In this work we develop a new theory to analyse the process of routing in large-scale ad-hoc wireless networks. We use a path integral formulation to examine the properties of the paths generated by different routing strategies in these kinds of networks. Using this theoretical framework, we calculate the statistical distribution of the distances between any source to any destination in the network, hence we are able to deduce a length parameter that is unique for each routing strategy. This parameter, defined as the effective radius, effectively encodes the routing information required by a node. Analysing the afore- mentioned statistical distribution for different routing strategies, we obtain a threefold result for practical Large-Scale Wireless Ad-Hoc Networks: 1) We obtain the distribution of the lengths of all the paths in a network for any given routing strategy, 2) We are able to identify "good" routing strategies depending on the evolution of its effective radius as the number of nodes, N , increases to infinity, 3) For any routing strategy with finit e effective radius, we demonstrate that, in a large-scale network, is equivalent to a random routing strategy and that its transport capacity scales asp Nbit-meters per second, thus retrieving the scaling law that Gupta and Kumar (2000) obtained as the limit for single-route large-scale wireless networks.
The distribution of distances between source and destination nodes has been calculated before @cite_8 @cite_6 . Both cited approaches are dependent on a two-dimensional geometry which is justifiable up to some extent. In this work we opt for a three-dimensional formulation of the problem in order not to restrict the topology analyzed. But we are aware that the dimensionality of the routing problem in Wireless Ad-Hoc Networks is not a well defined problem.
@cite_6 @cite_8
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Since ad hoc and sensor networks can be composed of a very large number of devices, the scalability of network protocols is a major design concern. Furthermore, network protocols must be designed to prolong the battery lifetime of the devices. However, most existing routing techniques for ad hoc networks are known not to scale well. On the other hand, the so-called geographical routing algorithms are known to be scalable but their energy efficiency has never been extensively and comparatively studied. In a geographical routing algorithm, data packets are forwarded by a node to its neighbor based on their respective positions. The neighborhood of each node is constituted by the nodes that lie within a certain radio range. Thus, from the perspective of a node forwarding a packet, the next hop depends on the width of the neighborhood it perceives. The analytical framework proposed in this paper allows to analyze the relationship between the energy efficiency of the routing tasks and the extension of the range of the topology knowledge for each node. A wider topology knowledge may improve the energy efficiency of the routing tasks but increases the cost of topology information due to signaling packets needed to acquire this information. The problem of determining the optimal topology knowledge range for each node to make energy efficient geographical routing decisions is tackled by integer linear programming. It is shown that the problem is intrinsically localized, i.e., a limited topology knowledge is sufficient to make energy efficient forwarding decisions. The leading forwarding rules for geographical routing are compared in this framework, and the energy efficiency of each of them is studied. Moreover, a new forwarding scheme, partial topology knowledge forwarding (PTKF), is introduced, and shown to outperform other existing schemes in typical application scenarios. A probe-based distributed protocol for knowledge range adjustment (PRADA) is finally introduced that allows each node to efficiently select online its topology knowledge range. PRADA is shown to rapidly converge to a near-optimal solution. We consider routing problems in ad hoc wireless networks modeled as unit graphs in which nodes are points in the plane and two nodes can communicate if the distance between them is less than some fixed unit. We describe the first distributed algorithms for routing that do not require duplication of packets or memory at the nodes and yet guarantee that a packet is delivered to its destination. These algorithms can be extended to yield algorithms for broadcasting and geocasting that do not require packet duplication. A by product of our results is a simple distributed protocol for extracting a planar subgraph of a unit graph. We also present simulation results on the performance of our algorithms. We present a study of transport on complex networks with routing based on local information. Particles hop from one node of the network to another according to a set of routing rules with different degrees of congestion awareness, ranging from random diffusion to rigid congestion-gradient driven flow. Each node can be either source or destination for particles and all nodes have the same routing capacity, which are features of ad-hoc wireless networks. It is shown that the transport capacity increases when a small amount of congestion awareness is present in the routing rules, and that it then decreases as the routing rules become too rigid when the flow becomes strictly congestion-gradient driven. Therefore, an optimum value of the congestion awareness exists in the routing rules. It is also shown that, in the limit of a large number of nodes, networks using routing based on local information jam at any nonzero load. Finally, we study the correlation between congestion at node level and a betweenness centrality measure. Existing position-based unicast routing algorithms which forward packets in the geographic direction of the destination require that the forwarding node knows the positions of all neighbors in its transmission range. This information on direct neighbors is gained by observing beacon messages each node sends out periodically. Due to mobility, the information that a node receives about its neighbors becomes outdated, leading either to a significant decrease in the packet delivery rate or to a steep increase in load on the wireless channel as node mobility increases. In this paper, we propose a mechanism to perform position-based unicast forwarding without the help of beacons. In our contention-based forwarding scheme (CBF) the next hop is selected through a distributed contention process based on the actual positions of all current neighbors. For the contention process, CBF makes use of biased timers. To avoid packet duplication, the first node that is selected suppresses the selection of further nodes. We propose three suppression strategies which vary with respect to forwarding efficiency and suppression characteristics. We analyze the behavior of CBF with all three suppression strategies and compare it to an existing greedy position-based routing approach by means of simulation with ns-2. Our results show that CBF significantly reduces the load on the wireless channel required to achieve a specific delivery rate compared to the load a beacon-based greedy forwarding strategy generates.