Abstract: Self-stabilizing TDMA Algorithms for Timeslot Assignment and Alignment in Wireless Ad-hoc Networks without External Reference

Time division multiple access (TDMA) is a method for sharing communication media. In wireless communications, TDMA algorithms often divide the radio time into timeslots of uniform size, \xi, and then combine them into frames of uniform size, \tau. We consider TDMA algorithms that allocate at least one timeslot in every frame to every node. Given a maximal node degree, \delta, and no access to external reference, we consider the problem of the existence of collision-free self-stabilizing TDMA algorithms that have constant communication delay of \tau. We demonstrate that this problem has no solution when \tau < = max((2-\epsilon)\delta,\chi), where \epsilon>0, and \chi is the chromatic number for distance-2 vertex coloring. We observe the bound relevance to the bandwidth utilization when the network topology is a planar graph. As a complement to this lower bound, we focus on proving the existence of probabilistic collision-free self-stabilizing TDMA algorithms that have constant communication delay of \tau. We consider basic settings (no hardware support for collision detection and no prior clock synchronization), and the collision of concurrent transmissions from transmitters that are at most two hops apart. In the context of self-stabilizing systems that have no external reference, we are the first to study this problem (to the best of our knowledge). Bio