## Section: New Results

### Wireless Access Networks

Participants : Jean-Claude Bermond, David Coudert, Afonso Ferreira, Jérôme Galtier, Luisa Gargano, Cristiana Gomes, Dorian Mazauric, Christelle Molle, Julian Monteiro, Napoleão Nepomuceno, Nicolas Nisse, Stéphane Pérennes, Patricio Reyes, Hervé Rivano, Ugo Vaccaro, Joseph Yu.

Mascotte has conducted an intense research effort on wireless access networks. From the technological and architectural point of view, the field is broad, from mesh (or multi-hop cellular) networks to *ad-hoc* and sensor networks. Nevertheless, many questions and approaches are generic from an algorithmic and structural viewpoint.

In particular, we have studied three of the more prominent performance metrics for radio networks. Using combinatorial optimization and centralized algorithmic with a network design flavor, transport capacity and energy consumption of the networks have been studied. Using distributed algorithmic with a protocol flavor, fast data gathering and call scheduling are investigated. Our approach is complementary with those developed in other INRIA project-teams such as Planete , Maestro , Swing (ex Ares ) or Pops . The complementarity has been exploited through an ARC collaboration with Ares and Pops , a joint Ph.D. between Maestro and Mascotte and, recently, an ANR VERSO project in which Maestro , Mascotte and Swing are involved.

At the international level, our researches are comparable and collaborative with some groups in renowned research centers such as CTI of Patras in Greece, Universities of Roma or Salerno in Italy, the Technion Institute in Israël, SFU in Vancouver, Canada, UFC, Universidade Federal do Ceará, Fortaleza, Brazil, or the University of Sao Paulo in Brazil.

We studied a wide range of issues of wireless networks, from the design of efficient cross-layer medium access, call scheduling and routing techniques and energy efficient optimization, to the development of theoretical tools for analyzing and evaluating dynamic networks. Some graph coloring problems motivated by channel assignment in wireless networks are detailed in Section 6.5 and the optimization techniques and wireless simulation tools that we have developed are also cited in Section 6.4 .

#### Transport capacity of wireless access networks

The specific challenges of multihop wireless networks lead to a strong research effort on efficient protocols design where the offered capacity is a key objective. More specifically, the routing strategy largely impacts the network capacity, i.e. the throughput offered to each flow.

In these settings, [15] focuses on optimizing the capacity of wireless mesh networks defined as the fair throughput offered to each flow. In order to get theoretical bounds on the network performances, we develop optimization models integrating the cross-layer characteristics of radio communications. More precisely, we study the joint routing and scheduling problem. We develop, for the linear relaxation of the problem, a resolution method based on the column generation process. We derive a linear formulation which focuses on the transport capacity available on the network cuts. We prove the equivalence of the models, and adapt the resolution method into a cross line and column generation process. Through tests, we point out a contention area located around the mesh gateways which constraints the network capacity. These results are applied to a quantitative study of the effects of acknowledgments on the capacity. We then present a stability study of a protocol which routes a traffic injected arbitrarily. We improve existing results by showing the stability even if the total traffic injected is a maximum flow. All this research work has been implemented in the open-source library MASCOPT (Mascotte Optimisation) dedicated to network optimization problems.

[68] deals with the rate allocation problem for downlink in a Multi-hop Cellular Network. A mathematical model is provided to assign transmission rates in order to reach an optimal and fair solution. We prove and valid experimentally that under some conditions that are often met, the problem can be reduced to a single-hop cellular network problem.

[79] is dedicated to a specific work about the impact of the MAC layer type on the capacity of the network. Using linear programming models, we compare the capacity of a network with MAC link per link acknowledgment to the case where the acknowledgments are done by the transport layer (TCP like).

[46] provides a complete framework based on linear programming to compute upper and lower bounds on the capacity of a CSMA-CA based network according to a physical topology and a given routing protocol. This framework is itself independent of the network topology and the routing protocols, and provides therefore a relevant tool for comparing them. We apply our models to a comparative analysis of a well-known flat routing protocol OLSR against two main self-organized structure approaches, VSR and localized CDS.

