## Section: New Results

### Technology specific solutions

*Participants: Jin Cui, Walid Bechkit, Khaled Boussetta, Hervé Rivano, Fabrice Valois.*

#### Temperature-Aware Algorithms for Wireless Sensor Networks

Temperature variations have a significant effect on low power wireless sensor networks as wireless communication links drastically deteriorate when temperature increases. A reliable deployment should take temperature into account to avoid network connectivity problems resulting from poor wireless links when temperature increases. A good deployment needs also to adapt its operation and save resources when temperature decreases and wireless links improve. Taking into account the probabilistic nature of the wireless communication channel, in [12] we investigated the effect of temperature on percolation-based connectivity in large scale wireless sensor networks and showed that more energy can be saved by allowing some nodes to go to deep sleep mode when temperature decreases and links improve. Based on this result, we proposed a simple, yet efficient, Temperature-Aware MAC plugin (TA-MAC), which can be potentially used with any MAC protocol, enabling it to dynamically adapt the network effective density in order to allow further energy savings, while maintaining network connectivity. We carried out simulations and demonstrated that sate of the art protocols augmented with the TA-MAC plugin allow a significant energy efficiency improvement.

Going one step further, we developed a mathematical model that provides the most energy efficient deployment in function of temperature without compromising the correct operation of the network by preserving both connectivity and coverage [3] . We used our model to design three temperature-aware algorithms that seek to save energy (i) by putting some nodes in hibernate mode as in the SO (Stop-Operate) algorithm in TA-MAC, or (ii) by using transmission power control as in PC (Power-Control), or (iii) by doing both techniques as in SOPC (Stop-Operate Power-Control). All proposed algorithms are fully distributed and solely rely on temperature readings without any information exchange between neighbors, which makes them low overhead and robust. Our results identified the optimal operation of each algorithm and showed that a significant amount of energy can be saved by taking temperature into account.

#### Resilience in Wireless Sensor Networks

The concept of resilience for routing protocols in wireless sensor networks has been proposed and developed in the team in the last few years. In our previous works, a general overview of the resilience, including definition, metric and resilient techniques based on random behavior and data replication have been proposed. Following these previous methods, in [6] we proposed a new resilient solution based on network coding techniques, to improve resilience in wireless sensor networks for smart metering applications. More precisely, using our resilience metric based on a performance surface, we compared several variants of a well-known gradient based routing protocol with the previous methods (random routing and packet replications) and the new proposed methods (two network coding techniques). The proposed methods outperformed the previous methods in terms of data delivery success even in the presence of high attack intensity.

We also continued to study the resilience of routing protocols against malicious insiders willing to disrupt network communications. Previously, the simulation results showed that introducing randomness in routing protocols increases uncertainty for an adversary, making the protocols unpredictable. When combined with data replication, it permits route diversification between a source and a destination, thus enhancing the resilience. In [15] , we proposed a theoretical framework to quantify analytically the performance of random protocols against attacks based on biased random walks on a torus lattice. The objective is to evaluate analytically the influence of bias and data replication introduced to random walks. The bias allows to decrease the route length by directing random walks toward the destination, thus reducing the probability of a data packet to meet a malicious insider along the route; however, it decreases also the degree of randomness (entropy). When random protocols are combined with data replication, the reliability is improved thanks to route diversity despite an additional overhead in terms of energy consumption.

#### Data aggregation in Wireless Sensor Networks

Aggregation functions are intended to save energy and capacity in Wireless Sensor Networks, by avoiding unnecessary transmissions. Aggregation functions take benefit from spatial and/or temporal correlations to forecast or to compress the real data which are collected. Although several works have focused on data aggregation in Wireless Sensor Networks, there is a lack of a formal unified framework that can compare several aggregation functions suitable for a given network topology, a given application and a target accuracy. In [14] , we address this question by proposing a Markov Decision Process that can help to evaluate the performances of aggregation functions. The performances are expressed using two new proposed metrics, which can assess the energy and capacity savings of aggregation functions. As illustrative examples, we use our Markov Decision Process to evaluate and analyze the performances of basic aggregation functions (e.g. average) and more complex ones (time series, polynomial functions).

#### Data Gathering in Mesh Networks

In the gathering problem in mesh networks, a particular node in a graph, the base station, aims at receiving messages from some nodes in the graph. At each step, a node can send one message to one of its neighbors (such an action is called a call). However, a node cannot send and receive a message during the same step. Moreover, the communication is subject to interference constraints, more precisely, two calls interfere in a step, if one sender is at distance at most ${d}_{I}$ from the other receiver. Given a graph with a base station and a set of nodes having some messages, the goal of the gathering problem is to compute a schedule of calls for the base station to receive all messages as fast as possible, i.e., minimizing the number of steps (called makespan). The gathering problem is equivalent to the personalized broadcasting problem where the base station has to send messages to some nodes in the graph, with same transmission constraints.

In [5] , we focused on the gathering and personalized broadcasting problem in grids. Moreover, we considered the non-buffering model: when a node receives a message at some step, it must transmit it during the next step. In this setting, though the problem of determining the complexity of computing the optimal makespan in a grid is still open, we presented linear (in the number of messages) algorithms that compute schedules for gathering with ${d}_{I}\in 0,1,2$. In particular, we presented an algorithm that achieves the optimal makespan up to an additive constant 2 when ${d}_{I}=0$. If no messages are “close” to the axes (the base station being the origin), our algorithms achieve the optimal makespan up to an additive constant 1 when ${d}_{I}=0$, 4 when ${d}_{I}=2$, and 3 when both ${d}_{I}=1$ and the base station is in a corner.