Lacra Pavel

An extension of duality to a game-theoretic framework

This paper extends some duality results from a standard optimization setup to a noncooperative (Nash) game framework. A Nash game (NG) with coupled constraints is considered. Solving directly such a coupled NG requires coordination among possibly all players. An alternative approach is proposed based on its relation to a special constrained optimization problem for the NG-game cost function, with respect to the second argument that admits a fixed-point solution. Specific separability properties of the NG-game cost are exploited and duality results are developed. This duality extension leads naturally to a hierarchical decomposition into a lower-level NG with no coupled constraints, and a higher-level system optimization problem. In the second part of the paper these theoretical results are applied to a coupled NG with coupled constraints as encountered in optical networks.

A noncooperative game approach to OSNR optimization in optical networks

We consider a game theory framework for power control in optical networks. Channel optical signal-to-noise ratio (OSNR) optimization is formulated as an m-player noncooperative game, based on a general network OSNR model. Conditions for existence and uniqueness of the game equilibrium solution are given. An iterative algorithm for power control is proposed, that uses only channel specific feedback measurements and is shown to converge to the equilibrium solution.

Nash equilibrium design and optimization

The general problem of Nash equilibrium design is investigated from an optimization perspective. Within this context, a specific but fairly broad class of noncooperative games are considered that have been applied to a variety of settings including network congestion control, wireless uplink power control, and optical power control. The Nash equilibrium design problem is analyzed under various knowledge assumptions (full versus limited information) and design objectives (QoS versus utility maximization). Among other results, the “price of anarchy” is shown not to be an inherent feature of games that incorporate pricing mechanisms, but merely a misconception that often stems from arbitrary choice of game parameters. Moreover, a simple linear pricing is sufficient for design of Nash equilibrium according to a chosen global objective for a general class of games and under suitable information assumptions.

OSNR optimization in optical networks: modeling and distributed algorithms via a central cost approach

This paper addresses the problem of optical signal-to-noise ratio (OSNR) optimization in optical networks. An analytical OSNR network model is developed for a general multilink configuration, that includes the contribution of amplified spontaneous emission and crosstalk accumulation. The network OSNR optimization problem is formulated such that all channels maintain a desired individual OSNR level, while input optical power is minimized. Conditions for existence and uniqueness of the optimal solution are given. An iterative, distributed algorithm for channel power control is proposed, which is shown to converge geometrically to the optimal solution. The algorithm is valid for general network configurations, and uses only local measurements or decentralized feedback. Convergence is proved for both synchronous and asynchronous operation, which is particularly important for adaptation in a dynamic environment

Game Theory for Control of Optical Networks

Optical networks epitomize complex communication systems, and they comprise the Internets infrastructural backbone. The first of its kind, this book develops the mathematical framework needed from a control perspective to tackle various game-theoretical problems in optical networks. In doing so, it aims to help design control algorithms that optimally allocate the resources of these networks. With its fresh problem-solving approach, Game Theory in Optical Networks is a unique resource for researchers, practitioners, and graduate students in applied mathematics and systems/control engineering, as well as those in electrical and computer engineering.

Dynamics and stability in optical communication networks: a system theory framework

This paper addresses the problem of dynamics analysis in optical networks from a system control perspective. A general framework for finding the transfer matrix representation of an optical network is developed, based on linear fractional transformations. Under the natural assumption of equal time-delay for all channels in a link, the network transfer matrix is simplified such that channel cross-coupling is evidenced. The optical network stability problem is then reformulated as a robust stability problem and stability conditions are developed by applying @m-analysis.

Control design for transient power and spectral control in optical communication networks

This paper presents control applications to power control in optical communication networks. We consider transient power control across optical communication links, and spectral power control at composite optical amplifier sites. A decentralized network control strategy is proposed that ensures robust handling of dynamic network reconfiguration, with minimization of optical power transient excursions across network. We present control system design aspects as well as experimental results based on an actual implemented case.

Games with coupled propagated constraints in optical networks with multi-link topologies

We consider games in optical networks in the class of m-player games with coupled utilities and constraints. Nash equilibria of such games can be computed based on recent extension of duality to a game theoretical framework. This work extends previous results on games with coupled constraints in optical links to multi-link topologies. Coupled constraints in optical networks are propagated along links, which introduces additional complexities for analysis. Specifically, convexity of the propagated constraints is no longer automatically ensured. We show that convexity is satisfied for single-sink multi-link topologies. The general case of multi-links with arbitrary sources and sinks is dealt with by a partitioned game with stages. We exploit the single-sink structure of each stage and the ladder-nested form of the game and we discuss iterative computation of equilibria based on a three-level hierarchical algorithm and prove its convergence under certain conditions.

A system performance approach to OSNR optimization in optical networks

This paper studies a constrained optical signal-to-noise ratio (OSNR) optimization problem in optical networks from the perspective of system performance. A system optimization problem is formulated with the objective of achieving an OSNR target for each channel while satisfying the total power constraint. In order to establish existence of a unique optimal solution, the conditions are derived, which can be used as a basis for an admission control scheme. The original problem is then converted to a relaxed system problem by using a barrier function and solved by a distributed iterative algorithm. Next, the system optimization framework developed is compared to the game theoretic one in [1]. The effects of parameters in both formulations are investigated to study efficiency of Nash equilibria in the OSNR game and pricing mechanisms affecting overall system performance. The theoretical analysis is supported by numerical simulations and experiments conducted on an optical fiber link.

A control theoretic approach to noncooperative game design

This paper investigates design of noncooperative games from a control theoretic perspective. Pricing mechanisms are used as a design tool to ensure that the Nash equilibrium of a broad class of noncooperative games satisfies certain global objectives such as welfare maximization. The class of games considered provide a theoretical basis for a variety of decentralized resource allocation and control problems including network congestion control, wireless uplink power control, and optical power control. The game design problem is analyzed under full and limited information assumptions for dynamic systems and nonseparable utility functions. Stability properties of the game and pricing dynamics are studied under the assumption of timescale separation and in two separate time-scales. Thus, sufficient conditions are derived, which allow the designer to place the Nash equilibrium solution or to guide the system trajectory to a desired region or point. The obtained results are illustrated with examples.