TDMA scheduling problem avoiding interference in multi-hop wireless sensor networks

In this paper, we consider a multi-hop sensor network, where the network topology is a tree, TDMA (time division multiple access) is employed as medium access control, and all data generated at sensor nodes are delivered to a sink node (the base station) located on the root of the tree through the network. It is reported that if a transmission schedule that avoids interference between sensor nodes completely can be computed, TDMA is preferable to CSMA/CA (carrier sense multiple access with collision avoidance) in performance. In general, the TDMA scheduling problem to find the shortest schedule is formulated as a combinatorial optimization problem, where each combination corresponds to a schedule. However, solving such a combinatorial optimization problem is difficult, especially for large-scale multi-hop sensor networks. The reason of the difficulty is that the number of the combinations increases exponentially with the increase of the number of nodes. In this paper, to formulate the TDMA scheduling problem, we propose a min-max model and a min-sum model. The min-max model yields the shortest schedule, but it is difficult to solve large-scale problems. The min-sum model does not guarantee providing the shortest schedule; however, it may give us good schedules over a short amount of computation time, compared to the min-max model. Numerical examples show that the min-sum model can provide good schedules in a reasonable CPU time, even when the min-max model fails to compute the shortest schedule in a reasonable CPU time.