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Queueing networks with infinite servers in each node (an application in logistics)

Ferreira, Manuel Alberto M.
Fonte: Slovak University of Technology Publicador: Slovak University of Technology
Tipo: Conferência ou Objeto de Conferência
Publicado em //2004 ENG
Relevância na Pesquisa
75.92%
After a report of results about queueing systems with infinite servers, namely considering its busy period, we intend to build a model, using networks of queues with infinite servers in each node, to study a two echelons repair system of a fleet of aircraft,of shipping or of trucking. The customers are the failures. And its service time is the time that goes from the instant at which they occur till the one at which they are completely repaired. The failures repairs occur in a base or in a remote station. The whole failures detected in the base are repaired there. Some of the failures detected in the station are repaired in the base, and the others in the station. The results referred above, about the infinite servers queues busy period, allow the determination of the two echelons repair system performance measures. In this application we work over models of Carrillo (1991) and Ferreira (1996) that we improve and complete. We will illustrate the theory with a very simple and short numerical example.

Modelling and differential costs evaluation of a two echelons repair system through infinite servers nodes queuing networks

Ferreira, Manuel Alberto M.
Fonte: Hikari, Ltd. Publicador: Hikari, Ltd.
Tipo: Artigo de Revista Científica
Publicado em //2013 ENG
Relevância na Pesquisa
65.92%
After a short report of results on infinite servers queues systems, focusing on its busy period, using networks of queues with infinite servers nodes a model is constructed to study a two echelons repair system. These repair systems may be useful, for instance, in the operation of a fleet of aircraft, of shipping or of trucks. Additionally it is shown how this model may be used in the evaluation of differential costs.

Stochastic processes in networks of queues with exponential service times and only one class of customers

Ferreira, Manuel Alberto M.
Fonte: Hikari, Ltd Publicador: Hikari, Ltd
Tipo: Artigo de Revista Científica
Publicado em //2014 ENG
Relevância na Pesquisa
95.96%
Two networks of queues models, presented initially by Jackson, in the open case, and Gordon and Newell, in the closed case, stochastic processes are presented and studied in some of their details and problems. The service times are exponentially distributed and there is only one class of customers.

Networks of queues models with several classes of customers and exponential service times

Ferreira, Manuel Alberto M.
Fonte: Hikari, Ltd Publicador: Hikari, Ltd
Tipo: Artigo de Revista Científica
Publicado em //2015 ENG
Relevância na Pesquisa
95.99%
The main target of this paper is to present the Markov chain C that, not giving explicitly the queue lengths stationary probabilities, has the necessary information to its determination for open networks of queues with several classes of customers and exponential service times, allowing to overcome ingeniously this problem. The situation for closed networks, in the same conditions, much easier is also presented.

Two interfering queues in packet-radio networks

Fonte: Laboratory for Information and Decision Systems, Massachusetts Institute of Technology Publicador: Laboratory for Information and Decision Systems, Massachusetts Institute of Technology
Formato: 33 p.; application/pdf
ENG
Relevância na Pesquisa
45.6%
M. Sidi and A. Segall.; Bibliography: p. 14.; "June, 1981."; U.S. Department of Defense contract No. N00014-75-C-1183

Approximations for manufacturing networks of queues with overtime

Fonte: Sloan School of Management, Massachusetts Institute of Technology Publicador: Sloan School of Management, Massachusetts Institute of Technology
Formato: 21, [20] leaves; 1927072 bytes; application/pdf
ENG
Relevância na Pesquisa
55.6%
Gabriel R. Britan, Devanath Tirupati.; Includes bibliographical references.

On the large deviations behaviour of acyclic networks of G/G/1 queues

Fonte: Massachusetts Institute of Technology, Laboratory for Information and Decision Systems] Publicador: Massachusetts Institute of Technology, Laboratory for Information and Decision Systems]
Formato: 43 p.; 2556523 bytes; application/pdf
ENG
Relevância na Pesquisa
45.6%
Dimitris Bertsimas, Ioannis Ch. Paschalidis, John N. Tsitsiklis.; Includes bibliographical references (p. 39-41).; Supported by a Presidential Young Investigator award. DDM-9158118 Supported by the ARO. DAAL03-92-G-0115 Supported by funds from the Draper Laboratory.

