Navegação descentralizada de múltiplos pacotes em redes de transporte e estudo sobre a influência da velocidade máxima permitida nas vias de uma cidade com desordem - Silva, Samuel Morais da (2020)
We investigate by numerical simulation and finite-size analysis the impact of long-range shortcuts on a spatially embedded transportation network. Our networks are built from two-dimensional (d = 2) square lattices to be improved by the addition of long-range shortcuts added with probability P(ri j) _ rai j [J. M. Kleinberg, Nature 406, 845 (2000)]. Considering those improved networks, we performed numerical simulation of multiple discrete package navigation and found a limit for the amount of packages flowing through the network. Such limit is characterized by a critical probability of creating packages pc, where above this value a transition to a congested state occurs. Moreover, pc is found to follow a power-law, pc _ Lg , where L is the network size. Our results indicate the presence of an optimal value of amin _ 1:7, where the parameter g reaches its minimum value and the networks are more resilient to congestion for larger system sizes. Interestingly, this value is close to the analytically found value of a for the optimal navigation of single packages in spatially embedded networks, where aopt = d. Finally, we show that the power spectrum for the number of packages navigating the network at a given time step t, which is related with the divergence of the expected delivery time, follows a universal Lorentzian function, regardless the topological details of the networks. The inadequate functioning of the vehicle transport system in a city causes damage from the economic, environmental and public health point of view to the population. This phenomenon usually happens due to the presence of a high demand as to the volume of traffic in relation to the capacity of the ways of behaving such demand in some specific regions of the city. In this work, we propose a systematic study about a model that presents traffic dynamics with spatial and temporal constraints. The model includes a queuing implementation on the streets of a city, and from this implementation, we try to understand under what conditions the system becomes vulnerable to the presence of congestion. Initially we propose an idealized description for the cities, where these are represented by means of a two-dimensional network composed by roads connected to each other. In a first approach we consider the limited volume routes, and in these we apply the Spatial Point Queue Model (SPQM). Based on this model, we investigated the occurrence of a phase transition between a free state of complete fluidity for the vehicles and a congested state where cars can not reach their destinations. The phase transition was characterized as a function of the parameter t, which is associated to the maximum traffic speed of the cars in the tracks. From this study we observed that the relationship between, maximum speed in the roads and the existence of congestion does not happen in a trivial way. This behavior is observed in the condition of a fixed demand of cars in the network with origin and destiny established of random form. For this condition, we find a regime where a greater number of cars can reach their destinations if we reduce the maximum speed on the roads. We then apply the same model to the road network of some urban centers, such as Fortaleza, Boston and Porto. For these centers, we conclude that the model can be efficient in predicting the existence of speed limits that improve traffic in real cities. We also investigated the behavior of the system When modifying the waiting time t through the Gaussian and power law distributions, with or without competition of way.