Lossy gossip and composition of metrics

We study the monoid generated by n-by-n distance matrices under tropical (or min-plus) multiplication. Using the tropical geometry of the orthogonal group, we prove that this monoid is a finite polyhedral fan of dimension n(n-1)/2, and we compute the structure of this fan for n up to 5. The monoid captures gossip among n gossipers over lossy phone lines, and contains the gossip monoid over ordinary phone lines as a submonoid. We prove several new results about this submonoid, as well. In particular, we establish a sharp bound on chains of calls in each of which someone learns something new.Comment: Minor textual edits, final versio

TFUZZY-OF: a new method for routing protocol for low-power and lossy networks load balancing using multi-criteria decision-making

The internet of things (IoT) based on a network layer perspective includes low-power and lossy networks (LLN) that are limited in terms of power consumption, memory, and energy usage. The routing protocol used in these networks is called routing over low-power and lossy networks (RPL). Therefore, the IoT networks include smart objects that need multiple routing for their interconnections which makes traffic load balancing techniques indispensable to RPL routing protocol. In this paper, we propose a method based on fuzzy logic and the technique for the order of prioritization by similarity to the ideal solution (TOPSIS) as a well-known multi-criteria decision-making method to solve the load balancing problem by routing metrics composition. For this purpose, a combination of both link and node routing metrics namely hop count, expected transmission count, and received signal strength indicator is used. The results of simulations show that this method can increase the quality of services in terms of packet delivery ratio and average end-to-end delay

Identities in unitriangular and gossip monoids

We establish a criterion for a semigroup identity to hold in the monoid of $n \times n$ upper unitriangular matrices with entries in a commutative semiring $S$. This criterion is combinatorial modulo the arithmetic of the multiplicative identity element of $S$. In the case where $S$ is idempotent, the generated variety is the variety $\mathbf{J_{n-1}}$, which by a result of Volkov is generated by any one of: the monoid of unitriangular Boolean matrices, the monoid $R_n$ of all reflexive relations on an $n$ element set, or the Catalan monoid $C_n$. We propose $S$-matrix analogues of these latter two monoids in the case where $S$ is an idempotent semiring whose multiplicative identity element is the `top' element with respect to the natural partial order on $S$, and show that each generates $\mathbf{J_{n-1}}$. As a consequence we obtain a complete solution to the finite basis problem for lossy gossip monoids.Comment: 14 page

Equational Reasonings in Wireless Network Gossip Protocols

Gossip protocols have been proposed as a robust and efficient method for disseminating information throughout large-scale networks. In this paper, we propose a compositional analysis technique to study formal probabilistic models of gossip protocols expressed in a simple probabilistic timed process calculus for wireless sensor networks. We equip the calculus with a simulation theory to compare probabilistic protocols that have similar behaviour up to a certain tolerance. The theory is used to prove a number of algebraic laws which revealed to be very effective to estimate the performances of gossip networks, with and without communication collisions, and randomised gossip networks. Our simulation theory is an asymmetric variant of the weak bisimulation metric that maintains most of the properties of the original definition. However, our asymmetric version is particularly suitable to reason on protocols in which the systems under consideration are not approximately equivalent, as in the case of gossip protocols

Reliable and timely event notification for publish/subscribe services over the internet

The publish/subscribe paradigm is gaining attention for the development of several applications in wide area networks (WANs) due to its intrinsic time, space, and synchronization decoupling properties that meet the scalability and asynchrony requirements of those applications. However, while the communication in a WAN may be affected by the unpredictable behavior of the network, with messages that can be dropped or delayed, existing publish/subscribe solutions pay just a little attention to addressing these issues. On the contrary, applications such as business intelligence, critical infrastructures, and financial services require delivery guarantees with strict temporal deadlines. In this paper, we propose a framework that enforces both reliability and timeliness for publish/subscribe services over WAN. Specifically, we combine two different approaches: gossiping, to retrieve missing packets in case of incomplete information, and network coding, to reduce the number of retransmissions and, consequently, the latency. We provide an analytical model that describes the information recovery capabilities of our algorithm and a simulation-based study, taking into account a real workload from the Air Traffic Control domain, which evidences how the proposed solution is able to ensure reliable event notification over a WAN within a reasonable bounded time window. © 2013 IEEE

Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey

Growing progress in sensor technology has constantly expanded the number and range of low-cost, small, and portable sensors on the market, increasing the number and type of physical phenomena that can be measured with wirelessly connected sensors. Large-scale deployments of wireless sensor networks (WSN) involving hundreds or thousands of devices and limited budgets often constrain the choice of sensing hardware, which generally has reduced accuracy, precision, and reliability. Therefore, it is challenging to achieve good data quality and maintain error-free measurements during the whole system lifetime. Self-calibration or recalibration in ad hoc sensor networks to preserve data quality is essential, yet challenging, for several reasons, such as the existence of random noise and the absence of suitable general models. Calibration performed in the field, without accurate and controlled instrumentation, is said to be in an uncontrolled environment. This paper provides current and fundamental self-calibration approaches and models for wireless sensor networks in uncontrolled environments