Typical applications like habitat or environmental monitoring, disaster detection, or military applications require sensor nodes that are capable of sensing, processing, and communicating. The advances in micro-sensor and radio technologies offer such nodes, which are composed of low-cost and low-powered hardware. Densely populated networks thus become quite realistic. As a consequence, it is expected that in the majority of cases sensor nodes carry a limited and irreplaceable power supply. Even if the batteries might be replaceable, the cost and maintenance overhead would be unacceptably high. Thus, focusing on the energy consumption is unavoidable if application-driven WSN are intended for real-world deployments.

Because the radio communication consumes a large fraction of energy, the costs of data transmissions are most critical and should be kept to a minimum. Generally, routing algorithms that aim at minimizing the energy costs use shortest path algorithms, with the energy required for the transmission between two adjacent nodes used as the edge costs. However, as the results of EEF have shown, minimizing the energy costs might have a negative effect on the data delivery ratio. Thus, forward algorithms that cause low energy costs but high loss rates are commonly not efficient. In contrast, focusing on energy efficiency turned out to be a very promising forwarding scheme since it trades off the end-to-end delivery ratio of nodes reporting data to a sink node and the energy consumption in the network very well. Strategies solely based on the energy consumption or delivery ratios are clearly outperformed.

However, even if energy-efficient forwarding is employed, the overall lifetime of the network need not be extend necessarily. Once the forwarding paths are determined, they remain stable as long as their costs do not change. Thus, it is likely that nodes on the optimal paths are used quite often and consume more energy than others if the traffic load is not balanced within the network. As such nodes quickly run out of energy, the likelihood of malfunctions or network partitions increases. This problem is addressed by maximum lifetime algorithms that aim at preventing the early burn out of such paths, either focusing on the lifetime of single nodes or the entire network. As the definition of lifetime is not always consistent, comparing different approaches is quite difficult. Often lifetime is defined in different ways, e.g., by the time the first node in the network runs out of energy, the time until the entire energy in the network is consumed, or by the time the first network partitions occur. Also definitions referring to the time till at least a fraction of α nodes are alive or at least an α coverage is maintained can be found. A common definition is maybe the time until the first node dies as it can be easily used by linear programs tackling the maximum lifetime problem.

In comparison to existing work focusing on the maximum lifetime problem, we emphasize more the existence of packet losses and propose forwarding strategies that avoid lossy links, which might cause a high energy consumption due to retransmissions. Most of the work in the literature assume that two nodes are always able to communicate with each other as long as their distance is lower than the maximum radio range of the transceiver. However, as recent measurements have shown, this is not true because many regions within the communication area show high variations. Asymmetric links might occur quite often, which might have a deep impact on the network lifetime if much energy is consumed along lossy forwarding paths.

Furthermore, relying on maximizing the lifetime might not lead to good delivery ratios or a low energy consumption if both are not taken into account explicitly. For example, concerning the energy consumption it may sometimes even better to use forwarding paths with high loss rates because packets may then be dropped early on the forwarding paths such that no further energy is consumed at all. Forwarding data over such paths might thus be good if only the energy consumption or the network lifetime is considered. Concerning the packet delivery ratio it is contradictory and senseless. Thus, we should keep this trade-off in mind.

As stated above, energy-efficient forwarding (EEF) strategies may have the disadvantage that some paths are used more frequently than others. Thus, the majority of nodes along these paths consume more energy, maybe decreasing the nodes' lifetime significantly. Thus, maximizing the network lifetime may be an orthogonal problem that needs to be taken into account, additionally to the energy efficiency of the network. However, it mainly depends on the definition of lifetime and the performance aims which are supposed to be optimized. For example, if the network lifetime is defined by the time until all nodes in the network are dead, the lifetime is maximized by a minimum energy consumption strategy, without considering the end-to-end packet delivery ratio or the energy efficiency of forwarding paths. On the other hand, if the lifetime is defined by the first node that runs out energy, a forwarding strategy aiming at maximizing the minimum residual energy on a path would be optimal. However, it should be noted that solely focusing on the network lifetime may lead to worse packet delivery ratios.

Hence, the idea is to combine energy-efficient forwarding with maximum lifetime forwarding in order to find a good trade-off between both performance aims. With E^eff being the best energy efficiency of the forwarding path, each node tries to optimize max{E^eff * E^l} by considering all its neighbors as potential forwarders. E^l denotes the expected lifetime of the entire forwarding path towards the sink, which is influenced by the minimum residual energy along that path. Using the expected lifetime rather than the minimum lifetime takes the delivery ratio of forwarding paths better into account. Because the worst node (regarding its residual energy) along the path consumes energy for forwarding the packet only if the packet do not get lost before, the expected lifetime is more opportunistic and estimates the real path costs better. According to MEEF and SEEF, we called this strategy multi-link and single-link lifetime-efficient forwarding (MLEF and SLEF).