Results 1  10
of
141
Charging and rate control for elastic traffic
 European Transactions on Telecommunications
, 1997
"... This paper addresses the issues of charging, rate control and routing for a communication network carrying elastic traffic, such as an ATM network offering an available bit rate service. A model is described from which max–min fairness of rates emerges as a limiting special case; more generally, the ..."
Abstract

Cited by 856 (5 self)
 Add to MetaCart
(Show Context)
This paper addresses the issues of charging, rate control and routing for a communication network carrying elastic traffic, such as an ATM network offering an available bit rate service. A model is described from which max–min fairness of rates emerges as a limiting special case; more generally, the charges users are prepared to pay influence their allocated rates. In the preferred version of the model, a user chooses the charge per unit time that the user will pay; thereafter the user’s rate is determined by the network according to a proportional fairness criterion applied to the rate per unit charge. A system optimum is achieved when users ’ choices of charges and the network’s choice of allocated rates are in equilibrium. 1
A game theoretic framework for bandwidth allocation and pricing in broadband networks
 IEEE/ACM TRANS. ON NETWORKING
, 2000
"... In this paper, we present a game theoretic framework for bandwidth allocation for elastic services in highspeed networks. The framework is based on the idea of the Nash bargaining solution from cooperative game theory, which not only provides the rate settings of users that are Pareto optimal from ..."
Abstract

Cited by 225 (11 self)
 Add to MetaCart
(Show Context)
In this paper, we present a game theoretic framework for bandwidth allocation for elastic services in highspeed networks. The framework is based on the idea of the Nash bargaining solution from cooperative game theory, which not only provides the rate settings of users that are Pareto optimal from the point of view of the whole system, but are also consistent with the fairness axioms of game theory. We first consider the centralized problem and then show that this procedure can be decentralized so that greedy optimization by users yields the system optimal bandwidth allocations. We propose a distributed algorithm for implementing the optimal and fair bandwidth allocation and provide conditions for its convergence. The paper concludes with the pricing of elastic connections based on users ’ bandwidth requirements and users’ budget. We show that the above bargaining framework can be used to characterize a rate allocation and a pricing policy which takes into account users’ budget in a fair way and such that the total network revenue is maximized.
A Convex Optimization Approach to the Rational Covariance Extension Problem
 SIAM J. Control Optim
, 1999
"... In this paper we present a convex optimization problem for solving the rational covariance extension problem. Given a partial covariance sequence and the desired zeros of the modeling filter, the poles are uniquely determined from the unique minimum of the corresponding optimization problem. In this ..."
Abstract

Cited by 62 (24 self)
 Add to MetaCart
(Show Context)
In this paper we present a convex optimization problem for solving the rational covariance extension problem. Given a partial covariance sequence and the desired zeros of the modeling filter, the poles are uniquely determined from the unique minimum of the corresponding optimization problem. In this way we obtain an algorithm for solving the covariance extension problem, as well as a constructive proof of Georgiou's seminal existence result and his conjecture, a stronger version of which we have resolved in [7]. K3 words. rational covariance extension, partial stochastic realization, trigonometric moment problem, spectral estimation, speech processing, stochastic modeling AMS subject classifications.30ERR 60G35, 62M15, 93A30,93E0 1.
Utilityoptimal randomaccess control
 IEEE Trans. on Wireless Communications
, 2007
"... Abstract — This paper designs medium access control (MAC) protocols for wireless networks through the network utility maximization (NUM) framework. A networkwide utility maximization problem is formulated, using a collision/persistenceprobabilistic model and aligning selfish utility with total soci ..."
Abstract

Cited by 49 (10 self)
 Add to MetaCart
(Show Context)
Abstract — This paper designs medium access control (MAC) protocols for wireless networks through the network utility maximization (NUM) framework. A networkwide utility maximization problem is formulated, using a collision/persistenceprobabilistic model and aligning selfish utility with total social welfare. By adjusting the parameters in the utility objective functions of the NUM problem, we can also control the tradeoff between efficiency and fairness of radio resource allocation. We develop two distributed algorithms to solve the utilityoptimal randomaccess control problem, which lead to random access protocols that have slightly more message passing overhead than the current exponentialbackoff protocols, but significant potential for efficiency and fairness improvement. We provide readilyverifiable sufficient conditions under which convergence of the proposed algorithms to a global optimality of network utility can be guaranteed, and numerical experiments that illustrate the value of the NUM approach to the complexityperformance tradeoff in MAC design. Index Terms — Wireless network, medium access control (MAC), mathematical programming/optimization, network utility maximization, network control by pricing.
On the convergence of concaveconvex procedure
 In NIPS Workshop on Optimization for Machine Learning
, 2009
"... The concaveconvex procedure (CCCP) is a majorizationminimization algorithm that solves d.c. (difference of convex functions) programs as a sequence of convex programs. In machine learning, CCCP is extensively used in many learning algorithms like sparse support vector machines (SVMs), transductive ..."
Abstract

