Self-Stabilizing Supervised Publish-Subscribe Systems

In this paper we present two major results: First, we introduce the first self-stabilizing version of a supervised overlay network by presenting a self-stabilizing supervised skip ring. Secondly, we show how to use the self-stabilizing supervised skip ring to construct an efficient self-stabilizing publish-subscribe system. That is, in addition to stabilizing the overlay network, every subscriber of a topic will eventually know all of the publications that have been issued so far for that topic. The communication work needed to processes a subscribe or unsubscribe operation is just a constant in a legitimate state, and the communication work of checking whether the system is still in a legitimate state is just a constant on expectation for the supervisor as well as any process in the system

Bounds for self-stabilization in unidirectional networks

A distributed algorithm is self-stabilizing if after faults and attacks hit the system and place it in some arbitrary global state, the systems recovers from this catastrophic situation without external intervention in finite time. Unidirectional networks preclude many common techniques in self-stabilization from being used, such as preserving local predicates. In this paper, we investigate the intrinsic complexity of achieving self-stabilization in unidirectional networks, and focus on the classical vertex coloring problem. When deterministic solutions are considered, we prove a lower bound of $n$ states per process (where $n$ is the network size) and a recovery time of at least $n(n-1)/2$ actions in total. We present a deterministic algorithm with matching upper bounds that performs in arbitrary graphs. When probabilistic solutions are considered, we observe that at least $\Delta + 1$ states per process and a recovery time of $\Omega(n)$ actions in total are required (where $\Delta$ denotes the maximal degree of the underlying simple undirected graph). We present a probabilistically self-stabilizing algorithm that uses $\mathtt{k}$ states per process, where $\mathtt{k}$ is a parameter of the algorithm. When $\mathtt{k}=\Delta+1$, the algorithm recovers in expected $O(\Delta n)$ actions. When $\mathtt{k}$ may grow arbitrarily, the algorithm recovers in expected O(n) actions in total. Thus, our algorithm can be made optimal with respect to space or time complexity

HSkip+: A Self-Stabilizing Overlay Network for Nodes with Heterogeneous Bandwidths

In this paper we present and analyze HSkip+, a self-stabilizing overlay network for nodes with arbitrary heterogeneous bandwidths. HSkip+ has the same topology as the Skip+ graph proposed by Jacob et al. [PODC 2009] but its self-stabilization mechanism significantly outperforms the self-stabilization mechanism proposed for Skip+. Also, the nodes are now ordered according to their bandwidths and not according to their identifiers. Various other solutions have already been proposed for overlay networks with heterogeneous bandwidths, but they are not self-stabilizing. In addition to HSkip+ being self-stabilizing, its performance is on par with the best previous bounds on the time and work for joining or leaving a network of peers of logarithmic diameter and degree and arbitrary bandwidths. Also, the dilation and congestion for routing messages is on par with the best previous bounds for such networks, so that HSkip+ combines the advantages of both worlds. Our theoretical investigations are backed by simulations demonstrating that HSkip+ is indeed performing much better than Skip+ and working correctly under high churn rates.Comment: This is a long version of a paper published by IEEE in the Proceedings of the 14-th IEEE International Conference on Peer-to-Peer Computin

Stabilizing data-link over non-FIFO channels with optimal fault-resilience

Self-stabilizing systems have the ability to converge to a correct behavior when started in any configuration. Most of the work done so far in the self-stabilization area assumed either communication via shared memory or via FIFO channels. This paper is the first to lay the bases for the design of self-stabilizing message passing algorithms over unreliable non-FIFO channels. We propose a fault-send-deliver optimal stabilizing data-link layer that emulates a reliable FIFO communication channel over unreliable capacity bounded non-FIFO channels

Design and analysis of adaptive hierarchical low-power long-range networks

A new phase of evolution of Machine-to-Machine (M2M) communication has started where vertical Internet of Things (IoT) deployments dedicated to a single application domain gradually change to multi-purpose IoT infrastructures that service different applications across multiple industries. New networking technologies are being deployed operating over sub-GHz frequency bands that enable multi-tenant connectivity over long distances and increase network capacity by enforcing low transmission rates to increase network capacity. Such networking technologies allow cloud-based platforms to be connected with large numbers of IoT devices deployed several kilometres from the edges of the network. Despite the rapid uptake of Long-power Wide-area Networks (LPWANs), it remains unclear how to organize the wireless sensor network in a scaleable and adaptive way. This paper introduces a hierarchical communication scheme that utilizes the new capabilities of Long-Range Wireless Sensor Networking technologies by combining them with broadly used 802.11.4-based low-range low-power technologies. The design of the hierarchical scheme is presented in detail along with the technical details on the implementation in real-world hardware platforms. A platform-agnostic software firmware is produced that is evaluated in real-world large-scale testbeds. The performance of the networking scheme is evaluated through a series of experimental scenarios that generate environments with varying channel quality, failing nodes, and mobile nodes. The performance is evaluated in terms of the overall time required to organize the network and setup a hierarchy, the energy consumption and the overall lifetime of the network, as well as the ability to adapt to channel failures. The experimental analysis indicate that the combination of long-range and short-range networking technologies can lead to scalable solutions that can service concurrently multiple applications

The robustness of democratic consensus

In linear models of consensus dynamics, the state of the various agents converges to a value which is a convex combination of the agents' initial states. We call it democratic if in the large scale limit (number of agents going to infinity) the vector of convex weights converges to 0 uniformly. Democracy is a relevant property which naturally shows up when we deal with opinion dynamic models and cooperative algorithms such as consensus over a network: it says that each agent's measure/opinion is going to play a negligeable role in the asymptotic behavior of the global system. It can be seen as a relaxation of average consensus, where all agents have exactly the same weight in the final value, which becomes negligible for a large number of agents.Comment: 13 pages, 2 fig