Monotone Control of Queueing and Production/Inventory Systems

Veatch, Michael H.; Wein, Lawrence M.
Fonte: Massachusetts Institute of Technology, Operations Research Center Publicador: Massachusetts Institute of Technology, Operations Research Center
Tipo: Trabalho em Andamento Formato: 1214972 bytes; application/pdf
EN_US
Relevância na Pesquisa
55.59%
Weber and Stidham (1987) used submodularity to establish transition monotonicity (a service completion at one station cannot reduce the service rate at another station) for Markovian queueing networks that meet certain regularity conditions and are controlled to minimize service and queueing costs. We give an extension of monotonicity to other directions in the state space, such as arrival transitions, and to arrival routing problems. The conditions used to establish monotonicity, which deal with the boundary of the state space, are easily verified for many queueing systems. We also show that, without service costs, transition-monotone controls can be described by simple control regions and switching functions, extending earlier results. The theory is applied to production/inventory systems with holding costs at each stage and finished goods backorder costs.

Scheduling Networks of Queues: Heavy Traffic Analysis of a Multistation Closed Network

Chevalier, Philippe B.; Wein, Lawrence M.
Fonte: Massachusetts Institute of Technology, Operations Research Center Publicador: Massachusetts Institute of Technology, Operations Research Center
Tipo: Trabalho em Andamento Formato: 2007841 bytes; application/pdf
EN_US
Relevância na Pesquisa
55.59%
We consider the problem of finding an optimal dynamic priority sequencing policy to maximize the mean throughput rate in a multistation, multiclass closed queueing network with general service time distributions and a general routing structure. Under balanced heavy loading conditions, this scheduling problem can be approximated by a control problem involving Brownian motion. Although a unique, closed form solution to the Brownian control problem is not derived, an analysis of the problem leads to an effective static sequencing policy, and to an approximate means of comparing the relative performance of arbitrary static policies. Three examples are given that illustrate the effectiveness of our procedure.

Monotone Control of Queueing and Production/Inventory Systems

Veatch, Michael H.; Wein, Lawrence M.
Fonte: Massachusetts Institute of Technology, Operations Research Center Publicador: Massachusetts Institute of Technology, Operations Research Center
Tipo: Trabalho em Andamento Formato: 1214972 bytes; application/pdf
EN_US
Relevância na Pesquisa
55.59%
Weber and Stidham (1987) used submodularity to establish transition monotonicity (a service completion at one station cannot reduce the service rate at another station) for Markovian queueing networks that meet certain regularity conditions and are controlled to minimize service and queueing costs. We give an extension of monotonicity to other directions in the state space, such as arrival transitions, and to arrival routing problems. The conditions used to establish monotonicity, which deal with the boundary of the state space, are easily verified for many queueing systems. We also show that, without service costs, transition-monotone controls can be described by simple control regions and switching functions, extending earlier results. The theory is applied to production/inventory systems with holding costs at each stage and finished goods backorder costs.

Running in circles : packet routing on ring networks

Bradley, William F. (William Francis), 1973-
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 156 p.; 11749248 bytes; 11749004 bytes; application/pdf; application/pdf
ENG
Relevância na Pesquisa
45.67%
I analyze packet routing on unidirectional ring networks, with an eye towards establishing bounds on the expected length of the queues. Suppose we route packets by a greedy "hot potato" protocol. If packets are inserted by a Bernoulli process and have uniform destinations around the ring, and if the nominal load is kept fixed, then I can construct an upper bound on the expected queue length per node that is independent of the size of the ring. If the packets only travel one or two steps, I can calculate the exact expected queue length for rings of any size. I also show some stability results under more general circumstances. If the packets are inserted by any ergodic hidden Markov process with nominal loads less than one, and routed by any greedy protocol, I prove that the ring is ergodic.; by William F. Bradley.; Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2002.; Includes bibliographical references (p. 151-154) and index.

