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Energy efficient MAC protocols have been developed for wireless sensor and mobile ad hoc networks so that inactive nodes can transition into sleep state to conserve energy. It has been recognized that maintaining a continuously awake connected dominating set (CDS) serves to reduce the route setup latency. Under the mobile backbone network (MBN) architecture introduced by Rubin et al., a mobile backbone (Bnet) is dynamically constructed to provide a topological covering of the network. The MBN employs a hybrid routing algorithm under which flows that travel a distance longer than a threshold are directed along routes across the Bnet. In turn, a limited span network-wide global route discovery process is applied for routing shorter distance flows. In this paper, we introduce and analyze an MBN based power saving protocol (MBN-PS) that employs this hybrid routing scheme. Under the MBN-PS scheme, dynamically elected backbone nodes are kept awake, while inactive non-backbone nodes can reside in sleep state. We analytically show that, when the number of network flows is above a minimal level, the throughput per watt efficiency attained in an ad hoc network under complete backbone coverage is better than that achieved by a corresponding network that does not form a backbone. We present a model for the calculation of the bit-per-joule performance of the network as a function of the distance threshold. We confirm the validity of our analytical approach through simulations. Using our method, a network designer is able to choose the optimal distance threshold to be used by this scheme, based on traffic loading conditions.