Gonçalo Jacinto

An analytical framework to infer multihop path reliability in MANETs

Due to complexity and intractability reasons, most of the analytical studies on the reliability of communication paths in mobile ad hoc networks are based on the assumption of link independence. In this paper, an analytical framework is developed 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 a set of integro-differential equations and provide a recursive scheme for their computation. Finally, numerical results illustrate the computation of the metrics; these results are compared with independent link approximation results.

Nearest Neighbor Connectivity in Two-Dimensional Multihop MANETs

A Mobile Ad Hoc Network (MANET) is characterized to be a network with free, cooperative, and dynamic nodes, self-organized in a random topology, without any kind of infrastructure, where the communication between two nodes usually occurs using multihop paths. The number of hops used in the multihop path is an important metric for the design and performance analysis of routing protocols in MANETs. In this paper, we derive the probability distribution of the hop count of a multihop path between a source node and a destination node, fixed at a known distance from each other, and when a fixed number of nodes are uniformly distributed in a region of interest. This distribution is obtained by the Poisson randomization method. To obtain the multihop path, we propose a novel routing model in which the nearest distance routing protocol (NR) is analyzed. Numerical results are obtained to evaluate the performance of the NR.

Hop Count Distributions of the Furthest and Nearest Distance Routing Protocols in Mobile Ad Hoc Networks

In this paper, 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. To achieve efficient progress towards the destination, a new dynamic propagation model is proposed. The analysis is based on the Poisson randomization technique which also allows us to obtain the hop count distribution when nodes are scattered according to a Poisson process. Numerical results are obtained to illustrate the shape of the hop count distribution for both protocols.

Estimation of the traffic intensity in a piecewise-stationary Mt/Gt/1 queue with probing

We use a probing strategy to estimate the time dependent traffic intensity in an Mt/Gt/1 queue, where the arrival rate and the general service-time distribution change from one time interval to another, and derive statistical properties of the proposed estimator. We present a method to detect a switch from a stationary interval to another using a sequence of probes to improve the estimation. At the end, we compare our results with two estimators proposed in the literature for the M/G/1 queue.

Probing a M/G/1 queue with general input and service times

We consider the estimation of the arrival rate and the service time moments of a M/G/1 queue with probing, i.e., with special customers (probes) entering the system. The probe inter-arrival times are i.i.d. and probe service times follow a general positive distribution. The only observations used are the arrival times, service times and departure times of probes. We derive the main equations from which the quantities of interest can be estimated. Two particular probe arrivals, deterministic and Poisson, are investigated.

Application of Item Response Theory to Mathematics High School Exams in Portugal

Item response theory (IRT) provides statistical models that relate an examinee’s response to a test item to an underlying latent trait that is measured by the items. Unlike classical test theory, IRT models focus on the responses to individual questions instead on the total score obtained in the test.

Modelling the Duration of Multihop Paths in Mobile Ad Hoc Networks

Mobile ad hoc networks are characterized by having nodes that are cooperative and communicate without any kind of infrastructure. The mobility and multihop capability of these networks lead the network topology to change rapidly and unpredictably; this aspect must be incorporated in effective models to describe the dynamics of multihop paths.When modeling the duration of multihop paths, a great part of the literature assumes that the links of multihop paths behave independently. This simplifies the modeling and reduces the complexity of computations. However, each link shares a common node with each of its neighbor links, turning the independent link assumption generally not valid. In this chapter, we use a piecewise deterministic Markov model that characterizes the random behaviour of a multihop path not assuming independent links. We obtain the mean path duration of multihop paths and compare the results for the used model with the ones obtained by assuming independent links. Numerical results illustrate that independent link approximation results underestimate the mean path duration, with the most significant differences being observed with low node mobility and higher path durations.