Departure processes from MAP/PH/1 queues

Green, David Anthony
Fonte: Universidade de Adelaide Publicador: Universidade de Adelaide
Tipo: Tese de Doutorado Formato: 883455 bytes; 221144 bytes; application/pdf; application/pdf
Publicado em //1999 EN
Relevância na Pesquisa
46.1%
A MAP/PH/1 queue is a queue having a Markov arrival process (MAP), and a single server with phase-type (PH -type) distributed service time. This thesis considers the departure process from these type of queues. We use matrix analytic methods, the Jordan canonical form of matrices, non-linear filtering and approximation techniques. The departure process of a queue is important in the analysis of networks of queues, as it may be the arrival process to another queue in the network. If a simple description were to exist for a departure process, the analysis of at least feed-forward networks of these queues would then be analytically tractable. Chapter 1 is an introduction to some of the literature and ideas surrounding the departure process from MAP/PH/1 queues. Chapter 2 sets up the basic notation and establishes some results which are used throughout the thesis. It contains a preliminary consideration of PH -type distributions, PH -renewal processes, MAP s, MAP/PH/1 queues, non-linear filtering and the Jordan canonical form. Chapter 3 is an expansion of "The Output process of an MMPP/M/1 queue", where the question of whether a MAP description can exist for the departure process of a non-trivial MAP/M/1 queue is considered. In a 1994 paper...

Optimization of Multiclass Queueing Networks: Polyhedral and Nonlinear Characterizations of Achievable Performance

Bertsimas, Dimitris J.; Paschalidis, Ioannis Ch; Tsitsiklis, John N.
Fonte: Massachusetts Institute of Technology, Operations Research Center Publicador: Massachusetts Institute of Technology, Operations Research Center
Tipo: Trabalho em Andamento Formato: 2800138 bytes; application/pdf
EN_US
Relevância na Pesquisa
45.78%
We consider open and closed multiclass queueing networks with Poisson arrivals (in open networks), exponentially distributed class dependent service times, and with class dependent deterministic or probabilistic routing. For open networks, the performance objective is to minimize, over all sequencing and routing policies, a weighted sum of the expected response times of different classes. Using a powerful technique involving quadratic or higher order potential functions, we propose variants of a method to derive polyhedral and nonlinear spaces which contain the entire set of achievable response times under stable and preemptive scheduling policies. By optimizing over these spaces, we obtain lower bounds on achievable performance. In particular, we obtain a sequence of progressively more complicated nonlinear approximations (relaxations) which are progressively closer to the exact achievable space. In the special case of single station networks (multiclass queues and Klimov's model) and homogenous multiclass networks, our characterization gives exactly the achievable region. Consequently, the proposed method can be viewed as the natural extension of conservation laws to multiclass queueing networks. For closed networks, the performance objective is to maximize throughput. We similarly find polyhedral and nonlinear spaces that include the performance space and by maximizing over these spaces we obtain an upper bound on the optimal throughput. We check the tightness of our bounds by simulating heuristic scheduling policies for simple open networks and we find that the first order approximation of our method is at least as good as simulation-based existing methods. In terms of computational complexity and in contrast to simulation-based existing methods...

Modeling Travel Times in Dynamic Transportation Networks; A Fluid Dynamics Approach

Kachani, Soulaymane; Perakis, Georgia
Fonte: Massachusetts Institute of Technology, Operations Research Center Publicador: Massachusetts Institute of Technology, Operations Research Center
Tipo: Trabalho em Andamento Formato: 2043933 bytes; application/pdf
EN_US
Relevância na Pesquisa
45.67%
In this paper, we take a fluid dynamics approach to determine the travel time in traversing a network's link. We propose a general model for travel time functions that utilizes fluid dynamics laws for compressible flow to capture a variety of flow patterns such as the formation and dissipation of queues, drivers' response to upstream congestion or decongestion and drivers' reaction time. We examine two variants of the model, in the case of separable velocity functions, which gives rise to two families of travel time functions for the problem; a polynomial and an exponential family. We analyze these travel time functions and examine several special cases. Our investigation also extends to the case of non-separable velocity functions starting with an analysis of the interaction between two links, and then extending it to the general case of acyclic networks.

