Large Deviations for Gaussian Queues demonstrates how the Gaussian traffic model arises naturally, and how the analysis of the corresponding queuing model can be performed. The text provides a general introduction to Gaussian queues, and surveys recent research into the modelling of communications networks.

Coverage includes:. Large Deviations for Gaussian Queues assumes minimal prior knowledge. It is ideally suited for postgraduate students in applied probability, operations research, computer science and electrical engineering. The book's self-contained style makes it perfect for practitioners in the communications networking industry and for researchers in related areas. Review "The book maybe useful for specialists connected with queuing theory and working in applied probability. Markov Processes and Related Fields , 5 1 , Branching processes in the analysis of the heights of trees.

Acta Inform.

Coupled samples in simulation. Operations Research , 38 1 , Dumas and A. Harris ergodicity of a multiclass queuing network via its associated fluid limit model. A multiclass network with non-linear, non-convex, non-monotonic stability conditions. Queues with periodic service and changeover time. Operations Res. Integration by parts for Poisson processes. Large deviations for a general class of random vectors. Annals of Probability , 12 1 , Two coupled processors: the reduction to a Riemann-Hilbert problem. Gebiete , 47 3 , Growth rate and ergodicity conditions for a class of random trees.

A state-dependent polling model with Markovian routing. Asymptotics and scalings for large closed product-form networks via the Central Limit Theorem. Limit laws for large product-form networks: connections with the Central Limit Theorem. Markov Processes and Related Fields , 2 2 , Fayolle and J. A nonlinear integral operator encountered in the bandwidth sharing of a star-shaped network. Gzipped PostScript , 12 pages, bytes [] G. To appear. Fayolle, I. Mitrani, and R. Sharing a processor among many job classes. Analysis of a stack algorithm for random multiple-access communication.

Theory , 31 2 , Algebraic generating functions for two-dimendional random walks. Asymptotic probabilities of languages with generalized quantifiers. IEEE Comput. Press, Los Alamitos, CA, Malyshev, and M. Cambridge University Press, Best-effort networks: modeling and performance analysis via large networks asymptotics. Birth and death processes on certain random trees: Classification and stationary laws. Probability Theory and Related Fields , 3 , Digital Object Identifier: On random walks arising in queueing systems: ergodicity and transience via quadratic forms as Lyapounov functions.

Mathematical theory of queueing systems Ithaca, NY, On the Berry-Esseen theorem. Asymptotic analysis of adaptative rate control for diverse sources with delayed feedback. Mean waiting time for a token ring with station dependent overheads. Computer Science Press, Rockville, Maryland, Some properties of open queueing networks. Problemy Peredachi Informatsii , 25 3 , G-networks with triggered batch state-dependent movement. Fox and Paul Glasserman. Estimating derivatives via Poisson equation. Probability in the Engineering and Informational Sciences , 5 4 , Monotonicity and stability of periodic polling models.

Stability of a polling model with a Markovian scheme. Analysis of some networks with interaction. On the rates of convergence of Erlang's model. Fu and Jian-Qiang Hu. On choosing the characterization for smoothed perturbation analysis. Extensions and generalizations of smoothed perturbation analysis in a generalized semi-Markov process framework. Journal of Optimization Theory and Applications , 65 1 , Belief propagation inference with a prescribed fixed point. Preprint, A queueing theory approach for a multi-speed exclusion process.

Belief-propagation algorithm for a traffic prediction system based on probe vehicles. Belief propagation and Bethe approximation for traffic prediction.

## A Nonstationary Offered-Load Model for Packet Networks

A belief propagation approach to traffic prediction using probe vehicles. Learning multiple belief propagation fixed points for real time inference. Physica A: Statistical Mechanics and its Applications , 1 , Gail, S. Hantler, and B. Augmented infinitesimal perturbation analysis: an alternate explanation.

Gajrat, A. Hordijk, V. Malyshev, and F. Fluid approximations of Markov decision chains. Related Fields , 3 1 , Blocking probabilities for large multirate Erlang loss systems. Advances in Applied Probability , 25 4 , Georgiadis and Wojtek Szpankowski. Stability of token passing rings. Queueing Systems, Theory and Applications , 11 , Gibbens and F. Distributed connection acceptance control for a connectionless network.

Key and D. ITC 16, Elsevier. Resource pricing and the evolution of congestion control. Automatica , 35 12 , December Smoothed perturbation analysis for a class of discrete event systems. Time-changing and truncating K-capacity queues from one K to another. Journal of Applied Probability , 28 3 , Some guidelines and guarantees for common random numbers.

Management Science , 38 6 , Strongly consistent steady-state derivative estimates. Smoothing complements and randomized score functions. Stochastic monotonicity and conditional Monte Carlo for likelihood ratio. Preprint , October Filtered Monte Carlo. Preprint , April Gradient Estimation via Perturbation Analysis. Kluwer Academic Publishers, Norwell, Massachusetts, Structural conditions for perturbation analysis of queueing systems. Journal of the ACM , 38 4 , Derivative estimates from simulation of continuous-time Markov chains. Operations Research , 40 2 , Processes with associated increments.

