Ternary Schedules for Energy-Limited Sensor Networks

Abstract

Medium access control for multihop wireless sensor networks (WSNs) must be energy efficient because the battery-operated nodes are not practical to recharge. We give constructions for ternary schedules in which each node is in one of three states: transmitting, receiving, or asleep. For each hop (v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> , v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> ), communication is effective only when v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> is transmitting, v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> is receiving, and no other node in proximity of v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> is also transmitting. Since sensor nodes are prone to failure, the schedules should be independent of the detailed topology while supporting spatial reuse. We use arc-decompositions of the complete lambda-fold directed graph Koarr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> into directed complete bipartite subgraphs Koarr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a,b</sub> as a model for ternary scheduling in WSNs. We associate the vertices of Koarr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> with the nodes of the WSN, and occurrences of Koarr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a,b</sub> s (blocks) in the decomposition with time slots in the schedule. A block with out-vertices A and in-vertices B corresponds to a slot in which the a nodes in A are transmitting, the b in B are receiving, and all others are asleep. Such a decomposition of lambdaKoarr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> guarantees that every ordered pair of nodes in the WSN can communicate in lambda time slots.