Cited by 48 (1 self)
 Add to MetaCart
(Show Context)
The concaveconvex procedure (CCCP) is a majorizationminimization algorithm that solves d.c. (difference of convex functions) programs as a sequence of convex programs. In machine learning, CCCP is extensively used in many learning algorithms like sparse support vector machines (SVMs), transductive SVMs, sparse principal component analysis, etc. Though widely used in many applications, the convergence behavior of CCCP has not gotten a lot of specific attention. Yuille and Rangarajan analyzed its convergence in their original paper, however, we believe the analysis is not complete. Although the convergence of CCCP can be derived from the convergence of the d.c. algorithm (DCA), its proof is more specialized and technical than actually required for the specific case of CCCP. In this paper, we follow a different reasoning and show how Zangwill’s global convergence theory of iterative algorithms provides a natural framework to prove the convergence of CCCP, allowing a more elegant and simple proof. This underlines Zangwill’s theory as a powerful and general framework to deal with the convergence issues of iterative algorithms, after also being used to prove the convergence of algorithms like expectationmaximization, generalized alternating minimization, etc. In this paper, we provide a rigorous analysis of the convergence of CCCP by addressing these questions: (i) When does CCCP find a local minimum or a stationary point of the d.c. program under consideration? (ii) When does the sequence generated by CCCP converge? We also present an open problem on the issue of local convergence of CCCP. 1
Solving Nonlinear Multicommodity Flow Problems By The Analytic Center Cutting Plane Method
, 1995
"... The paper deals with nonlinear multicommodity flow problems with convex costs. A decomposition method is proposed to solve them. The approach applies a potential reduction algorithm to solve the master problem approximately and a column generation technique to define a sequence of primal linear prog ..."
Abstract

Cited by 39 (16 self)
 Add to MetaCart
The paper deals with nonlinear multicommodity flow problems with convex costs. A decomposition method is proposed to solve them. The approach applies a potential reduction algorithm to solve the master problem approximately and a column generation technique to define a sequence of primal linear programming problems. Each subproblem consists of finding a minimum cost flow between an origin and a destination node in an uncapacited network. It is thus formulated as a shortest path problem and solved with the Dijkstra's dheap algorithm. An implementation is described that that takes full advantage of the supersparsity of the network in the linear algebra operations. Computational results show the efficiency of this approach on wellknown nondifferentiable problems and also large scale randomly generated problems (up to 1000 arcs and 5000 commodities). This research has been supported by the Fonds National de la Recherche Scientifique Suisse, grant #12 \Gamma 34002:92, NSERCCanada and ...
Linkstate routing with hopbyhop forwarding can achieve optimal traffic engineering
 In INFOCOM
, 2008
"... Abstract — Linkstate routing with hopbyhop forwarding is widely used in the Internet today. The current versions of these protocols, like OSPF, split traffic evenly over shortest paths based on link weights. However, optimizing the link weights for OSPF to the offered traffic is an NPhard proble ..."
Abstract

Cited by 38 (4 self)
 Add to MetaCart
(Show Context)
Abstract — Linkstate routing with hopbyhop forwarding is widely used in the Internet today. The current versions of these protocols, like OSPF, split traffic evenly over shortest paths based on link weights. However, optimizing the link weights for OSPF to the offered traffic is an NPhard problem, and even the best setting of the weights can deviate significantly from an optimal distribution of the traffic. In this paper, we propose a new linkstate routing protocol, PEFT, that splits traffic over multiple paths with an exponential penalty on longer paths. Unlike its predecessor, DEFT [1], our new protocol provably achieves optimal traffic engineering while retaining the simplicity of hopbyhop forwarding. A gain of 15 % in capacity utilization over OSPF is demonstrated using the Abilene topology and traffic traces. The new protocol also leads to significant reduction in the time needed to compute the best link weights. Both the protocol and the computational methods are developed in a new conceptual framework, called Network Entropy Maximization, where a specific notion of entropy is used to identify the traffic distributions that are not only optimal but also realizable by linkstate routing.
MultiHour, MultiTraffic Class Network Design for Virtual Pathbased Dynamically Reconfigurable WideArea ATM Networks
 IEEE/ACM Trans. on Networking
, 1995
"... Virtual Path (VP) concept has been gaining attention in terms of effective deployment of ATM (Asynchronous Transfer Mode) networks in recent years. In a recent paper, we have outlined a framework and models for network design and management of dynamically reconfigurable ATM networks based on the vir ..."
Abstract