## Michel Mandjes - Citations Google Scholar

Journal of Applied Probability , 29 2 , Stationary waiting time derivatives. Queueing Systems, Theory and Applications , 12 4 , Glynn and Ward Whitt. Mathematics of Operations Research , 13 4 , Operations Research , 37 1 , Glynn, Benjamin Melamed, and Ward Whitt. Estimating customer and time averages. Preprint , November A GSMP formalism for discrete event systems. Proceedings of the IEEE , 77 1 , Likelihood ratio gradient estimation for stochastic systems.

Communications of the ACM , 33 10 , Pathwise convexity and its relation to convergence of time-average derivatives. Management Science , 38 9 , Subexponential distributions. Smoothed conditional perturbation analysis of discrete event dynamical systems. Preprint , August Control , 40 8 , Abrams, P. Haigs, and J. Comfort, editors, Proceedings of the Winter Simulation Conference , pages , Propagation of chaos for a fully connected loss network with alternate routing.

Chaos hypothesis for a system interacting through shared resources. Theory Related Fields , 2 , Dynamic asymptotic results for a generalized star-shaped loss network. Large deviations at equilibrium for a large star-shaped loss network. A statistical physics approach to large networks. In Probabilistic models for nonlinear partial differential equations Montecatini Terme, , pages Springer, Berlin, Point processes and random measures.

Greenberg, V. Malyshev, and S. Stochastic model of massively parallel computation. Markov Processes and Related Fields , 1 4 , Round-robin scheduling for max-min fairness in data networks. Zazanis, and Rajan Suri. Convergence properties of infinitesimal perturbation analysis estimates. Management Science , 34 11 , Measure valued differentiation for stochastic processes: the finite horizon case. Technical Report , Eurandom, Measure valued differentiation for stochastic processes: the random horizon case. Optimization and perturbation analysis of queueing networks. Journal of Optimization Theory and Applications , , Kluwer Academic Publishers, Eyler, and T.

A gradient technique for general buffer storage design in a serial production line. International Journal of Production Research , 17 6 , Optimizing discrete event dynamic systems via the gradient surface method. In Proceedings of the 30th Conference on Decision and Control , pages , Sreenivas, and P.

- The Mystery of Edwin Drood (Oxford World’s Classics)!
- Large deviations for gaussian queues. Modelling communication networks;
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- Mobile Robots in Rough Terrain: Estimation, Motion Planning, and Control with Application to Planetary Rovers (Springer Tracts in Advanced Robotics).

Ordinal optimization of DEDS. Asymptotic analysis of product-form distributions related to large interconnection networks. Theoretical Computer Science , , Topics in matrix analysis. Consistency of infinitesimal perturbation analysis estimators with rates. Convexity of sample path performance and strong consistency of infinitesimal perturbation analysis estimates. Ibe and Xian Cheng. Performance analysis of asymmetric single-buffer polling systems. Performance Evaluation , 10 1 , Selecta Math.

Selected translations. On the transient behavior of the processor sharing queue. Jones and Arne Magnus. Application of Stieltjes fractions to birth-death processes. South Florida, Tampa, Fla. Academic Press. Jungreis, F. Kochman, V. Miller, A. Puha, and R. A birth-death process in binary trees. Kabanov and R. On convergence in variation of the distributions of multivariate point processes.

Gebiete , 63 4 , Palm distributions of point processes and their applications to statistical inference. Contemporary Mathematics , , Kel'bert and Yu. Circuit-switching networks with FIFO plus justifying blockout service on infinite graphs. A Poisson limit theorem for hybrid star networks: mean field approximation.

Problemy Peredachi Informatsii , 25 1 , On a class of packet-switching networks on an infinite graph. Kel'bert, R. Kopeika, and R. On a class of hybrid switching networks with small transit flows. Kelly, A. Maulloo, and D.

Rate control for communication networks: shadow prices, proportional fairness and stability. Journal of the Operational Research Society , 49 3 , Reversibility and Stochastic Networks. The Clifford Paterson lecture, modelling communication networks, present and future. A , , Differential qos and pricing in networks: Where flow control meets game theory.

On queues in heavy traffic. B , , On queues in which customers are served in random order. Cambridge Philos. Kipnis and Ph. A dynamic storage process. PWN, Warszawa, The analysis of random polling systems. Operations Research , 36 5 , Asymptotic expansions for large closed queueing networks. Journal of the ACM , 37 1 , Asymptotic analysis of closed queueing networks with bottlenecks. Hasegawa, H. Takagi, and Y. Limit non-stationary behavior of large closed queueing networks with bottlenecks.

Queueing Systems, Theory and Applications , 14 , Another approach to asymptotic expansions for large closed queueing networks. Operations Research Letters , , Konheim and Bernd Meister. Waiting lines and times in a system with polling. Journal of the ACM , 21 3 , Sensitivity analysis for stationary and ergodic queues. Advances in Applied Probability , 24 3 , Sensitivity analysis for stationary and ergodic queues: Additional results.

