In and , V. Mancuso, in collaboration with O. Gurewitz ( Ben Gurion University, Israel), J. Shi and E.W. Knightly ( Rice University, USA), tackles the problem of throughput unfairness for IEEE 802.11-based wireless mesh nodes. This unfairness is shown to be strongly correlated with the spatial distribution of the wireless nodes. The work in gives experimental evidence of the problem, provides an analytical model that allows one to understand the origin of the protocol unfairness, and proposes a MAC-based solution to unfairness. In , the spatial unfairness is tackled via elastic rate limiting strategies to be implemented in a few selected network nodes.

D. Mazauric and P. Nain, in collaboration with J-C. Bermond ( Inriaproject-team Mascotte) and V. Misra ( University of Columbia, USA), have investigated the problem of distributed transmission scheduling in wireless networks. Due to interference constraints, “neighboring links” cannot be simultaneously activated, otherwise transmissions will fail. In , , they consider any binary model of interference. Traffic is assumed to be single-hop, time is slotted and calls arrive randomly on each link during a time slot. They design a fully distributed local algorithm which works for any arbitrary binary interference model and with a constant overhead (w.r.t. the network size and the backlog in the queues). Furthermore, as opposed to other existing algorithms, their algorithm performs without knowing the queue backlogs at the “neighboring links”, an information which is typically difficult to collect in a wireless network with interference. Sufficient conditions for stability under Markovian assumptions are derived. The performance of the proposed algorithm (throughput, stability) is investigated via simulations. The results show that its performance favorably compares to that of previously proposed schemes.

In collaboration with T. Başar ( University of Illinois at Urbana-Champaign, USA) and F. De Pellegrini ( Create-Net, Italy), E. Altman has pursued and intensified his research on the optimal control of DTNs. Two main frameworks have been used: (i) the monotone framework, where it is assumed that the number of mobiles having a packet is a non-decreasing function of time, together with trajectorial pathwise arguments, give rise to optimal threshold type policies , and (ii) the linear quadratic framework, where when two-hop routing is enforced then the system's dynamic is often linear in the state and control. If the costs functions to be minimized can be expressed as quadratic functions of the state and/or of the control then optimal control policies can be obtained explicitly using the theory of linear quadratic regulator. This approach was carried out in .

The paper by E. Altman and P. Nain, in collaboration with J.-C. Bermond ( Inriaproject-team Mascotte), has appeared in the proceedings of Infocom 2009. It concerned yet other aspects of optimization related to optimal forwarding and thus of storage of evolving files. The interested reader is referred to Maestro 2008 activity report for more details.

Other issues related to distributed optimal control and to learning in case of unknown parameters have appeared in . These results by E. Altman and G. Neglia, together with F. De Pellegrini and D. Miorandi ( Create-Net, Italy) have already been described in Maestro 2008 activity report.

The particular structure of two-hop routing is useful for getting explicit expressions for the dynamics and for the optimal control not only in the linear quadratic control context but also in the case of competition between mobile nodes. In , E. Altman considers the stochastic framework with finite number of mobiles and obtains simple new closed-form expressions for the performance measures as a function of the controls. After studying both cooperative and competitive scenarios (through a team and a non-cooperative game formulations), the convergence to a mean field limit is established. This is extended to the more granular chunk level modeling of the system.

The ability of DTNs to deliver packets from a source to a destination comes at a cost of resources needed for storage of many copies of the packets in mobile (relay) nodes. An efficient way of coding the packet can substantially increase the diversity and have a significant impact on the system's capacity. This is illustrated in where E. Altman, together with F. De Pellegrini ( Create-Net, Italy) study the impact of various coding mechanisms on the system performance in terms of tradeoff between throughput and energy.

Various models of DTNs with two-hop routing can be described and analyzed using branching processes. In , E. Altman and D. Fiems ( University of Gent, Belgium) identify such examples in which a file is dessiminated in the network. They study the performance measures under varying Markov environment. They obtain the first two order-moments of the number mobiles in the system that possess a copy of the file.

In , , G. Neglia, G. Reina, and S. Alouf address the problem of designing adaptive epidemic-style forwarding mechanisms for message delivery in DTNs. The approach is based on a new analytical framework for multi-agent optimization through distributed subgradient methods. They investigate how this framework can be adapted to the considered networking problem and perform a preliminary evaluation, which shows promising results in terms of convergence speed.