#### Minimizing the energy consumption

[60] , [89] investigate the problem of determining feasible radio configurations in fixed broadband wireless networks, focusing on power efficiency. Under this scenario, a power-efficient configuration can be characterized by a modulation constellation size and a transmission power level. Every link holds a set of power-efficient configurations, each of them associating a capacity with its energy cost. We introduce a joint optimization of data routing and radio configuration that minimizes the total energy consumption while handling all the traffic requirements simultaneously. An exact mathematical formulation of the problem is presented. It relies on a minimum cost multicommodity flow with step increasing cost functions, which is very hard to optimize. We then propose a piecewise linear convex function, obtained by linear interpolation of power-efficient points, that provides a good approximation of the energy consumption on the links, and present a relaxation of the previous formulation that exploits the convexity of the cost functions. This yields lower bounds on the total energy expenditure, and finally heuristic algorithms based on the fractional optimum are employed to produce feasible configuration solutions. Our models are validated through extensive experiments, and the results testify the potentialities behind this novel approach.

[116] , [84] focuses on the energy consumption of *ad-hoc* and sensor networks through the viewpoint of congestion. Congestion not only causes packet loss
and increases queueing delay, but also leads to unnecessary energy
consumption. Two types of congestion can occur:
node-level congestion, which is caused by buffer overflow in the node, or
link-level congestion, when wireless channels are shared by several nodes
arising in collisions.
A measure of link-level congestion in static wireless ad-hoc and
sensor networks randomly deployed over an area is studied. The measure of congestion
considered is the inverse of the greatest eigenvalue of the adjacency
matrix of the random graph. This measure gives an approximation of the
average
quantity of wireless links of a certain length on the network.
We survey the results to find this measure in Bernoulli
random graphs. We use tools from random graph and random matrix theory
to extend this measure on Geometric random graphs.

#### Fast data gathering

Several works of Mascotte have dealt with gathering (data collection) in wireless multi hop networks when interferences constraints are present.

[17] concerns the study of the algorithmic and the complexity of the gathering communications in radio networks. The goal is to find the minimum number of steps needed to achieve such a gathering and design algorithms achieving this minimum. For special topologies such as the path and the grid, we have proposed optimal or near optimal solutions. We also considered the systolic (or continuous) case where we want to maximize the throughput (bandwidth) offered to each node.

[87] , [103] , [52] suppose that the time is slotted and that during one time slot (step) each node can transmit to one of its neighbor at most one data item. Each device is equipped with a half duplex interface; so a node cannot both receive and transmit simultaneously. During a step only non interfering transmissions can be done. In other words, the non interfering calls done during a step will form a matching. Under these settings, the best known algorithm, in terms of the makespan or completion time, in grid networks was a multiplicative 1.5-approximation algorithm. In such topologies, we give a very simple +2 approximation algorithm and then a more involved +1 approximation algorithm. Moreover, our algorithms work when no buffering is allowed in intermediary nodes, i.e., when a node receives a message at some step, it must transmit it during the next step.

[25] considers interference constraint modeled by a fixed integer d 1, which implies that nodes within distance d in the graph from one sender cannot receive messages from another node. We give protocols and lower bounds when the network is a path and the destination node is either at one end or at the center of the path. These protocols are shown to be optimal for any d in the first case, and for 1d4 , in the second case.

#### Distributed call scheduling

Distributed call scheduling in wireless networks is a challenging problem to tackle. Indeed, even when interferences are not considered, computing an optimal call scheduling with local information is still an open question.

