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The concept of extended slash distribution is introduced. For the extended slash distribution of the sum of two independent logistic random variables, the characteristic function, moments, absolute...

We consider the random variables Zi=βi2Yi/∑k=1mβk2Yk where Yi,i=1…,m are independent inverted chi-square r.v. with νi degrees of freedom. The probability density function of Z=(Z1,Z2,…Zm) is obtain...

Three new models for the flow–density relationship are proposed in this work. The resulting flow–density curves are concave in the whole range of feasible values for the parameters. These models have four parameters, three of them being the jam density, the free-flow speed and the kinematic wave speed. The fourth parameter is a shape parameter. The models allow for a great flexibility for fitting of real traffic flow and density data. A remarkable property of these models is the fact that they yield a bilinear fundamental diagram when the shape parameter tends to infinity. The models have been tested with freeway data and urban data. The results demonstrate that the models achieve an excellent goodness of fit and yield realistic estimates of the parameters. The models proposed in this work are a valuable tool not only for fitting flow–density data but also for its use in traffic flow dynamic models.

Some recent developments in path generation have been based on neural network mechanism databases, which instantaneously provide an approximate solution of the synthesis problem. We describe a way to reduce the design space, ensuring that the neural network always yields a consistent crank-rocker mechanism with optimal transmission angle. Moreover, instead of the usual strategy of using Fourier coefficients, we propose a new method based on wavelet descriptors to represent the shape of the path, where the points do not need to be sampled at a constant time interval. Numerical results demonstrate the superiority of this wavelet-based neural network over the Fourier-based network in finding the optimal mechanism. They also show the accuracy of the proposed approach in providing near optimal crank-rocker mechanism solutions for path generation.

A procedure for the enumeration of the graphs of 1-dof planetary gear trains is presented. The planetary gear trains enumerated have a single input shaft and a single output shaft. These gear trains should satisfy certain functional constraints that avoid the existence of idle links. These constraints are derived. The enumeration of the graphs exploits the resulting particular features of the structure of planetary gear trains by proceeding gradually through different levels of that structure. The procedure includes a check for isomorphism among the resulting graphs. Finally, the graphs of the planetary gear trains having up to 9 links are presented. Those graphs containing embedded structures are identified.

A model of the evolution of speed perturbations in dense traffic flow is presented in this work. Traffic volume is assumed to be at capacity and a given vehicle undergoes a temporary speed drop. This speed drop may propagate through the traffic flow until it is either dissipated or causes the stoppage of the traffic flow. The two events are random and occur with a certain probability. The proposed model leads to a set of recurrence equations for the speed drop and its duration. The simulation of those equations allows the estimation of the normalization probability, that is, the probability that the perturbation vanishes. An analytical approximation for the normalization probability is also proposed. The approximation is based on a result from Brownian motion theory. The agreement with the simulation results is fairly good given the simplicity of the approximation. The model and its analytical approximation allows one to conjecture which could be the most important parameters that determine the evolution of the perturbation. The implications of this conjecture are commented and the assumptions of the model are contrasted with related work.

A procedure for solving, suboptimally, the traveling salesman problem is presented. The set of points on the traveling salesman tour is distributed over a region having the shape of a circular or ring sector. The procedure is based on an optimal partition of the sector and reduces the tour construction to a sorting problem. Namely, the tour is constructed by visiting the points in radial or angular order depending on the part of the sector on which they are located. The optimal partition is derived by a continuous approximation of the set of points. It is defined by a single parameter and simple analytical expressions for it are obtained. A great number of numerical tests were carried out to evaluate the performance of the procedure. These tests allowed a measure of the difference from the optimum solution that could be obtained for problems up to a few hundred points. The results show that the euclidean length of the tours produced by the partition procedure grows, on average, like AN , where A is the region area and N the number of points. The initial tours are improved by means of the Or’s algorithm and the final tours obtained are nearly as good as those given by more intrincate improvement heuristics. The whole procedure, that is, the tour construction and improvement heuristics, is rather simple to implement on a computer, which makes it very appealing to use in routing software.