This research has been partially supported by the Ist Fetgrant Bionets(see Section ) and the NoE EuroNF(see Section ).

U. Acer, G. Neglia, L. Rocha, together with P. Giaccone, D. Hay, and S. Tarapiah (Politecnico di Torino, Italy) have opened a new research direction by investigating routing in DTNs where the underlying node mobility is known in advance but can be modified by random effects. They have called these networks “quasi-deterministic” DTNs. This research direction has been the object of the Colorproject Crasquidem(see Section ) and is described in  . In June 2009 the Torino public transportation society has started being involved in this research.

In E. Altman, in collaboration with M. Khouzani and S. Sarkar ( University of Pennsylvany, USA), considers a defense strategy in a DTN networks under a virus attack. The authors study a policy that quarantines nodes that are not vaccinated against the virus by reducing the communication range. This countermeasure involves a trade-off: reducing the communication range suppresses the spread of the malware, however, it also negatively affects the performance of the network as the end-to-end communication delay increases. The authors model the propagation of the malware as a deterministic epidemic. Using an optimal control framework, they select the optimal communication range that captures the above trade-off by minimizing a global cost function. Using Pontryagin's Maximum Principle, the authors derive structural characteristics of the optimal communication range as a function of time for two different cost functions.

In , V. Kavitha and E. Altman study the concept of Ferry based Wireless Local Area Network (FWLAN), in which a number of isolated nodes are scattered over some area and where communication between a node and the outer world, or communication between the nodes, are made possible via a message ferry. The ferry has a predetermined cyclic path; it collects messages from a node and delivers messages to it when it is in the vicinity of the node. They use the mathematical theory of polling systems to study the performance of the FWLAN. They consider three different architectures and each one of them is mapped into an appropriate polling system. The polling disciplines that are needed for modeling the FWLAN involve non-standard variants of the so-called gating disciplines. The goal is to design the routes of the ferry as well as the points where it should stop to distribute and collect messages. This mathematical modeling brings another dimension to the classical related vehicle routing problem due to the radio channel: the cyclic path of the ferry need not touch every node. The distance between the node and the ferry at the point when communication occurs determines the transmission rate and hence the service time and thus the system capacity.

A key criterion used to measure communication protocol efficiency in Wireless Sensor Networks (WSNs) is the energy consumption and the lifetime of these networks. In collaboration with J. Champ, C. Saad and V. Boudet ( University of Montpellier II, Cnrs), A.-E. Baert has pursued her work on energy-aware protocol engineering for sensor networks. Existing criteria to measure network lifetime in WSNs have been surveyed and two new criteria (Average Node Percentage and Monitored Interest Point Percentage) have been introduced in .

In these authors have proposed the Dynamic Localized Broadcast Incremental Power Protocol(DLBIP), a new localized broadcast protocol whose principle is to use dynamic broadcast trees to improve lifetime. The study is based on the best known localized algorithm, namely LBIP, which is based on a centralized one, BIP, whose principle consists in constructing a broadcast tree rooted at the source node, taking into account the specificities of wireless networks. DLBIP can guarantee the reception of broadcast messages in the network in the sense that over 90% of the sensors receive the broadcast messages.

E. Altman, in collaboration with A. Kumar and V. Ramaiyan ( IISc, Bangalore, India), considers in a dense, ad hoc wireless network, confined to a small region. The wireless network is operated as a single cell, namely only one successful transmission is supported at a time. Data packets are sent between source destination pairs by multihop relaying. It is assumed that nodes self-organize into a multihop network such that all hops are of length dmeters, where dis a design parameter. There is a contention based multi-access scheme, and it is assumed that every node always has data to send, either originated from it or a transit packet (saturation assumption). In this scenario, the authors seek to maximize a measure of the transport capacity of the network (measured in bit-meters per second) over power controls (in a fading environment) and over the hop distance d, subject to an average power constraint. The authors first argue that for a dense collection of nodes confined to a small region, single cell operation is efficient for single user decoding transceivers. Then, operating the dense ad hoc wireless network (described above) as a single cell, the authors study the hop length and power control that maximizes the transport capacity for a given network power constraint.

