We study the scaling properties of a georouting scheme in a wireless multi-hop network of @math mobile nodes. Our aim is to increase the network capacity quasi linearly with @math while keeping the average delay bounded. In our model, mobile nodes move according to an i.i.d. random walk with velocity @math and transmit packets to randomly chosen destinations. The average packet delivery delay of our scheme is of order @math and it achieves the network capacity of order @math . This shows a practical throughput-delay trade-off, in particular when compared with the seminal result of Gupta and Kumar which shows network capacity of order @math and negligible delay and the groundbreaking result of Grossglausser and Tse which achieves network capacity of order @math but with an average delay of order @math . We confirm the generality of our analytical results using simulations under various interference models.
On the practical side, many protocols have been proposed for wireless multi-hop networks. These protocols may be classified in topology-based and position-based protocols. Topology-based protocols @cite_6 @cite_8 @cite_18 need to maintain information on routes potentially or currently in use, so they do not work effectively in environments with high frequency of topology changes. For this reason, there has been an increasing interest in position-based routing protocols. In these protocols, a node needs to know its own position, the one-hop neighbors' positions, and the destination node's position. These protocols do not need control packets to maintain link states or to update routing tables. Examples of such protocols can be found in @cite_10 @cite_1 @cite_16 @cite_9 @cite_12 @cite_14 @cite_2 @cite_4 . In contrast to our work, they do not analyze the trade-off between the capacity and the delay of the network under these protocols and their scaling properties.
@cite_18 @cite_14 @cite_4 @cite_8 @cite_9 @cite_1 @cite_6 @cite_2 @cite_16 @cite_10 @cite_12
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Each node in a wireless multi-hop network can adjust the power level at which it transmits and thus change the topology of the network to save energy by choosing the neighbors with which it directly communicates. Many previous algorithms for distributed topology control have assumed an ability at each node to deduce some location-based information such as the direction and the distance of its neighbor nodes with respect to itself. Such a deduction of location-based information, however, cannot be relied upon in real environments where the path loss exponents vary greatly leading to significant errors in distance estimates. Also, multipath effects may result in different signal paths with different loss characteristics, and none of these paths may be line-of-sight, making it difficult to estimate the direction of a neighboring node. In this paper, we present Step Topology Control (STC), a simple distributed topology control algorithm which reduces energy consumption while preserving the connectivity of a heterogeneous sensor network without use of any location-based information. The STC algorithm avoids the use of GPS devices and also makes no assumptions about the distance and direction between neighboring nodes. We show that the STC algorithm achieves the same or better order of communication and computational complexity when compared to other known algorithms that also preserve connectivity without the use of location-based information. We also present a detailed simulation-based comparative analysis of the energy savings and interference reduction achieved by the algorithms. The results show that, in spite of not incurring a higher communication or computational complexity, the STC algorithm performs better than other algorithms in uniform wireless environments and especially better when path loss characteristics are non-uniform. 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. The topology of a wireless multi-hop network can be controlled by varying the transmission power at each node. In this paper, we give a detailed analysis of a cone-based distributed topology-control (CBTC) algorithm. This algorithm does not assume that nodes have GPS information available; rather it depends only on directional information. Roughly speaking, the basic idea of the algorithm is that a node u transmits with the minimum power p sub u, spl alpha required to ensure that in every cone of degree spl alpha around u, there is some node that u can reach with power p sub u, spl alpha . We show that taking spl alpha =5 spl pi 6 is a necessary and sufficient condition to guarantee that network connectivity is preserved. More precisely, if there is a path from s to t when every node communicates at maximum power then, if spl alpha spl les 5 spl pi 6, there is still a path in the smallest symmetric graph G sub spl alpha containing all edges (u,v) such that u can communicate with v using power p sub u, spl alpha . On the other hand, if spl alpha >5 spl pi 6, connectivity is not necessarily preserved. We also propose a set of optimizations that further reduce power consumption and prove that they retain network connectivity. Dynamic reconfiguration in the presence of failures and mobility is also discussed. Simulation results are presented to demonstrate the effectiveness of the algorithm and the optimizations. 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.