A Connectivity Model for Agreement in Dynamic Systems

Abstract

The consensus problem is a fundamental paradigm in distributed systems, because it captures the difficulty to solve other agreement problems. Many current systems evolve with time, e.g., due to node mobility, and consensus has been little studied in these systems so far. Specifically, it is not well established how to define an appropriate set of assumptions for consensus in dynamic distributed systems. This paper studies a hierarchy of three classes of time-varying graphs, and provides a solution for each class to the problem of Terminating Reliable Broadcast (TRB). The classes introduce increasingly stronger assumptions on timeliness, so that the trade-off between weakness versus implementability and efficiency can be analysed. Being TRB equivalent to consensus in synchronous systems, the paper extends this equivalence to dynamic systems.

Solving k-Set Agreement Using Failure Detectors in Unknown Dynamic Networks

“…The connectivity model would then need to be adapted, since the synchrony of processes allows the algorithm to take advantage of the time windows provided by γ-journeys. Such a change would be a challenge, because the other approaches used to ensure reachability in a TVG ( [19]) rely on point to point communications, which is not applicable in an unknown network.…”

“…In fact, even if the edge between p i and p j is active infinitely often and the message is sent infinitely often, the message might always be sent in between two activation periods of the edge, thus never crossing it. To solve this problem, Gómez-Calzado et al defined in [19] the notion of timely journeys for the case of synchronous systems. We extend this solution into γ-journeys for the case of asynchronous communications.…”

“…With a γ-journey, processes are given an additional time window of γ units of time to send the message. In [19], this time was used to detect the activation of the edge. This solution is appropriate for point-to-point communications in a known network, since it allows the emitter of the message to resend the message to the receiver whenever the edge appears again.…”

“…Biely et al provide another algorithm for consensus in a similar model in [1], with weaker connectivity assumptions. In order to better formulate timeliness assumptions in the Time-Varying Graph formalism of [11], Gómez-Calzado et al introduce in [19] the notion of timely journeys. They also propose an algorithm solving the Terminating Reliable Broadcast, which is equivalent to consensus in their synchronous model.…”

Routing in Mobile Wireless Sensor Networks: A Leader-Based Approach

“…However, high mobility conditions could prevent many transmissions to successfully deliver messages [ 9 ]. On the one hand, any wireless communication requires a minimum time to be completed.…”