Corinne Touati

Generalized nash bargaining solution for bandwidth allocation

For over a decade, the Nash Bargaining Solution (NBS) concept from cooperative game theory has been used in networks to share resources fairly. Due to its many appealing properties, it has recently been used for assigning bandwidth in a general topology network between applications that have linear utility functions. In this paper, we use this concept for allocating the bandwidth between applications with general concave utilities. Our framework includes in fact several other fairness criteria, such as the max-min criteria. We study the impact of concavity on the allocation and present computational methods for obtaining fair allocations in a general topology, based on a dual Lagrangian approach and on Semi-Definite Programming.

Fair and Efficient User-Network Association Algorithm for Multi-Technology Wireless Networks

Recent mobile equipment (as well as the norm IEEE 802.21) offers the possibility for users to switch from one technology to another (vertical handover). This allows flexibility in resource assignments and, consequently, increases the potential throughput allocated to each user. In this paper, we design a fully distributed algorithm based on trial and error mechanisms that exploits the benefits of vertical handover by finding fair and efficient assignment schemes. On the one hand, mobiles gradually update the fraction of data packets they send to each network based on the rewards they receive from the stations. On the other hand, network stations send rewards to each mobile that represent the impact each mobile has on the cell throughput. This reward function is closely related to the concept of marginal cost in the pricing literature. Both the station and the mobile algorithms are simple enough to be implemented in current standard equipment. Based on tools from evolutionary games, potential games and replicator dynamics, we analytically show the convergence of the algorithm to fair and efficient solutions. Moreover, we show that after convergence, each user is connected to a single network cell which avoids costly repeated vertical handovers. To achieve fast convergence, several simple heuristics based on this algorithm are proposed and tested. Indeed, for implementation purposes, the number of iterations should remain in the order of a few tens.

Fair power and transmission rate control in wireless networks

In third generation mobile networks, transmission rates can be assigned to both real time and non real time applications. We address in this paper the question of how to allocate transmission rates in a manner that is both optimal and fair. As optimality criterion we use the Pareto optimality notion, and as fairness criterion we use a general concept of which the max-min fairness (which is the standardized fairness concept in ATM networks) and the proportional fairness (which characterizes fairness obtained by transport protocols for the Internet) are special cases. We formulate the fair allocation problems as optimization problems and propose an approximating solution.

Non-Cooperative Scheduling of Multiple Bag-of-Task Applications

Multiple applications that execute concurrently on heterogeneous platforms compete for CPU and network resources. In this paper we analyze the behavior of K non-cooperative schedulers using the optimal strategy that maximize their efficiency while fairness is ensured at a system level ignoring applications characteristics. We limit our study to simple single-level master-worker platforms and to the case where each scheduler is in charge of a single application consisting of a large number of independent tasks. The tasks of a given application all have the same computation and communication requirements, but these requirements can vary from one application to another. In this context, we assume that each scheduler aims at maximizing its throughput. We give closed-form formula of the equilibrium reached by such a system and study its performance. We characterize the situations where this Nash equilibrium is optimal (in the Pareto sense) and show that even though no catastrophic situation (Braess-like paradox) can occur, such an equilibrium can be arbitrarily bad for any classical performance measure.

Nash equilibrium based fairness

There are several approaches of sharing resources among users. There is a noncooperative approach wherein each user strives to maximize its own utility. The most common optimality notion is then the Nash equilibrium. Nash equilibria are generally Pareto inefficient. On the other hand, we consider a Nash equilibrium to be fair as it is defined in a context of fair competition without coalitions (such as cartels and syndicates). We show a general framework of systems wherein there exists a Pareto optimal allocation that is Pareto superior to an inefficient Nash equilibrium. We consider this Pareto optimum to be ‘Nash equilibrium based fair.’ We further define a ‘Nash proportionately fair’ Pareto optimum. We then provide conditions for the existence of a Pareto-optimal allocation that is, truly or most closely, proportional to a Nash equilibrium. As examples that fit in the above framework, we consider noncooperative flow-control problems in communication networks, for which we show the conditions on the existence of Nash-proportionately fair Pareto optimal allocations.

Self-optimizing routing in MANETs with multi-class flows

In this paper we show how game theory and Gibbs sampling techniques can be used to design a self-optimizing algorithm for minimizing end-to-end delays for all flows in a multi-class mobile ad hoc network (MANET). This is an improvement over the famed Ad-Hoc On-demand Distance Vector (AODV) protocol, that computes the routes with minimal number of hops for each flow in a multi-flow ad-hoc network. Here, the load of each flow is taken into account to choose the best route (in terms of delays) among a fixed number of routes. The algorithm can be implemented in a fully distributed and asynchronous way and is guaranteed to converge to the global optimal configuration. Numerous numerical experiments show that the gain over AODV, computed over a large number of networks, is quite substantial.

Selection of efficient pure strategies in allocation games

In this work we consider allocation games and we investigate the following question: under what conditions does the replicator dynamics select a pure strategy?

Capacity planning, quality of service and price wars

We model the relationship between capacity, Quality of Service (QoS) and offered prices of service providers in a competitive e-services market. Capacity and QoS are linked through simple queueing formulae while QoS and price are coupled through distributions on customer preferences. We study the sensitivity of market share of providers to price, capacity and market size. We revisit the notion of price wars that has been shown to lead to zero profits for all providers and conclude that our more general model does admit some form of anomalous behavior, but which need not lead to zero profits.

No regrets: Distributed power control under time-varying channels and QoS requirements

The problem of power control in wireless networks consists of adjusting transmit power in order to achieve a target SINR level in the presence of noise and interference from other users. In this paper, we examine the performance of the seminal Foschini-Miljanic (FM) power control scheme in networks where channel conditions and users quality of service (QoS) requirements vary arbitrarily with time (e.g. due to user mobility, fading, etc.). Contrary to the case of static and/or ergodic channels, the system optimum power configuration may evolve over time in an unpredictable fashion, so users must adapt to changes in the wireless medium (or their own requirements) “on the fly”, without being able to anticipate the system evolution. To account for these considerations, we provide a formulation of power control as an online optimization problem and we show that the FM dynamics lead to no regret in this dynamic context. Specifically, in the absence of maximum transmit power constraints, we show that the FM power control scheme performs at least as well as (and typically outperforms) any fixed transmit profile, irrespective of how the system varies with time; finally, to account for maximum power constraints that occur in practice, we introduce an adjusted version of the FM algorithm which retains the convergence and no-regret properties of the original algorithm in this constrained setting.

A User Centered Multi-Objective Handoff Scheme for Hybrid 5G Environments

In this paper, we propose a user centered handoff scheme for hybrid 5G environments. The handoff problem is formulated as a multi-objective optimization problem which maximizes the achievable data receiving rate and minimizes the block probability simultaneously. When a user needs to select a new Base Station (BS) in handoff, the user will calculate the achievable data receiving rate and estimate the block probability for each available BS based on limited local information. By taking the throughput metric into consideration, the formulated multi-objective optimization problem is then transformed into a maximization problem. We solve the transformed maximization problem to calculate the network selection result in a distributed method. The calculated network selection result is proved to be a Pareto Optimal solution of the original multi-objective optimization problem. The proposed scheme guarantees that based on limited local information, each user can select a new BS with high achievable data receiving rate and low block probability in handoff. Comprehensive experiment has been conducted. It is shown that the proposed scheme promotes the total throughput and ratio of users served significantly.