1,721,028 research outputs found
On the Microscopic Modeling of Vehicular Traffic on General Networks
Full text linkWe introduce a formalism to deal with the microscopic modeling of vehicular traffic on a road network. Traffic on each road is unidirectional, and the dynamics of each vehicle is described by a follow-the-leader model. From a mathematical point of view, this amounts to defining a system of ODEs on an arbitrary network. A general existence and uniqueness result is provided, while priorities at junctions are shown to hinder the stability of solutions. We investigate the occurrence of the Braess paradox in a time-dependent setting within this model. The emergence of Nash equilibria in a nonstationary situation results in the appearance of Braess-type paradoxes, and this is supported by numerical simulations
Infectious Diseases Spreading Fought by Multiple Vaccines Having a Prescribed Time Effect
Full text linkWe propose a framework for the description of the effects of vaccinations on the spreading of an epidemic disease. Different vaccines can be dosed, each providing different immunization times and immunization levels. Differences due to individuals\u27 ages are accounted for through the introduction of either a continuous age structure or a discrete set of age classes. Extensions to gender differences or to distinguish fragile individuals can also be considered. Within this setting, vaccination strategies can be simulated, tested and compared, as is explicitly described through numerical integrations.23 page
Well posedness and control in renewal equations with nonlocal boundary conditions
Full text linkA large class of biological models leads to initial boundary value problems for nonhomogeneous balance laws, possibly with nonlocal boundary conditions. Here, for these equations, a general well posedness result is proved, a full set of stability estimates is provided, and sample control problems are tackled
Nash Equilibria in Traffic Networks with Multiple Populations and Origins–Destinations
Full text linkDifferent populations of vehicles travel along a network. Each population has its origin, destination and travel costs — which may well be unbounded. Under the only requirement of the continuity of the travel costs, we prove the existence of a Nash equilibrium for all populations. Conditions for its uniqueness are also provided. A few cases are treated in detail to show specific situations of interest
Nonlocal Mixed Systems With Neumann Boundary Conditions
No full textWe prove well posedness and stability in (Formula presented.) for a class of mixed hyperbolic–parabolic nonlinear and nonlocal equations in a bounded domain with no flow along the boundary. While the treatment of boundary conditions for the hyperbolic equation is standard, the extension to (Formula presented.) of classical results about parabolic equations with Neumann conditions is here achieved
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