Convergence of Desynchronization Primitives in Wireless Sensor Networks: A Stochastic Modeling Approach

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 evaluation 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 convergence 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.

Distributed time division multiple access protocol for multi-hop wireless sensor networks

“…However the experimental trend of the expected delay agrees very well with both simulations and models. This result is also similar to the trend of the expected delay from our previous work [5], even though the experiment has been implemented with the different hardware platform. Eventually, we found that the expected delay is based on the value of α.…”

“…As demonstrated in Figure 4, the number of firing time until convergence to steady state, k SS depends on the value of the coupling constant, α. However, we found that the expected delay until convergence to steady state does not follow closely the theoretical results from the simulation and the stochastic modeling from our previous work [5]. This is because we tested in the real world implementation where disturbance from wireless interference of co-existing networks (e.g., WiFi networks using the same unlicensed channels of the 2.4GHz band) cannot be excluded.…”

“…Nodes will initially desynchronize requiring k SS periods to TDMA behavior in steady state, requiring k SS T s. We have proposed a stochastic model demonstrating the expected influence of design settings, k SS which is controlled by α [5], as well as system parameters W tot , W hid and A, on the expected delay.…”

Decentralized multichannel medium access control

“…These features make Desync quite popular [12,35]. Regarding the convergence speed of Desync, an operational estimate of the number of firing rounds required to reach convergence was established in [8,9].…”

Fast Desynchronization for Decentralized Multichannel Medium Access Control

“…Regarding the study of the convergence speed of desynchronization algorithms, mostly estimates based on simulations or empirical measurements have been derived. In effect, only lower bounds [14], [19], order-of-convergence estimates [2], [6], [19] and operational estimates [25] have been established. However, no upper bounds are currently known for the convergence speed of desynchronization algorithms, despite the fact that such bounds provide for worst-case guarantees of time and 0 θ i+1 (t i−1 ) Fig.…”