## Section: New Results

### Massive mobile dense wireless networks

Participants : Cédric Adjih, Khaldoun Al Agha, Emmanuel Baccelli, Youghourta Benfattoum, Lin Chen, Philippe Jacquet, Nour Kadi, Saoucène Mahfoudh, Steven Martin, Yacine Mezali, Pascale Minet, Paul Mühlethaler, Georges Rodolakis, Yutaka Takahashi, Yasser Toor.

#### Executive summary

Scaling properties of mobile ad hoc network lead to an increase of global capacity when the network density increases or when the packets can be stored for a while in mobile nodes instead of being immediately retransmitted.

Gupta and Kumar have shown in 2000 that the transport capacity per node in a multihop ad hoc
network decreases in *1 / sqrt(N log N)* ,
*N* being the number of nodes in the
network.
Therefore the global capacity of the network increases in
*sqrt(N) / sqrt(log N)* .
This is a surprising result since in wired network a collection of nodes connected to a single communication resource has a transport capacity that just remains constant (*i.e.*
the average per node capacity decreases in *1/N* ).

Therefore adding space to a multihop wireless network increases the capacity: this is the space capacity paradox.

When nodes randomly move, it turns to be more advantageous to store packets for a while on mobile routers instead of forwarding them immediately like hot potatoes. When the mobile router moves closer to the destination, then it can delivers packets on a much smaller number of hops. Of course the delivery delay is much longer, but the network capacity also increases by slowing non urgent packets. This is the time capacity paradox: by slowing packets, nodes mobility increases network capacity. This was hinted the first time by Grossglauser and Tse in 2002.

The great challenge is to find the good protocol and tunings that allow to adjust the delivery delay from zero to infinity in order to get a continuous increase in capacity. The challenge is two-sided: one has to keep the delivery delay between reasonable bounds and one has to consider realistic mobility models.

Existing protocols for Mobile Ad Hoc Networks (MANET) are highly efficient in routing data between mobile nodes that belong to the same connected component (cf. the protocols which have received the RFC status by the manet group of IETF). What about a disconnected network where source and destination may be located in two different connected components? In this case usual routing protocols drop packet due to host unreachable as no end-to-end route exists at that time.

A simple idea is to allow the router that has no available route to the destination to keep the packet in buffer until the conditions become more appropriate for forwarding. The forwarding conditions will change because of mobility: the router can move closer to the destination so that they belong to the same connected component and the packet can be delivered.

Indeed, the network may be continuously partitionned due to high mobility, and the traditional approach to allow a mobile node to wait for the network to be fully connected (i.e. form a unique component) or to wait to be in range of the destination may lead to unacceptable delays. Furthermore, concrete applications, such as Defence and Disaster-Relief, cannot always rely on such assumptions.

Nevertheless, even if the communicating nodes may never be within the same connected component, it is important to observe that a “communication path” may be available through time using intermediate nodes that are temporarily within reach of each other while moving, hence making such networks viable for critical applications. Depending on the nature of the environment, these networks are now commonly referred as Intermittently Connected MANET and Delay Tolerant Networks.

In between stands the problem of the fully connected betwork that forms a single connected component, but for which maintening full knowledge of the topology would simply make the network collapse under its huge control traffic. In fact this is the main problem that wireless network engineering has to face, in most experiments the generation of control traffic is the main source of disruption.

#### Scientific achievements

##### Scaling and spatial capacity in non uniform wireless networks

We found a more precise instance of Gupta- Kumar result by using a simple but realistic network model based on slotted ALOHA with Poisson traffic. It turns out that when the traffic density increases then the average node neighborhood area shrinks so that the average encircled traffic load remains constant with an analytical expression..

In their original model Gupta and Kumar assume that the traffic density is constant, which is far from realistic. However we have derived similar generalized results when the traffic density is not uniform. In this case, the heavier is the local traffic, the smaller are the local neighborhood and the larger is the number of hops needed to cross the congested region. Therefore the shortest paths (in hop number as computed by OLSR) will have a natural tendancy to avoid congested are. The path tend to follow trajectory that have analogy in non linear optic with variable indices.

