3,061 research outputs found

    Perfect Simulation of M/G/cM/G/c Queues

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    In this paper we describe a perfect simulation algorithm for the stable M/G/cM/G/c queue. Sigman (2011: Exact Simulation of the Stationary Distribution of the FIFO M/G/c Queue. Journal of Applied Probability, 48A, 209--213) showed how to build a dominated CFTP algorithm for perfect simulation of the super-stable M/G/cM/G/c queue operating under First Come First Served discipline, with dominating process provided by the corresponding M/G/1M/G/1 queue (using Wolff's sample path monotonicity, which applies when service durations are coupled in order of initiation of service), and exploiting the fact that the workload process for the M/G/1M/G/1 queue remains the same under different queueing disciplines, in particular under the Processor Sharing discipline, for which a dynamic reversibility property holds. We generalize Sigman's construction to the stable case by comparing the M/G/cM/G/c queue to a copy run under Random Assignment. This allows us to produce a naive perfect simulation algorithm based on running the dominating process back to the time it first empties. We also construct a more efficient algorithm that uses sandwiching by lower and upper processes constructed as coupled M/G/cM/G/c queues started respectively from the empty state and the state of the M/G/cM/G/c queue under Random Assignment. A careful analysis shows that appropriate ordering relationships can still be maintained, so long as service durations continue to be coupled in order of initiation of service. We summarize statistical checks of simulation output, and demonstrate that the mean run-time is finite so long as the second moment of the service duration distribution is finite.Comment: 28 pages, 5 figure

    Bayesian inference for queueing networks and modeling of internet services

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    Modern Internet services, such as those at Google, Yahoo!, and Amazon, handle billions of requests per day on clusters of thousands of computers. Because these services operate under strict performance requirements, a statistical understanding of their performance is of great practical interest. Such services are modeled by networks of queues, where each queue models one of the computers in the system. A key challenge is that the data are incomplete, because recording detailed information about every request to a heavily used system can require unacceptable overhead. In this paper we develop a Bayesian perspective on queueing models in which the arrival and departure times that are not observed are treated as latent variables. Underlying this viewpoint is the observation that a queueing model defines a deterministic transformation between the data and a set of independent variables called the service times. With this viewpoint in hand, we sample from the posterior distribution over missing data and model parameters using Markov chain Monte Carlo. We evaluate our framework on data from a benchmark Web application. We also present a simple technique for selection among nested queueing models. We are unaware of any previous work that considers inference in networks of queues in the presence of missing data.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS392 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Fluid flow switching servers : control and observer design

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    Teletraffic analysis of ATM systems : symposium gehouden aan de Technische Universiteit Eindhoven op 15 februari 1993

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    Final report on the evaluation of RRM/CRRM algorithms

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    Deliverable public del projecte EVERESTThis deliverable provides a definition and a complete evaluation of the RRM/CRRM algorithms selected in D11 and D15, and evolved and refined on an iterative process. The evaluation will be carried out by means of simulations using the simulators provided at D07, and D14.Preprin
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