E. Altman and A. Silva have pursued their line of research started on 2007 and dedicated to studying the routing in very dense static ad hoc. Their results obtained since 2007, and described in the activity reports of the last two years, have been summarized in a journal paper that has now appeared .

In the context of the Anrgrant Winem(see Section ), V. Mancuso and S. Alouf have surveyed the strategies adopted by base station manufacturers and operators on the road towards a low-cost and environment-friendly wireless networking. Most of the current green best practices concern the rationalization of (i) capital expenditures, by optimizing the base station site architecture and the distribution of the sites over the targeted coverage area, and (ii) operational expenditures, by minimizing the energy consumption of electronic devices and reducing the need for cooling systems. In addition, new software-based management tools have been coming into play, which try to enforce a sleep mode on those equipments that are expected to handle low or no traffic during the off-peak hours.

E. Altman and S. Ramanath have been working within the ADR SelfNetas part of the joint INRIA Alcatel-Lucent Bell Labs (see Section ).

In S. Ramanath and E. Altman, in collaboration with V. Kumar ( Alcatel-Lucent Bell Labs) and M. Debbah ( Institut Eurecom), present a systematic study of the uplink capacity and coverage of pico-cell wireless networks. Both the one dimensional and the two dimensional cases are investigated. The goal is to compute the size of pico-cells that maximizes the spatial throughput density. To achieve this goal, the authors consider fluid models that allow them to obtain explicit expressions for the interference and the total received power at a base station. They also study the impact of various parameters on the performance: the path loss factor, the spatial reuse factor and the receiver structure (matched filter or multiuser detector). Finally, the authors relate the performance of the fluid models to that of the original discrete system, and show that the fluid model provides a bound for the discrete one.

In , S. Ramanath, E. Altman and V. Kavitha, in collaboration with V. Kumar and L. Thomas ( Alcatel-Lucent Bell Labs), address the problem of fair assignment of base station locations in a cellular network. The authors use the generalized -fairness criterion, which encompasses a contimuum set of fair assignments parametrized by a real number . The set includes that of global, proportional, harmonic or max-min fairness in the study. They derive explicit expression for -fair base station locations under large population limits in the case of simple one dimensional models. They show analytically that as increases asymptotically, the optimal location for a single base station converges to the center of the cell. The authors validate the analysis via numerical examples. They further study throughput achievable as a function of -fair base-station placement, path-loss factor and noise variance via numerical examples. They also address the problem of optimal placement of two base stations and obtain similar conclusions.

In , E. Altman, jointly with H. Kameda ( University of Tsukuba, Japan), C. Touati and A. Legrand ( Inriaproject-team Mescal), has proposed a new fairness concept for resource sharing among users. The starting point is that a Nash equilibrium is often considered to be fair since it is by definition an outcome of a competition with no collusions. On the other hand, a Nash equilibrium can be non-efficient since it can be dominated by other policies. The authors establish the existence of efficient policies that are on the one hand Pareto optimal and on the other hand proportional to a Nash equilibrium. These properties are used to define a new fairness criterion.

In , E. Altman, S. Soudan, D. Divakaran and P. Primet ( Inriaproject-team Reso) study competitive situations that occur as a result of the differentiation between short and long flows. A long session can be presented as a number of short sessions in order to avoid being recognized and treated as a long session. The authors characterize the equilibrium.

In  G. Neglia, together with D. Menasche, D. Towsley and S. Zilberstein ( University of Massachusetts at Amherst, USA) study the problem of how to combine files into bundles in swarming systems. In particular, they analyze the case of a monopoly where a single publisher decides how to aggregate its files so as to satisfy user demands while mitigating its serving costs. They establish conditions for the existence and uniqueness of an equilibrium and have shown how the publisher's bundling strategy affects its profit. Moreover, they also consider the competitive case where bundling decisions of one publisher affect the outcome of other publishers. Using normal form games they analyze the impact of different system parameters on the Nash equilibrium.

