M/G/1 queue:LCFS-PR versus FCFS

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    Consider a stable M/G/1 system in which, at time t= 0 , there are exactly n customers with residual service times equal to v1, v2, … , vn . In addition, assume that there is an extra customer c who arrives at time t= 0 and has a service requirement of x. The externalities which are created by c are equal to the total waiting time that others will save if her service requirement is reduced to zero. In this work, we study the joint distribution (parameterized by n, v1, v2, … , vn, x) of the externalities created by c when the underlying service distribution is either last-come, first-served with preemption or first-come, first-served. We start by proving a decomposition of the externalities under the above-mentioned service disciplines. Then, this decomposition is used to derive several other results regarding the externalities: moments, asymptotic approximations as x→ ∞ , asymptotics of the tail distribution, and a functional central limit theorem.</p

    Moderate deviations of many-server queues in the Halfin-Whitt regime and weak convergence methods

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    This paper obtains logarithmic asymptotics of moderate deviations of the stochastic process of the number of customers in a many--server queue with generally distributed interarrival and service times in the Halfin--Whitt heavy traffic regime. The deviation function is expressed in terms of the solution to a Fredholm equation of the second kind. The proof uses characterisation of large deviation relatively compact sequences of probability measures as exponentially tight ones

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Heavy Loads and Heavy Tails

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    The present paper is concerned with the stationary workload of queues with heavy-tailed (regularly varying) characteristics. We adopt a transform perspective to illuminate a close connection between the tail asymptotics and heavy-traffic limit in infinite-variance scenarios. This serves as a tribute to some of the pioneering results of J.W. Cohen in this domain. We specifically demonstrate that reduced-load equivalence properties established for the tail asymptotics of the workload naturally extend to the heavy-traffic limit
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