159 research outputs found
Optimal design of simulation experiments with nearly saturated queues
Simulation Models;Interpolation;Queueing Network;Extrapolation
Optimization flow control -- I: Basic algorithm and convergence
We propose an optimization approach to flow control where the objective is to maximize the aggregate source utility over their transmission rates. We view network links and sources as processors of a distributed computation system to solve the dual problem using a gradient projection algorithm. In this system, sources select transmission rates that maximize their own benefits, utility minus bandwidth cost, and network links adjust bandwidth prices to coordinate the sources' decisions. We allow feedback delays to be different, substantial, and time varying, and links and sources to update at different times and with different frequencies. We provide asynchronous distributed algorithms and prove their convergence in a static environment. We present measurements obtained from a preliminary prototype to illustrate the convergence of the algorithm in a slowly time-varying environment. We discuss its fairness property
Особенности программной реализации численно-аналитического метода расчёта моделей нестационарных систем обслуживания
A numerical-analytical method for non-stationary queueing systems models computation is presented. The solution of Chapman—Kolmogorov equations is found in the analytical form. The algorithm and its practical implementation with Java language are discussed. Computation time and results precision for the presented method and the Runge—Kutta type method used in Matlab are compared.В статье описывается численно-аналитический метод расчёта моделей нестационарных систем обслуживания. Находится решение системы уравнений Чепмена — Колмогорова в аналитическом виде. Приводится алгоритм построения решения и особенности его программной реализации на языке Java. Также приводятся результаты сравнения времени работы и точности выходных данных метода со временем работы и точностью выходных данных численного метода типа Рунге — Кутты, который используется в Matlab для решения аналогичных задач
Simple and explicit bounds for multi-server queues with (and sometimes better) scaling
We consider the FCFS queue, and prove the first simple and explicit
bounds that scale as (and sometimes better). Here
denotes the corresponding traffic intensity. Conceptually, our results can be
viewed as a multi-server analogue of Kingman's bound. Our main results are
bounds for the tail of the steady-state queue length and the steady-state
probability of delay. The strength of our bounds (e.g. in the form of tail
decay rate) is a function of how many moments of the inter-arrival and service
distributions are assumed finite. More formally, suppose that the inter-arrival
and service times (distributed as random variables and respectively)
have finite th moment for some Let (respectively )
denote (respectively ). Then
our bounds (also for higher moments) are simple and explicit functions of
, and
only. Our bounds scale gracefully even when the number of
servers grows large and the traffic intensity converges to unity
simultaneously, as in the Halfin-Whitt scaling regime. Some of our bounds scale
better than in certain asymptotic regimes. More precisely,
they scale as multiplied by an inverse polynomial in These results formalize the intuition that bounds should be tighter
in light traffic as well as certain heavy-traffic regimes (e.g. with
fixed and large). In these same asymptotic regimes we also prove bounds for
the tail of the steady-state number in service.
Our main proofs proceed by explicitly analyzing the bounding process which
arises in the stochastic comparison bounds of amarnik and Goldberg for
multi-server queues. Along the way we derive several novel results for suprema
of random walks and pooled renewal processes which may be of independent
interest. We also prove several additional bounds using drift arguments (which
have much smaller pre-factors), and make several conjectures which would imply
further related bounds and generalizations
Tractable stochastic analysis in high dimensions via robust optimization
Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 201-207).Modern probability theory, whose foundation is based on the axioms set forth by Kolmogorov, is currently the major tool for performance analysis in stochastic systems. While it offers insights in understanding such systems, probability theory, in contrast to optimization, has not been developed with computational tractability as an objective when the dimension increases. Correspondingly, some of its major areas of application remain unsolved when the underlying systems become multidimensional: Queueing networks, auction design in multi-item, multi-bidder auctions, network information theory, pricing multi-dimensional financial contracts, among others. We propose a new approach to analyze stochastic systems based on robust optimization. The key idea is to replace the Kolmogorov axioms and the concept of random variables as primitives of probability theory, with uncertainty sets that are derived from some of the asymptotic implications of probability theory like the central limit theorem. In addition, we observe that several desired system properties such as incentive compatibility and individual rationality in auction design and correct decoding in information theory are naturally expressed in the language of robust optimization. In this way, the performance analysis questions become highly structured optimization problems (linear, semidefinite, mixed integer) for which there exist efficient, practical algorithms that are capable of solving problems in high dimensions. We demonstrate that the proposed approach achieves computationally tractable methods for (a) analyzing queueing networks (Chapter 2) (b) designing multi-item, multi-bidder auctions with budget constraints, (Chapter 3) (c) characterizing the capacity region and designing optimal coding and decoding methods in multi-sender, multi-receiver communication channels (Chapter 4).by Chaithanya Bandi.Ph.D
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