- in memoriam: José Rodrigues Dias (1951-2023)
- in memoriam: Vladimir Goncharov (1962-2017)
- in memoriam: Graça Carita (1975-2016)
- Notícias
- Eventos
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Seminários
- The representation theory of the unitriangular group and other related groups
- On Computational Properties of Cauchy Problems
- Sets as Properties
- Artinian algebras and Jordan type
- Iterated Systems, Networks and Applications
- Isogeometric Analysis: mathematical and implementational aspects, with applications
- Sampling elusive populations: methods and applications
- Existence, non-existence and multiplicity results for some third-order periodic problems
- Convergence: what’s logic got to do with it?
- The Mathematics of Fires
- Old-age mortality deceleration and the modal age at death: insights from dynamic laws of adult mortality
- Stochastic differential equations models of animal growth and profit optimization in cattle raising
- Multidisciplinary approach for a real problem: modeling road traffic accidents
- The finite elements method and Freefem software
- DeepParticle: deep-learning invariant measure by minimizing Wasserstein distance on data generated from an interacting particle
- Kinematics: classification methods and combinatorial invariants for complex motion in biology
- Fractional Poisson Analysis in one Dimension
- Mathematics driven by epidemics
- ALMOST-POSITIONED NUMERICAL SEMIGROUPS
- A Delta approximation method on estimation for SDE mixed models
- Classificação de uma família de nós de Lorenz redutíveis
- Categoria de Lusternik-Schinrelmann e Grupos de Lie
- Euclides, Taylor, e a perspectiva esférica enquanto objecto matemático
- Time Series Clustering
- Condições geométricas para a existência e unicidade de projeção
- Sobre o volume de campos vetoriais
- Multiple criteria optimization: methods and applications
- Selective Base Revisions
- Nonautonomous attractors and bifurcation structures on nonautonomous families of flat topped tent maps
- Strongly nonlinear third order impulsive boundary value problems
- Solvability of second order coupled systems on the half-line
- Stochastic differential equations: brief introduction and profit optimization in fisheries
- Positioned Numerical Semigroups
- Tipo de Jordan de álgebras artinianas
- Complexidade em sistemas dinâmicos de baixa dimensão
- CFD Analysis in cerebral aneurysms
- Variational problems involving nonlocal supremal functionals
- Different Types of Stabilities in Times of Instability
- Non-linear systems of PDEs. Two examples from applications.
- Modelação de eventos extremos – uma introdução: aplicação ao decatlo e ao heptatlo atlético
- Comportamento assimptótico de soluções de problemas com valores na fronteira
- A característica de Euler de hipersuperfícies de espaços forma
- Brief introduction to stochastic differential equations and applications in Biology and Finance
- Sampling strategies in rural and urban settings in Africa - Looking from the sky
- Epidemiologia espácio-temporal no controlo da tuberculose
- Connectivity and Reliability of Mobile Ad-Hoc Networks
- Mathematical modeling, optimal control and complex network of epidemic models: case study of COVID-19 in Portugal
- Feature selection for marine species origin prediction
- Provas de Mestrado
- Provas de Doutoramento
- Apontadores
Connectivity and Reliability of Mobile Ad-Hoc Networks
Mobile ad hoc networks (MANETs) are characterized as a network with free, cooperative, and mobile nodes, self-organized in random topologies, and without any kind of infrastructure. An inherent property of these networks is that the communication between two nodes usually occurs over a multihop path.
First we derive the probability distribution of the number of hops required for a source node to reach a destination node in a two-dimensional mobile ad hoc network when a fixed number of nodes are uniformly distributed in a finite region under the nearest- and furthest distance routing protocols. The analysis is based on the Poisson randomization technique.
Once a multihop path is established, the functionality of the network depends on the reliability of communication paths. We present an analytical framework to characterize the random behavior of a multihop path and derive path metrics to characterize the reliability of paths. This is achieved through the modeling of a multihop path as a PDMP (piecewise deterministic Markov process). Two path based metrics are obtained as expectations of functionals of the process: the mean path duration and the path persistence. We show that these metrics are the unique solution of aset of integro-differential equations and provide a recursive scheme for their computation.
Finally, numerical results illustrate the shape of the hop count distribution for both protocols and the computation of the metrics for the path reliability.