##### Time capacity and node mobility

We have defined a protocol that takes advantage of node mobility in a general way. In short the packet stay with its host router as long as the latter does not evade too fast from its next hop (computed via a shortest path protocol such as OLSR). In the way we understand “too fast” stands the tuning parameters we discussed above. There is no need to have node geographical location and to physically measure motion vector, since everything can be done via the analysis of the dynamic of neighborhood intersections. We analytically derived performance evaluation under random walk mobility models. We plan to simulate the protocol in a real mobility scenario. This algorithm has application in Intelligent Transport System.

##### Overhead reduction in large networks

The first limitation of multihop wireless network is the size of the overhead per node that increases linearly with the size of the network. This is a huge improvement compared to classic internet protocols which have quadratic overhead increases. Nevertheless this till limit the network size to some thousands. We have analyzed the performance of OLSR with Fisheye feature that significantly reduce the overhead with respect to distance. In theory the overhead reduction allows to network size of several order of magnitude. Anyhow the tuning of the overhead attenuation with distance must be carefully done when the network is mobile, in order to avoid tracking failure. We showed that an overhead reduction within square root of the network size achieve this goal.

An alternative way to overhead reduction is ad hoc hierarchical routing and Distributed Hashing Table. Work has just begun in this area.

##### Opportunistic routing

The model of wireless networks based on dynamic graph does not well assess the real processes in a wireless network. In particular the range of transmission can greatly vary between packets, the graph keeping only the average range. Opportunistic routing consists into taking advantage of temporary extension of the transmission range in orger to gain several hops.

We have strong established theoretical performance limits in opportunistic routing. The limits are based on realistic interference scenarios in slotted Aloha. We have also investigated the impact of mobility on this theoretical limits.

We have designed an opportunistic routing protocol whose performance are within a small margin of the theoretical limits.

##### Intermittent and delay tolerant networks

We consider the problem of routing in these networks, with the sole assumption that the speed of the node mobility is less than the speed of transmitting a packet to a neighbour. We compare this problem with sound propagation in liquid. We show that various pattern of mobility and network clustering can be described by a single parameter such as the information speed propagation.

We introduce new algorithms that route a packet toward a remote destination. The different algorithms vary depending on the buffering and the capacity capabilities of the network (i.e. if one or more copies of a packet can be sent and/or be kept). All algorithms are based on link aging rumors across connected components. The packet bounces from connected components to connected components, thanks to node mobility. We establish several analytical properties using an analogy with the sound propagation in liquid where molecules creates temporary connected components where sounds travel very fast.

Previous models assumed that the propagation of information path evolves like in a dynamic Erdos-Renyi graph leading to an epidemic flooding in O(log n) or O(1), n being the number of nodes in the network. We disprove the Erdos-Renyi model by showing via space-time considerations that the set of information path from a source to a destination is in fact much smaller than the path set in the Erdos-Renyi model. This lead to a much larger minimal delay in square root of n instead of log n. This correspond to a bounded maximal information propagation speed, whose estimate depends on the mobility model and the node density, and is root of multivariate explicit Bessel formulas.

##### Network Coding

We study network coding for multi-hop wireless networks. We focus on the case of broadcasting where one source transmits information to all nodes in the network. Our goal is energy-efficient broadcast, that is, minimizing the total number of transmissions for broadcasting to the entire network. Note that this is a different problem for the classical problem of capacity maximization ; and assuming we are far from the network capacity limit, hence in fact, we could assume interference-free transmissions.

Our previous results, they had shown that network coding (and a simple coding strategy) was able to reach optimality for assymptotically large and dense networks, with assympotically 100 % of the received transmissions being useful (innovative). We extended the results with the combined use of connected dominating sets and network coding: we were able to quantify (and bound) the benefits of network coding in networks where the area of the network stays fixed, and only the density increases.

We have proved that the performance of wireless random network coding are optimal in the following network model: the Erdos-Renyi random graph model and the unit disk random graph model. In particular we show in the Erdos-Renyi the network coding capacity rate outperform any Connected Dominating Set strategy by a factor of order log n. In the unit disk model we gain is larger than 60%. The result is based on the analysis of the connectivity stretch ratio of the random graphs. The connectivity stretch ratio is the ratio of the smallest degree over the connectivity number, and the connectivity stretch ratio tends to one in the two graph models.