Desynchronization is a fundamental approach in wireless sensor networks that allows for convergence to time-division multiple access (TDMA) of the medium without the need for clock synchronization and centralized coordination. The method is based on the concept of reactive listening of peri-odic fire message broadcasts between nodes sharing the given spectrum. We propose a novel framework to estimate the required iterations for convergence to fair TDMA scheduling. Unlike previous conjectures or bounds found in the literature, our estimation framework is based on a stochastic modeling approach. Experiments via imote2 TinyOS nodes and simu-lations demonstrate that the proposed estimates characterize the experimental desynchronization convergence iterations significantly better than existing conjectures or bounds. Index Terms—wireless sensor networks, desynchroniza-tion, stochastic modeling, TDMA. 1.

Abstract—Desynchronization approaches in wireless sensor networks converge to time-division multiple access (TDMA) of the shared medium without requiring clock synchronization amongst the wireless sensors, or indeed the presence of a central (coordinator) node. All such methods are based on the principle of reactive listening of periodic “fire ” or “pulse” broadcasts: each node updates the time of its fire message broadcasts based on received fire messages from some of the remaining nodes sharing the given spectrum. In this paper, we present a novel framework to estimate the required iterations for convergence to fair TDMA scheduling. Our estimates are fundamentally different from previous conjectures or bounds found in the literature as, for the first time, convergence to TDMA is defined in a stochastic sense. Our analytic results apply to the DESYNC algorithm and to pulse-coupled oscillator algorithms with inhibitory coupling. The experimental evalu-ation via iMote2 TinyOS nodes (based on the IEEE 802.15.4 standard) as well as via computer simulations demonstrates that, for the vast majority of settings, our stochastic model is within one standard deviation from the experimentally-observed convergence iterations. The proposed estimates are thus shown to characterize the desynchronization conver-gence iterations significantly better than existing conjectures or bounds. Therefore, they contribute towards the analytic understanding of how a desynchronization-based system is expected to evolve from random initial conditions to the desynchronized steady state. Index Terms—Wireless sensor networks, desynchronization, stochastic modeling, pulse coupled oscillators, TDMA. I.

Abstract—This paper introduces the Discrete Dithered Desyn-chronization (D3SYNC) algorithm which is a decentralized Time Division Multiple Access (TDMA) technique in which a set of network nodes computes iteratively a conflict-free schedule so that each node obtains a portion of a frame that is an integer multiple of a fixed slot size. The algorithm is inspired by the dynamics of Pulse Coupled Oscillators (PCO), but unlike its predecessors that divide arbitrarily the frame among the nodes in the network, the D3SYNC allocates discrete resources among the network nodes. Our paper proves the convergence of the D3SYNC algorithm and gives an upperbound on the convergence time of the algorithm. Index Terms—Pulse coupled oscillators, desynchronization, and decentralized scheduling. I.