Stationary distributions in a queueing system with vacation times and limited service. Kroese and Volker Schmidt. A continuous polling system with general service times. Advances in Applied Probability , 2 4 , Queueing systems on a circle. Single-server queues with spatially distributed arrivals. Kuelbs and T. Berry-Esseen estimates in Hilbert space and an application to the law of the iterated logarithm.

Annals of Probability , , Kung, T. Blackwell, and A. Credit-based flow control for ATM networks: credit update protocol, adaptative credit allocation, and statistical multiplexing. Kushner and Jichuan Yang. A Monte Carlo method for sensitivity analysis and parametric optimization of nonlinear stochastic systems: the ergodic case. Crazy maze.

Hebdogiciel 21, May Manuel d'utilisation de BigNet 2. On allocation of bandwidth in cable access networks. In preparation, Exact formula for sensitivity analysis of Markov chains. Computer Performance Modelling Handbook. Academic Press, Lavrentiev and B.

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## Une bibliographie sur les réseaux et files d'attente

Stochastic optimization by simulation: Some experiments with a simple steady-state queue. Convergence rates for steady-state derivative estimators. Management Science , 36 11 , A note on the interchange of derivative and expectation for LR gradient techniques. Preprint , June A queue with starter and a queue with vacations: delay analysis by decomposition. Polling systems with zero switch-over periods: a general method for analyzing the expected delay. Performance Evaluation , 13 2 , Polling systems: Applications, modeling and optimization.

Management Science , 22 2 , Operational Res.

### Description

Dominance relations in polling systems. Delay computation and dynamic behavior of nonsymmetric polling systems. Interacting particle systems. Springer-Verlag, New York, Stochastic models of interacting systems. Annals of Probability , 25 1 , Monotonicity of conditional distributions and growth models on trees.

Stochastic monotonicities in Jackson queueing networks. Sample path methods in the control of queues. Exponential bounds with applications to call admission. ACM , 44 3 , Probability Theory. Van Nostrand Company, fourth edition, Fixed utilization perturbation analysis.

Malyshev and M. Ergodicity, continuity and analyticity of countable Markov chains. Phase transition in a loss load sharing loss model. Annals of Applied Probability , 4 4 , Condensation in large closed Jackson networks. Annals of Applied Probability , 6 1 , Strong approximations for time-dependent queues.

Stochastic bounds for fast Jackson networks. Martin and Yu. Fast Jackson networks. Point processes in fast Jackson networks. Models for the dimensioning of ABR. Fairness and quality of service for elastic traffic. Arguments in favour of admission control for tcp flows. Stability of non-Markovian polling systems. Point process models of neuron networks: Stability results.

Mean field equations for elastic flows with rerouting. Q-ary collision resolution algorithms in random-access systems with free or blocked channel access. On pathwise behaviour of queues. A note on the pathwise version of Little's formula. On pathwise rate conservation for a class of semi-martigales. Stochastic Processes and their Applications , , McKenna and D. Integral representations and asymptotic expansions for closed Markovian queueing networks: Normal usage.

Bell System Technical Journal , , Asymptotic expansions and integral representations of moments of queue lengths in closed Markovian networks. Journal of the ACM , , McKenna, D. Mitra, and K. A class of closed Markovian queueing networks: Integral representations, asymptotic expansions and generalizations.

Transience of multiclass queueing networks via fluid limit models. Annals of Applied Probability , 5 4 , Asymptotic expansions for closed Markovian networks with state-dependent service rates. Sur les mesures de Palm de deux processus ponctuels stationnaires. Oublagha, L. Delay analysis of a credit-based control for ABR transfer. Pinsker and V.

The information creation rate in stationary Gaussian channels in the case of transmission with weak signals. Problemy Peredachi Informatsii , 30 4 , Optimal filtering of a Gaussian signal under almost Gaussian noise. Problemy Peredachi Informatsii , 31 4 , On error-free filtering of some stationary processes. Uspekhi Mat. Nauk , 52 2 , Pinsker, V. Prelov, and S. Sensitivity of channel capacity. Note on the heights of random recursive trees and random m-ary search trees. Random Structures Algorithms , 5 2 , A reversible nearest particle system on the homogeneous tree.

Journal of Theoretical Probability , 12 1 , Critical exponents for a reversible nearest particle system on the binary tree. Annals of Applied Probability , 28 1 , Queuing Models for Polled Multiqueues , November Reiman and Burton Simon. Light traffic limits of sojourn time distributions in Markovian queueing networks. Communications in Statistics--Stochastic Models , 4 2 , Open queueing systems in light traffic. Mathematics of Operations Research , 14 1 , Reiman and Alan Weiss. Light traffic derivatives via likelihood ratios. Sensitivity analysis for simulations via likelihood ratios.

Operations Research , 37 5 , Reiser and S.