## Section: New Results

### Characterizing urban capillary wireless networks.

Participants: Sandesh Uppoor, Diala Naboulsi, Rodrigue Domga Komguem, Anis Ouni, Alexandre Mouradian, Isabelle Augé-Blum, Hervé Rivano, Marco Fiore, Fabrice Valois

#### Properties of urban road traffic of interest to mobile networking.

The management of mobility is commonly regarded as one of the most critical issues in large-scale telecommunication networks. The problem is exacerbated when considering vehicular mobility, which is characterized by road-constrained movements, high speeds, sudden changes of movement direction and acceleration, and significant variations of these dynamics over daytime. The understanding of the properties of car movement patterns becomes then paramount to the design and evaluation of network solutions aimed at vehicular environments.

We first analyzed how the vehicular mobility in a large-scale urban region affects a cellular infrastructure intended to support on-board users. We studied the spatial and temporal distribution of traffic load induced by vehicular users, their spatial flows, their inter-arrival and residence times at cells [22] .

We then studied the topological features of a network built on moving vehicles, considering the instantaneous connectivity of the system [28] . Our results evidence the spatial and temporal diversity of road traffic, stressing the importance of a correct modeling of road traffic towards the reliable performance evaluation of network protocols. Additionally, the results outline how commonly adopted assumptions (e.g., Poisson user arrivals at the network base stations) do not hold under vehicular environments, and how the V2V-based network has low connectivity, availability, reliability and navigability properties.

#### The limits of RSSI-based localization.

Numerous localization protocols in Wireless Sensor Networks are based on Received Signal Strength Indicator. Because absolute positioning is not always available, localization based on RSSI is popular. More, no extra hardware is needed unlike solutions based on infra-red or ultrasonic. Moreover, the theory gives a RSSI as a function of distance. However, using RSSI as a distance metric involves errors in the measured values, resulting path-loss, fading, and shadowing effects. We did experimentation results from three large WSNs, each with up to 250 nodes [23] . Based on our findings from the 3 systems, the relation between RSSI and distance is investigated according to the topology properties and the radio environment. We underline the intrinsic limitations of RSSI as a distance metric, in terms of accuracy and stability. Contrary to what we assumed, collaborative localization protocol based on Spring-Relaxation algorithm can not smooth the distance-estimation errors obtained with RSSI measurements.

#### Modeling and optimization of wireless networks.

In critical real-time applications, when an event is detected, the Worst Case Traversal Time (WCTT) of the message must be bounded. However, despite this, real-time protocols for WSNs are rarely formally verified. The model checking of WSNs is a challenging problem for several reasons. First, WSNs are usually large scale so it induces state space explosion during the verification. Moreover, wireless communications produce a local broadcast behavior which means that a packet is received only by nodes which are in the radio range of the sender. Finally, the radio link is probabilistic. The modeling of those aspects of the wireless link in model checking is not straightforward and it has to be done in a way that mitigates the state space explosion problem. We are currently working on proposing a methodology adapted to WSNs, and based on Timed Automata (TA) and model-checking. First results are promising [19] , but needed to be further investigated.

While the large variety of routing protocols (geographical, gradient, reactive, ...) proposed in the literature provide a set of pertinent solutions for optimizing the energy consumption for multi-hop wireless networks, they do not permit to know the conditions of use of these protocols based on parameters such as: the dynamics of topology, traffic pattern, the density and diameter of the network, the load, etc. In [12] , we presented a theoretical model for evaluating the energy consumption for communication protocols taking into account both the dynamics of nodes and links, the properties of topology, the traffic pattern, the control/data packets and a realistic channel model. This model is applied successively to several protocols (GPSR, AODV, OLSR and PF) to highlight their optimum usage and it permits to conclude that Beacon-Less routing protocols are adapted for application with low traffic.

We continued developing optimization tools for building optimal solution to various problems of multi-hop wireless networks. Most of these contributions combine graph theoretical basis with Mixed Integer Linear Programming techniques, and are valuable for understanding the extremal behaviors of the systems and guide the development of efficient architectures and protocols. In this sense, we have considered a new edge coloring problem to model call scheduling optimization issues in wireless mesh networks: the proportional coloring [6] . It consists in finding a minimum cost edge coloring of a graph which preserves the proportion given by the weights associated to each of its edges. We show that deciding if a weighted graph admits a proportional coloring is pseudo-polynomial while determining its proportional chromatic index is NP-hard. We then give lower and upper bounds for this parameter that can be computed in pseudo-polynomial time. We finally identify a class of graphs and a class of weighted graphs for which the proportional chromatic index can be exactly determined.

Dealing with wireless mesh network, we have investigated the fundamental trade-off between transmitting energy consumption and network capacity [24] . The results on this trade-off have been computed using MILP models solved with column generation techniques. The main contribution relies in the ability to consider a realistic SINR model of the physical layer with a continuous power control and discrete transmission rate selection at each node. In order to model these functionalities, a strong formulation (in the sense that the linear relaxation gives relevant lower bounds) of the rate selection is introduced.

The behavior of beaconless geographic forwarding protocols for wireless sensor networks has also been modeled [9] . A realistic physical layer is taken into account by combining MILP models with simulation based inputs on the number of required retransmissions for realizing a transmission. The model is then able to compute energy efficient routings and allows for understanding the most efficient relay selection schemes, denoted Furthest Forward within Reliable neighbors (FFRe).