Enhancing Route lifetime in Vehicular Ad Hoc ‎Networks Based on Skellam Distribution Model

The emergence of smart cities and the need to use intelligent transportation systems has led to an increased reliance on vehicle ad hoc networks (VANET). The topology of VANET is highly dynamic, which results in a short effective routing time. This paper presents a two-stage algorithm to select a route that can sustain communication between vehicles for as long as possible while taking into account the variables that affect the VANET topology. The first stage uses Skellam distribution model to assess the connectivity probability of paths in ‎a 2d road network based on traffic-flow and the number of vehicles ‎joining and leaving the ‎network, accordingly, the path with the highest connectivity is chosen. In the second stage, the control packets sent only to vehicles on the selected path to detect routes between source and destination, thus reducing the overhead of control packets and increasing network stability. ‎ the algorithm adopts the principle of global evaluation to ‎estimate the lifetime ‎of the ‎detected ‎routes within the chosen path. ‎the route with the ‎best estimated ‎lifetime ‎is ‎chosen to be ‎the active route. ‎in the event of route failure, the validity of the next route in lifetime is confirmed to be adopted as the alternate route. The proposed algorithm was compared with both on-‎demand distance ‎vector routing protocol (AODV) protocol and the modified location-aided routing ‎‎(LAR) ‎protocol. The proposed algorithm showed greater network stability, higher performance in terms of longer lifetime route detection, less energy consumption and higher throughput.

Bayesian models for prediction of the set-difference in volleyball

We study and develop Bayesian models for the analysis of volleyball match outcomes as recorded by the set-difference. Due to the peculiarity of the outcome variable (set-difference) which takes discrete values from $-3$ to $3$, we cannot consider standard models based on the usual Poisson or binomial assumptions used for other sports such as football/soccer. Hence, the first and foremost challenge was to build models appropriate for the set-difference of each volleyball match. Here we consider two major approaches: (a) an ordered multinomial logistic regression model and (b) a model based on a truncated version of the Skellam distribution. For the first model, we consider the set-difference as an ordinal response variable within the framework of multinomial logistic regression models. Concerning the second model, we adjust the Skellam distribution to account for the volleyball rules. We fit and compare both models with the same covariate structure as in Karlis & Ntzoufras (2003). Both models are fitted, illustrated and compared within Bayesian framework using data from both the regular season and the play-offs of the season 2016/17 of the Greek national men’s volleyball league A1.

Data Analyses of European Soccer

<p>Using European soccer data sets, which contain data related to common European soccer leagues, players basic information, and teams’ goals, etc., this paper analyzes the characteristics of European soccer and players, explores data visualization regarding European soccer, and makes predictions of results of matches. Based on Python 3 and some of the packages inside, such as numpy, the author improves the data set to make it clear and user-friendly. Visualizations of data and basic statistics, including Poisson Distribution, are then utilized to determine the results. Finally, this paper analyzes the attacking and defending abilities of different leagues and teams in Europe, ascertains distributions of players’ attributes, and predicts match results by using Poisson distribution and Skellam Distribution. Generally, this paper analyzes data from leagues to matches to players. All these analyses are meaningful for the public to understand the characteristics of European soccer and the world behind the numbers.</p>

Approximation of the difference of two Poisson-like counts by Skellam

Poisson-like behavior for event count data is ubiquitous in nature. At the same time, differencing of such counts arises in the course of data processing in a variety of areas of application. As a result, the Skellam distribution – defined as the distribution of the difference of two independent Poisson random variables – is a natural candidate for approximating the difference of Poisson-like event counts. However, in many contexts strict independence, whether between counts or among events within counts, is not a tenable assumption. Here we characterize the accuracy in approximating the difference of Poisson-like counts by a Skellam random variable. Our results fully generalize existing, more limited, results in this direction and, at the same time, our derivations are significantly more concise and elegant. We illustrate the potential impact of these results in the context of problems from network analysis and image processing, where various forms of weak dependence can be expected.