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A multiactuator/multisensor model was studied in Ozaki et al (2007) to provide fault tolerance for WSANs Each sensor node sends a sensed value to multiple actuators and each actuator receives sensed values from multiple sensor nodes Such reporting model provides fault tolerance if any sensor or any actuator are faulty A semipassive coordination protocol was proposed in Ozaki et al (2007) One actuator plays a role of a coordinator, called primary actuator, while other actuators are backup actuators in an event area The protocol (Ozaki et al, 2007) consists of three phases: broadcast phase, decision phase, and update phase In the broadcast phase, if an event occurs, a sensor node sends a measured value to multiple actuators in the area Due to collision and noise in wireless channels, some actuators may not receive the value correctly.

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Each receiving backup actuator sends a message with the sensed value and the ID of the corresponding sensor node to the primary actuator Once the primary actuator receives a certain number of messages (greater than a predetermined threshold), it makes a decision on the measured value from the value set It can be a majority value from a discrete set, or, in the case of continuous values, a function lter could be used to remove extreme values and compute the average of the remaining ones The estimated value and other updates are then broadcasted to all the backup actuators Upon receiving this message, each backup actuator stores the received update values and acknowledges the receipt to the primary actuator The primary actuator (or one of primary actuators in case there are several of them) then makes a decision on possible action, including a con rmed update value.

In this way, a backup actuator can obtain the value from the decision message even if it misses the previous message containing the original updates Upon receiving the decision and updates, each backup actuator updates the state by using the value stored in the local storage Finally, the primary actuator acts on the decision made by sending a message to an actuation device, which acts based on received instruction If the primary actuator is faulty, for example, the update messages are delayed, the backup actuators suspect the primary actuator to be faulty due to time-out and send a negative acknowledgement message to the primary actuator Then, one of the backup actuators, for example, the backup actuator with the smallest ID, will take over the role of the primary actuator.

The new primary actuator computes an interval value from the received sensed values and sends an update message to the backup actuators, exactly as the faulty primary actuator was supposed to do The system will be recovered No speci c protocols were described in Ozaki et al (2007) for ooding tasks involved in the algorithm..

introduced in Section 15 in 1) The total expected hop count (number of packets) between two nodes at distance x is f (u, x ) = 1/[p(x )(1 (1 p(x ))u )] + u/[(1 (1 p(x ))u )] (see 1) The aEPR-u (expected progress routing with acknowledgements) selects the neighbor that maximizes (c a)/f (u, x ) The localized protocols in Kuruvila et al (2006) do not assume the hop by hop acknowledgements It was pointed out that the packet delivery rate approaches 1 if a large number of intermediate nodes are placed between the source and the destination and the distance between adjacent nodes approaches 0 On the basis of the observation, the end-to-end routing (EER) localized routing simply forwards the packet to neighbor A that maximizes p(x ), that is, the neighbor closest to C among neighbors that are closer to D than C .

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