Anchored desynchronization

Abstract

Abstract-Distributed algorithms based on pulse-coupled oscillators have been recently proposed in [4], [14] for achieving desynchronization of a system of identical nodes. Though these algorithms are shown to work properly by various computer simulations, they are still lack of rigorous theoretical proofs for both the convergence of the algorithms and the rates of convergence for these algorithms. On the other hand, all the nodes are not likely to be identical in many practical applications. In particular, there might be a node that needs to interact with the "outside" world and thus may not have the freedom to adjust its local clock. Motivated by all these, in this paper we consider the desynchronization problem in a system where there exists an anchored node that never adjusts the phase of its oscillator. For such a system, we propose a generic anchored desynchronization algorithm that achieves -desynchrony (defined in [4]) in O(n 2 ln( n )) rounds of firings. We also prove that our algorithm converges even for the generalized processor sharing (GPS) scheme, where every node is assigned a weight and the amount of resource received by a node is proportional to its weight. In comparison with the original algorithm in [4], we show that the rate of convergence of the original algorithm in [4] is not always better than ours and it is only better in the asymptotic regime.

On the stochastic modeling of desynchronization convergence in wireless sensor networks

“…In all desynchronization methods for WSNs [3,4,12], the number of convergence iterations required until the steady This work was funded by EPSRC grant EP/K033166/1. state plays a crucial role in latency, energy and bandwidth efficiency of WSN deployments.…”

“…state plays a crucial role in latency, energy and bandwidth efficiency of WSN deployments. Moreover, deriving estimates for the convergence iterations forms a crucial step in the analytic understanding of how the system evolves from a random setup to the steady state [12].…”

“…Deriving closed-form estimates for the required convergence iterations to SState is hard [2,4,9,12] due to the non-deterministic aspects of the desynchronization process, namely, the random initial condition of the phases and the random perturbations in the firing order of nodes due to noise. Hence, existing works focus on order-of-convergence [4] or lower bounds of convergence iterations of desynchronization, proven or conjectured via experimentation [3,9,10,12].…”

“…Hence, existing works focus on order-of-convergence [4] or lower bounds of convergence iterations of desynchronization, proven or conjectured via experimentation [3,9,10,12]. Moreover, these works consider only the noise-free case.…”

“…Desynchronization is a primitive leading to fair time-division multiple access (TDMA) scheduling without requiring clock synchronization among sensors or a coordinating node [3,4,6,7,[9][10][11][12][13]. The key concept behind desynchronization is reactive listening, according to which, nodes periodically broadcast fire messages and then update their next broadcast time based on the reception of fire messages from other nodes.…”