Cited by 32 (6 self)
 Add to MetaCart
Virtual Path (VP) concept has been gaining attention in terms of effective deployment of ATM (Asynchronous Transfer Mode) networks in recent years. In a recent paper, we have outlined a framework and models for network design and management of dynamically reconfigurable ATM networks based on the virtual path concept from a network planning and management perspective. Our approach has been based on statistical multiplexing of traffic within a traffic class by using a virtual path for the class and deterministic multiplexing of different virtual paths, and on providing dynamic bandwidth and reconfigurability through virtual path concept depending on traffic load during the course of the day. In this paper, we discuss in detail a multihour, multitraffic class network (capacity) design model for providing specified qualityofservice in such dynamically reconfigurable networks; this is done based on the observation that statistical multiplexing of virtual circuits for a traffic class in ...
From Finite Covariance Windows to Modeling Filters: A Convex Optimization Approach
 SIAM Review
, 2001
"... Thetrigonom5KO1 mrig tproblem is a classicalmass tproblem with numMO8S applications inm9M86VC5KS9 physics, and engineering. The rational covariance extensionproblem is a constrained version of thisproblem with the constraints arisingfrom the physical realizability of the corresponding solutions. Al ..."
Abstract

Cited by 32 (18 self)
 Add to MetaCart
(Show Context)
Thetrigonom5KO1 mrig tproblem is a classicalmass tproblem with numMO8S applications inm9M86VC5KS9 physics, and engineering. The rational covariance extensionproblem is a constrained version of thisproblem with the constraints arisingfrom the physical realizability of the corresponding solutions. Although themeCM um entropym ethod gives one wellknown solution, in several applications a wider class of solutions is desired. In a semMVV paper, Georgiou derived an existence result for a broad class of m dels. In this paper, we review the history of thisproblem going back to Caratheodory, as well as applications to stochasticsystem and signal processing. In particular, we present a convex optimC5M87M problem for solving the rational covariance extensionproblem with degree constraint. Given a partial covariance sequence and the desired zeros of the shaping filter, the poles are uniquelydetermC98 from the uniquemiqu um of the corresponding optimi CK6M problem In this way we obtain analgorithm for solving the covariance extension problem as well as a constructive proof of Georgiou's existence result and his conjecture, a generalized version of which we have recently resolved usinggeomCM6K mom ds. We also survey recent related results on constrained NevanlinnaPick interpolation in the context of a variationalform ulation of the generalmner tproblem Key words. rational covariance extension, interpolation, partial stochastic realization, trigonomon,C mrig tproblem spectralestim699SV speech processing, stochasticm deling, general mner tproblem AMS subject classifications. 30E05, 42A15, 49N15, 60G35, 62M15, 65K10, 93A30, 93E12 PII. S0036144501392194 1.
Some Approaches to Solving a MultiHour Broadband Network Capacity Design Problem with SinglePath Routing
, 1999
"... In this paper, we consider solution approaches to a multihour combined capacity design and routing problem which arises in the design of dynamically reconfigurable broadband communication networks that uses the virtual path concept. We present a comparative evaluation of four approaches, namely: a ..."
Abstract

Cited by 28 (8 self)
 Add to MetaCart
In this paper, we consider solution approaches to a multihour combined capacity design and routing problem which arises in the design of dynamically reconfigurable broadband communication networks that uses the virtual path concept. We present a comparative evaluation of four approaches, namely: a genetic algorithm; a Lagrangean relaxation based subgradient optimization method; a generalized proximal point algorithm with subgradient optimization; and finally, a hybrid approach where the subgradient based method is combined with a genetic algorithm. Our computational experience on a set of test problems of varying network sizes shows that the hybrid approach often is the desirable choice in obtaining the minimum cost network while the genetic algorithm based approach has the most difficulty in solving large scale problems. Keywords: Broadband network design, multihour network routing and capacity design, combinatorial optimization, genetic algorithm, duality and subgradient optimizati...