This paper analyses the stability and fairness of two classes of rate control algorithm for communication networks. The algorithms provide natural generalisations to large-scale networks of simple additive increase/multiplicative decrease schemes, and are shown to be stable about a system optimum characterised by a proportional fairness criterion. Stability is established by showing that, with an appropriate formulation of the overall optimisation problem, the network's implicit objective function provides a Lyapunov function for the dynamical system defined by the rate control algorithm. The network's optimisation problem may be cast in primal or dual form: this leads naturally to two classes of algorithm, which may be interpreted in terms of either congestion indication feedback signals or explicit rates based on shadow prices. Both classes of algorithm may be generalised to include routing control, and provide natural implementations of proportionally fair pricing.

https://link.springer.com/content/pdf/10.1057%2Fpalgrave.jors.2600523.pdf

Rate control for communication networks: shadow prices, proportional fairness and stability

A survey of current continuous nonlinear multi-objective optimization (MOO) concepts and methods is presented. It consolidates and relates seemingly different terminology and methods. The methods are divided into three major categories: methods with a priori articulation of preferences, methods with a posteriori articulation of preferences, and methods with no articulation of preferences. Genetic algorithms are surveyed as well. Commentary is provided on three fronts, concerning the advantages and pitfalls of individual methods, the different classes of methods, and the field of MOO as a whole. The Characteristics of the most significant methods are summarized. Conclusions are drawn that reflect often-neglected ideas and applicability to engineering problems. It is found that no single approach is superior. Rather, the selection of a specific method depends on the type of information that is provided in the problem, the user’s preferences, the solution requirements, and the availability of software.

Survey of multi-objective optimization methods for engineering

In this paper, we demonstrate the existence of fair end-to-end window-based congestion control protocols for packet-switched networks with first come-first served routers. Our definition of fairness generalizes proportional fairness and includes arbitrarily close approximations of max-min fairness. The protocols use only information that is available to end hosts and are designed to converge reasonably fast. Our study is based on a multiclass fluid model of the network. The convergence of the protocols is proved using a Lyapunov function. The technical challenge is in the practical implementation of the protocols.

https://www-inst.eecs.berkeley.edu/~ee228a/fa03/228A03/papers/Mo.pdf

Fair end-to-end window-based congestion control

In network design, the gap between theory and practice is woefully broad. This book narrows it, comprehensively and critically examining current network design models and methods. You will learn where mathematical modeling and algorithmic optimization have been under-utilized. At the opposite extreme, you will learn where they tend to fail to contribute to the twin goals of network efficiency and cost-savings. Most of all, you will learn precisely how to tailor theoretical models to make them as useful as possible in practice. Throughout, the authors focus on the traffic demands encountered in the real world of network design. Their generic approach, however, allows problem formulations and solutions to be applied across the board to virtually any type of backbone communication or computer network. For beginners, this book is an excellent introduction. For seasoned professionals, it provides immediate solutions and a strong foundation for further advances in the use of mathematical modeling for network design. (Less)

Routing, Flow, And Capacity Design In Communication And Computer Networks

We consider linear quadratic Gaussian (LQG) games in large population systems where the agents evolve according to nonuniform dynamics and are coupled via their individual costs. A state aggregation technique is developed to obtain a set of decentralized control laws for the individuals which possesses an epsiv-Nash equilibrium property. A stability property of the mass behavior is established, and the effect of inaccurate population statistics on an isolated agent is also analyzed by variational techniques.

Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$ -Nash Equilibria

This paper studies the capacity and flow assignment problem arising in the design of self-healing asynchronous transfer mode (ATM) networks using the virtual path concept. The problem is formulated here as a linear programming problem which is solved using standard methods. The objective is to minimize the spare capacity cost for the given restoration requirement. The spare cost depends on the restoration strategies used in the network. We compare several restoration strategies quantitatively in terms of spare cost, notably: global versus failure-oriented reconfiguration, path versus link restoration, and state-dependent versus state-independent restoration. The advantages and disadvantages of various restoration strategies are also highlighted. Such comparisons provide useful guidance for real network design. Further, a new heuristic algorithm based on the minimum cost route concept is developed for the design of large self-healing ATM networks using path restoration. Numerical results illustrate that the heuristic algorithm is efficient and gives near-optimal solutions for the spare capacity allocation and flow assignment for tested examples.

Restoration strategies and spare capacity requirements in self-healing ATM networks

Consideration is given to the problem of optimal flow control in a multiclass telecommunications environment where each user (or class) desires to optimize its performance while being fair to the other users (classes). The Nash (1950) arbitration scheme from game theory is shown to be a suitable candidate for a fair, optimal operation point in the sense that it satisfies certain axioms of fairness and is pareto optimal. This strategy can be realized by defining the product of individuals user performance objectives as the network optimization criterion. This provides the rationale for considering the product of user powers, as has been suggested in the literature. For delay constrained traffic, the constrained optimization problem of maximizing the product of user throughputs subject to the constraints leads to a Nash arbitration point. It is shown that these points are unique in throughput space, and the authors also obtain some convexity properties for power and delays with respect to throughputs in a Jackson network. >

Fairness in network optimal flow control: optimality of product forms

This paper studies the capacity and flow assignment problem arising in the design of self-healing ATM networks using the virtual path (VP) concept The problem is formulated as a linear programming problem which is solved using standard methods The objective is to minimize the spare capacity cost for the given restoration requirement The spare cost depends on the restoration strategies used in the network We compare several restoration strategies, notably, global versus failure-oriented reconfiguration, path versus link based restoration and state-dependent versus state-independent restoration, quantitatively in terms of spare cost The advantages and disadvanages of various restoration strategies are also highlighted Such comparisons provide useful guidance for real network design Further, a new heuristic algorithm is developed for the design of large self-healing ATM networks using path based restoration Numerical results illustrate that the heuristic algorithm is efficient and can give near-optimal solutions for spare capacity allocation and flow assignment

Application of learning automata theory to telephone traffic routing and control is described. Improved network performance is demonstrated through the comparative simulation of learning automata routing and the existing fixed rule alternate routing in simple telephone networks. Learning automata routing results in significantly lower blocking probability when selected overload conditions prevail and additional capacity exists elsewhere in the network.

Application of Learning Automata to Telephone Traffic Routing and Control

A unified framework for traffic control and bandwidth management in ATM networks is proposed. It bridges algorithms for real-time and data services. The central concept of this framework is adaptive connection admission. It employs an estimation of the aggregate equivalent bandwidth required by connections carried in each output port of the ATM switches. The estimation process takes into account both the traffic source declarations and the connection superposition process measurements in the switch output ports. This is done in an optimization framework based on a linear Kalman filter. To provide a required quality of service guarantee, bandwidth is reserved for possible estimation error. The algorithm is robust and copes very well with unpredicted changes in source parameters, thereby resulting in high bandwidth utilization while providing the required quality of service. The proposed approach can also take into account the influence of the source policing mechanism. The tradeoff between strict and relaxed source policing is discussed.

/pdf/a-framework-for-bandwidth-management-in-atm-networks-55f6l4rbk0.pdf

L.G. Mason

Papers

Restoration strategies and spare capacity requirements in self-healing ATM networks

Fairness in network optimal flow control: optimality of product forms

Restoration strategies and spare capacity requirements in self-healing ATM networks

Application of Learning Automata to Telephone Traffic Routing and Control

A framework for bandwidth management in ATM networks—aggregate equivalent bandwidth estimation approach