[114] investigates the problem of routing packets between undifferentiated sources and sinks in a network modeled by a multigraph. A distributed and local algorithm that transmits packets hop by hop in the network is provided and its behaviour is studied. At each step, a node transmits its queued packets to its neighbours in order to optimize a local gradient. This protocol is thus greedy since it does not require to record the history about the past actions, and lazy since it only needs informations of the neighborhood. We prove that this protocol is however optimal in the sense that the number of packets stored in the network stays bounded as soon as the sources injects a flow that another method could have exhausted. We therefore reinforce a result from the literature that worked for differentiated suboptimal flows.

[86] considers a weaker stability objective but coping with interferences. Two distributed algorithms are provided ensuring stability under a random packet arrival process. These algorithms improve on existing algorithms since they work under any binary interference model and under the cost of a constant length control phase.

In [86] [120] , we 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. Here, we consider any binary model of interference. We assume that traffic is single-hop and that time is slotted. We suppose also random arrivals on each link during each slot. We design a fully distributed local algorithm with the following properties: it works for any arbitrary binary interference model; it has a constant overhead (independent of the size of the network and the values of the queues); and it needs no knowledge. Indeed contrary to other existing algorithms, we do not need to know the values of the queues of the “neighboring links”, which are difficult to obtain in a wireless network with interference. We also give sufficient conditions for stability under Markovian assumptions. The performance of our algorithm (throughput, stability) have been investigated and compared via simulations to that of previously proposed schemes.

#### Routing in evolving graphs

The assessment of routing protocols for mobile wireless networks is a difficult task, because of the networks dynamic behavior and the absence of benchmarks. However, some of these networks, such as intermittent wireless sensors networks, periodic or cyclic networks, and some delay tolerant networks (DTNs), have more predictable dynamics, as the temporal variations in the network topology can be considered as deterministic, which may make them easier to study. Recently, a graph theoretic model, the evolving graphs was proposed to help capture the dynamic behavior of such networks, in view of the construction of least cost routing and other algorithms. The algorithms and insights obtained through this model are theoretically very efficient and intriguing. However, there were no study about the use of such theoretical results into practical situations.

In [29] , we analyze the applicability of the evolving Graph Theory in the construction of efficient routing protocols in realistic scenarios. Using the NS2 network simulator to first implement an evolving graph based routing protocol, we then use it as a benchmark when comparing the four major ad hoc routing protocols (AODV, DSR, OLSR and DSDV). Interestingly, our experiments show that evolving graphs have the potential to be an effective and powerful tool in the development and analysis of algorithms for dynamic networks, with predictable dynamics at least. In order to make this model widely applicable, however, some practical issues still have to be addressed and incorporated into the model, like adaptive algorithms. We also discuss such issues in this paper, as a result of our experience.

#### Fast IEEE 802.11 Handover for High Speed Vehicles

Providing a continous connection with a terrestrial backbone network from a vehicle moving at high speeds is still an open issue. Various options have already been considered and still being studied such as UMTS, WiMax, LEO Satellites, and so on. Despite some of these having already been implemented and commercially exploited (eg. satellite connexions on trains), most fail to offer a sufficiently reliable service to their customers over long periods of travel time (UMTS/3G) or suffer from a limited ability to support a large number of simultaneous users (satellites). Let's consider the case of trains. Ideally, on-board customers want a full-time connection of their laptop to a regular WiFi network, such that they don't need an additional device, and they want that network to provide a continuous and reliable connection to the Internet. Furthermore, many other devices onboard trains could benefit of such a continuous and reliable connection (eg. security cameras, broadcasting service, etc.), but these devices do not necessarily rely on TCP/IP. In [76] , [115] , we introduce a new system that allows fast handover between an on-board, fast moving IEEE 802.11 device and a series of 802.11 Access Points regularly placed along the road or track. This new device, called Spiderman, seamlessly alternates connections on two radio channels in order to hide the standard WiFi scanning and association delays. Another noticeable property of this new system is that it is fully implemented withen the OSI layer 2, which means that it does not depend on upper layers mobility mechanisms (in particular TCP/IP). A prototype of this system is currently under testing.