The problem of jamming plays an important role in ensuring the quality and security of wireless communications, especially at nowadays when wireless networks are quickly becoming ubiquitous. Jamming is a form of a denial of service attack in which an adversary can degrade the quality of the reception by creating interference. One can study jamming both in the purpose of protecting a wireless network against such attack or, on the contrary, in order to efficiently disrupt the communications of some adversary. In both cases jamming is part of a conflict for which game theory is an appropriate tool. In a series of papers , , E. Altman, K. Avrachenkov and A. Garnaev ( St. Petersburg State University, Russia) analyze the jamming in wireless networks with partial information available. In particular, in they study the scenario where users do not know how jamming efforts are distributed among sub-carriers and also do not know the fading channels gains with certainty. In the authors consider the scenario when a user either does not have a complete information about the total energy available to the jammer or the user is not sure if the jammer is present in the environment. In the same scenarios as in are considered but with a more general utility function, the -fairness utility function. Finally, in the case of several jammers is investigated.

In collaboration with S. Sarkar ( University of Pennsylvania, USA), R. El-Azouzi and Y. Hayel ( University of Avignon), E. Altman investigates in a game in which nchannels are available to a mobile. The authors consider some adversarial node that can prevent the mobile to obtain the information on the state of kout of the nchannels. Using a zero-sum Bayesian game model, they answer the questions of which state-dependent jamming policy is the most harmful and what is the best way for the other mobile to react.

In WiFi networks, mobile nodes compete for accessing the shared channel by means of a random access protocol called Distributed Coordination Function (DCF), which is long term fair. Selfish nodes could benefit from violating the protocol and increasing their transmission probability. In  , , , G. Neglia, I. Tinnirello and L. Giarre  ( University of Palermo, Italy) study the interaction of selfish nodes in two different scenarios. In the first, one mobile stations are simply interested to maximize their upload rate to a single Access Point (AP); in the second one, they are also interested in their downlink rate. The work highlights the poor performance in presence of selfish behaviors and study the role of the AP in WiFi networks in infrastructure mode. Simple changes to AP functionalities can be introduced to design the game in order to achieve optimal global performance at Nash equilibrium. This work has also been presented to a larger community of researchers through the signal processing magazine  .

In S. Lasaulce, M. Debbah ( Supelec) and E. Altman present an overview of foundations and tools of game theory that are relevant to wireless communications. Both finite as well as infinite populations of players are considered and various solution concepts (equilibria) are overviewed. Another survey paper by E. Altman in collaboration with R. El-Azouzi, Y. Hayel and H. Tembine ( University of Avignon) focuses on evolutionary games and their applications to wireless networks (see ).

In collaboration with R. El-Azouzi ( University of Avignon) and R. Sundaresan ( IISc, Bangalore, India), V. Kavitha and E. Altman study in a centralized dynamic scheduling decision that has to be made by a base station to fair share the resources, based on the current channel gains signaled by the mobiles. Mobiles can be non-cooperative in the sense that they may erroneously signal to improve their own utilities. The authors formulate this non cooperative scheduling problem by using a signaling game, where (1) mobiles (lead players) signal the base station of their channel value, (2) base station (follower) makes a scheduling decision using the signals, (3) scheduling decision determines the payoff for all mobiles, base station. It is shown that this signaling game admits only babbling equilibria: mobile's strategy is to signal regardless of its channel. The base station's strategy is to ignore the signals from mobiles. Various approaches are then proposed so as to enforce truthful signaling of the radio channel conditions including a distributed stochastic approximation approach that combines estimation and control.

In , E. Altman with A. Kumar, C. Singh and R. Sundaresan ( IISc, Bangalore, India) consider the question of determining locations of base stations (BSs) that may belong to the same or to competing service providers, taking into account the impact of these decisions on the behavior of intelligent mobile terminals who can connect to the base station that offers the best utility. They first study the Signal to Interference and Noise Ratio (SINR) association-game: the authors determine the cells corresponding to each base station, namely, the locations at which mobile terminals prefer to connect to a given base station than to others. SINR is used as the quantity that determines the association. They make some surprising observations: (i) displacing a base station a little in one direction may result in a displacement of the boundary of the corresponding cell to the opposite direction, and (ii) a cell corresponding to a BS may be the union of disconnected sub-cells. They further study the Stackelberg equilibrium in the combined BS location and mobile association problem: they determine where to locate the BSs so as to maximize the revenues obtained at the induced SINR mobile association game. They consider the cases of single frequency band and two frequency bands of operation. Finally, they study Stackelberg equilibria in two frequency systems with successive interference cancellations.

