Print Email Facebook Twitter Tail asymptotics of the M/G/∞ model Title Tail asymptotics of the M/G/∞ model Author Mandjes, M. Zuraniewski, P.W. Publication year 2011 Abstract This paper considers the so-called M/G/∞ model: jobs arrive according to a Poisson process with rate λ, and each of them stays in the system during a random amount of time, distributed as a non-negative random variable B; throughout it is assumed that B is light-tailed. With N(t) denoting the number of jobs in the system, the random process A(t) records the load imposed on the system in [0, t], i.e., A(t):= ∫t0 N(s)ds. The main result concerns the tail asymptotics of A(t)/t: we find an explicit function f(·) such that f(t) ∼ IP(A(t)/t > ρ(1+ε). for t large; here ρ: =λ double struck E sign B. A crucial issue is that A(t) does not have i.i.d. increments, which makes direct application of the classical Bahadur-Rao result impossible; instead an adaptation of this result is required. We compare the asymptotics found with the (known) asymptotics for ρ → ∞ (and t fixed). Copyright © Taylor & Francis Group, LLC. Subject Communication & InformationPNS - Performance of Networks & ServicesTS - Technical SciencesInformaticsInfinite-servers queuesLarge deviationsTail asymptoticsPoisson distributionRandom processesRandom variablesAsymptotic analysis To reference this document use: http://resolver.tudelft.nl/uuid:a86cf94e-d691-4a04-8a03-3d84ac35ec56 DOI https://doi.org/10.1080/15326349.2011.542730 TNO identifier 427571 ISSN 1532-6349 Source Stochastic Models, 27 (1), 77-93 Document type article Files To receive the publication files, please send an e-mail request to TNO Library.