Sensitivity analysis of permeability parameters for flows on Barcelona networks

Abstract

We consider the problem of optimizing vehicular traffic flows on\ud an urban network of Barcelona type, i.e. square network with\ud streets of not equal length. In particular, we describe the effects\ud of variation of permeability parameters, that indicate the amount\ud of flow allowed to enter a junction from incoming roads.\ud On each road, a model suggested by Helbing et al. (2007) [11]\ud is considered: free and congested regimes are distinguished,\ud characterized by an arrival flow and a departure flow, the latter\ud depending on a permeability parameter. Moreover we provide a\ud rigorous derivation of the model from fluid dynamic ones, using\ud recent results of Bretti et al. (2006) [3]. For solving the dynamics\ud at nodes of the network, a Riemann solver maximizing the through\ud flux is used, see Coclite et al. (2005) [4] and Helbing et al.\ud (2007) [11].\ud The network dynamics gives rise to complicate equations, where\ud the evolution of fluxes at a single node may involve time-delayed\ud terms from all other nodes. Thus we propose an alternative\ud hybrid approach, introducing additional logic variables. Finally we\ud compute the effects of variations on permeability parameters over\ud the hybrid dynamics and test the obtained results via simulations

Design and analysis of a discrete method for a time‐delayed reaction–diffusion epidemic model

“…The analysis of those models has been a fruitful topic of research in the literature. Moreover, the reliable computational simulation of those systems has also become a cornerstone in order to propose pertinent applications 20‐24 . In the case of models based on differential equations, consistency, stability, and convergence of the numerical methodologies have been the criteria for the reliability of the discretizations.…”

“…Moreover, the reliable computational simulation of those systems has also become a cornerstone in order to propose pertinent applications. [20][21][22][23][24] In the case of models based on differential equations, consistency, stability, and convergence of the numerical methodologies have been the criteria for the reliability of the discretizations. However, in light that the variables under study are populations, emphasis has been done on the development of finite-difference schemes that preserve the positivity and/or boundedness of the solutions of epidemic problems, [25][26][27] as well as other approaches for more complicated scenarios.…”