In E. Altman, jointly with G. Kasbekar and S. Sarkar ( University of Pennsylvania, USA), considers a scenario in which a regulator owns the spectrum in a certain region. A number of service providers lease spectrum from the regulator. Each service provider sets up a base station to serve mobile subscribers in the region. This gives rise to a hierarchical game with players at three levels: the mobile subscribers (level 1), the service providers (level 2) and the regulator (level 3). In the game at level 3, the regulator chooses the price at which to lease the spectrum. In the game at level 2, each service provider chooses the quantity of spectrum to lease from the regulator and the rate at which to charge the mobile subscribers. The authors consider the situation in which each service provider has two kinds of mobile subscribers: primary users, who receive high-priority service and secondary users who receive low-priority service. In the game at level 1, each mobile subscriber chooses a service provider to join and whether to become a primary or secondary user. Using game theoretic tools the authors compute the equilibrium strategies at all three levels.

In , E. Altman, A. Kumar ( IISc, Bangalore, India) and Y. Hayel ( University of Avignon) consider a resource allocation problem in a multichannel wireless access system being shared by several users for uplink transfer of elastic traffic. Each user can allocate its resources (e.g., radios, antennas or power) to one or more of the carriers. The authors consider a problem of noncooperative allocation of resources by the users, each user's objective being to maximize its own utility. The theory of potential games is used to solve this problem by transforming it into an equivalent global optimization one. Structural properties of the equilibrium policies are obtained using tools from Schur concave stochastic order. Finally, a distributed algorithm is introduced and is shown to converge to a Nash equilibrium of the system.

In collaboration with E. Sabir, R. El-Azouzi, Y. Hayel ( University Avignon) and E.-H. Bouyakhf ( University of Mohammed V, Morocco), V. Kavitha considers in finite number of users, with infinite buffer storage, sharing a single channel using the Aloha medium access protocol. They investigate the uplink case of a cellular system where each user will select a desired throughput. The users then participate in a non cooperative game wherein they adjust their transmit rate to attain their desired throughput. In contrast to the saturated case, the authors show that the game either has no Nash equilibrium or has infinitely many Nash Equilibria (NE). They further show that the region of NE coincides with an appropriate “stability region”. The authors discuss the efficiency of the equilibria in term of energy consumption and congestion rate. Next, they propose two learning algorithms using a stochastic iterative procedure that converges to the best Nash equilibrium. They approximate the control iterations by an equivalent ordinary differential equation in order to prove that the proposed stochastic learning algorithm converges to a Nash equilibrium even in the absence of any coordination or extra information. Extensive numerical examples and simulations are provided to validate the results.

In evolutionary games, various populations have an impact on each other through a large number of local interactions each involving a small number of players. Each such interaction defines a fitness that depends on the actions of each player involved. In , E. Altman, Y. Hayel, H. Tembine and R. El-Azouzi ( University of Avignon) add a notion of individual state to these games and consider the situation in which an action of a player determines not only its immediate fitness in given stage but also the transition probabilities to the next state. The player no longer maximizes her/his immediate fitness but rather maximizes the expected average cummulated fitness over time. The authors define an appropriate notion of equilibrium and propose a way to compute it. Applications to energy management problems are described by .

Population games are similar to evolutionary games with the difference that interactions are not any more local but involve a continuum of players. In , P. Wiecek ( University of Wroclaw, Poland), E. Altman and Y. Hayel ( University of Avignon) study a dynamic version of such games where each player has some individual state, and the actions of the player determine the transitions between the states. They use this formalism to solve a power control problem in a CDMA system (where all mobiles use the same spectrum of frequencies at the same time). To do so, they adapt the theory of anonymous sequential games by Jovanovic & Rosenthal, J Math. Econ, 1988.

Non-cooperative game theory has gained much interest as a paradigm for decentralized control in communication networks. It allows one to get rid of the need for a centralized controller. Decentralizing the decision making may result in situations where agents (decision makers) do not have the same view of the network. The global view of the network state cannot be available to an agent as fast as the information on its local state. Incorporating into the decentralized control paradigm this information asymmetry renders it applicable to a much wider class of situations. In , E. Altman, V. Kamble and A. Silva model the above information asymmetry using the one-step delay sharing information pattern from team theory and generalize it to the context of non-cooperative games. They study its properties and apply it to a distributed power control problem.