Strong Stationary Duality for M\"obius Monotone Markov Chains: Unreliable Networks

Lorek, Pawel; Szekli, Ryszard
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 01/01/2011
Relevância na Pesquisa
45.67%
For Markov chains with a partially ordered finite state space we show strong stationary duality under the condition of M\"obius monotonicity of the chain. We show relations of M\"obius monotonicity to other definitions of monotone chains. We give examples of dual chains in this context which have transitions only upwards. We illustrate general theory by an analysis of nonsymmetric random walks on the cube with an application to networks of queues.

Dynamics of Jackson networks: perturbation theory

Zeitak, Reuven
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 13/08/2007
Relevância na Pesquisa
45.68%
We introduce a new formalism for dealing with networks of queues. The formalism is based on the Doi-Peliti second quantization method for reaction diffusion systems. As a demonstration of the method's utility we compute perturbatively the different time busy-busy correlations between two servers in a Jackson network.; Comment: 15 pages, 1 figure

Throughput Optimal Scheduling Policies in Networks of Interacting Queues

Leonardi, Emilio
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.84%
This report considers a fairly general model of constrained queuing networks that allows us to represent both MMBP (Markov Modulated Bernoulli Processes) arrivals and time-varying service constraints. We derive a set of sufficient conditions for throughput optimality of scheduling policies that encompass and generalize all the previously obtained results in the field. This leads to the definition of new classes of (non diagonal) throughput optimal scheduling policies. We prove the stability of queues by extending the traditional Lyapunov drift criteria methodology.

Bayesian inference for queueing networks and modeling of internet services

Sutton, Charles; Jordan, Michael I.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.87%
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)

Stability and Capacity Regions or Discrete Time Queueing Networks

Neely, Michael J.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 17/03/2010
Relevância na Pesquisa
45.84%
We consider stability and network capacity in discrete time queueing systems. Relationships between four common notions of stability are described. Specifically, we consider rate stability, mean rate stability, steady state stability, and strong stability. We then consider networks of queues with random events and control actions that can be implemented over time to affect arrivals and service at the queues. The control actions also generate a vector of additional network attributes. We characterize the network capacity region, being the closure of the set of all rate vectors that can be supported subject to network stability and to additional time average attribute constraints. We show that (under mild technical assumptions) the capacity region is the same under all four stability definitions. Our capacity achievability proof uses the drift-plus-penalty method of Lyapunov optimization, and provides full details for the case when network states obey a decaying memory property, which holds for finite state ergodic systems and more general systems.; Comment: 19 pages

Collaborating queues: large service network and a limit order book

Yudovina, Elena
Fonte: University of Cambridge; Department of Pure Mathematics and Mathematical Statistics; Emmanuel College; Statistics Laboratory Publicador: University of Cambridge; Department of Pure Mathematics and Mathematical Statistics; Emmanuel College; Statistics Laboratory
Tipo: Thesis; doctoral; PhD
EN
Relevância na Pesquisa
45.84%
E-thesis pagination differs from hardbound copy kept in the Manuscripts Department, Cambridge University Library.; We analyse the steady-state behaviour of two different models with collaborating queues: that is, models in which "customers" can be served by many types of "servers", and "servers" can process many types of "customers". The first example is a large-scale service system, such as a call centre. Collaboration is the result of cross-trained staff attending to several different types of incoming calls. We first examine a load-balancing policy, which aims to keep servers in different pools equally busy. Although the policy behaves order-optimally over fixed time horizons, we show that the steady-state distribution may fail to be tight on the diffusion scale. That is, in a family of ever-larger networks whose arrival rates grow as O(r) (where r is a scaling parameter growing to infinity), the sequence of steady-state deviations from equilibrium scaled down by sqrt(r) is not tight. We then propose a different policy, for which we show that the sequence of invariant distributions is tight on the r^(1/2+epsilon) scale, for any epsilon > 0. For this policy we conjecture that tightness holds on the diffusion scale as well. The second example models a limit order book...