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Abstract-Power conservation is one of the most important issues in wireless ad hoc and sensor networks, where nodes are likely to rely on limited battery power. Transmitting at unnecessarily high power not only reduces the lifetime of the nodes and the network, but also introduces excessive interference. It is in the network designer's best interest to have each node transmit at the lowest possible power while preserving network connectivity. In this paper, we investigate the optimal common transmit power, defined as the minimum transmit power used by all nodes necessary to guarantee network connectivity. This is desirable in sensor networks where nodes are relatively simple and it is difficult to modify the transmit power after deployment. The optimal transmit power derived in this paper is subject to the specific routing and medium access control (MAC) protocols considered; however, the approach can be extended to other routing and MAC protocols as well. In deriving the optimal transmit power, we distinguish ourselves from a conventional graph-theoretic approach by taking realistic physical layer characteristics into consideration. In fact, connectivity in this paper is defined in terms of a quality of service (QoS) constraint given by the maximum tolerable bit error rate (BER) at the end of a multihop route with an average number of hops.

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In a self-organizing traffic information system, vehicles share and distribute the traffic information by rebroadcasting a received information packet to their neighbors. However, it is inefficient to let every vehicle rebroadcast the information packet, since the redundant packets waste the valuable (finite) radio channel bandwidth. Reducing the number of redundant packets, while still ensuring good coverage and reachability, is one of the main objectives in multi-hop broadcasting. In this paper, we propose a new probabilistic-based rebroadcast scheme, denoted as Irresponsible Forwarding, where each vehicle rebroadcasts a received information on the basis of (i) its distance from the source and (ii) the density of its neighbors. The key idea is that a node implicitly evaluates the probability that there is another node which can rebroadcast more successfully: if this probability is sufficiently high, then the node "irresponsibly" does not rebroadcast. Unlike the other existing probability assignment schemes, our scheme also takes the statistical distribution of the vehicles on the road into consideration. Moreover, it will be shown that, for sufficiently large values of the vehicle spatial density, the average number of rebroadcast packets can be regulated by properly tuning a single parameter.