Related papers: Continuity, Uniqueness and Long-Term Behavior of N…
In this paper we propose a LWR-like model for traffic flow on networks which allows one to track several groups of drivers, each of them being characterized only by their destination in the network. The path actually followed to reach the…
This paper develops a strategic model of trade between two regions in which, depending on the relation among output, financial resources and transportation costs, the adjustment of prices towards an equilibrium is studied. We derive…
Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental…
We investigate a hydrodynamic system of Navier--Stokes/Cahn--Hilliard type, which describes the motion of a two-phase flow of two incompressible fluids with unmatched densities coupled with a soluble chemical species. Derived from Onsager's…
Recent literature has proved that stable dynamic routing algorithms have solid theoretical foundation that makes them suitable to be implemented in a real protocol, and used in practice in many different operational network contexts. Such…
We discuss the control of a human crowd whose dynamics is governed by a regularized version of Hughes' model, cf. Hughes: A continuum theory for the flow of pedestrians. Transportation research part B: methodological, 36 (2002). We assume…
We study traffic flow on roads with a localized periodic inhomogeneity such as traffic signals, using a stochastic car-following model. We find that in cases of congestion, traffic flow can be optimized by controlling the inhomogeneity's…
We present a fluid-dynamic model for the simulation of urban traffic networks with road sections of different lengths and capacities. The model allows one to efficiently simulate the transitions between free and congested traffic, taking…
Examples of dynamical systems proposed by Z. Artstein and C. M. Dafermos admit non-unique solutions that track a one parameter family of closed circular orbits contiguous at a single point. Switching between orbits at this single point…
We consider a queueing system with $n$ parallel queues operating according to the so-called "supermarket model" in which arriving customers join the shortest of $d$ randomly selected queues. Assuming rate $n\lambda_{n}$ Poisson arrivals and…
We study statistical properties of a family of maps acting in the space of integer valued sequences, which model dynamics of simple deterministic traffic flows. We obtain asymptotic (as time goes to infinity) properties of trajectories of…
In this paper we present a new competitive packet routing model with edge priorities. We consider players that route selfishly through a network over time and try to reach their destinations as fast as possible. If the number of players who…
Theoretical advances in the study of non-equilibrium phenomena are briefly reviewed with emphasis on steady state properties of one-dimensional driven lattice gases. The presentation is focused on the totally asymmetric simple-exclusion…
We introduce a framework and develop a theory of transitory queueing models. These are models that are not only non-stationary and time-varying but also have other features such as the queueing system operates over finite time, or only a…
Recently we proposed an extension to the traffic model of Aw, Rascle and Greenberg. The extended traffic model can be written as a hyperbolic system of balance laws and numerically reproduces the reverse $\lambda$ shape of the fundamental…
In the optimal velocity model with a time lag, we show that there appear multiple exact solutions in some ranges of car density, describing a uniform flow, a stable and an unstable congested flows. This establishes the presence of…
We consider two scalar conservation laws with non-local flux functions, describing traffic flow on roads with rough conditions. In the first model, the velocity of the car depends on an averaged downstream density, while in the second model…
We consider a stable open queuing network as a steady non-equilibrium system of interacting particles. The network is completely specified by its underlying graphical structure, type of interaction at each node, and the Markovian transition…
The tandem fluid queueing model is a useful tool for performance analysis and control design for a variety of transportation systems. In this article, we study the joint impact of stochastic capacity and spillback on the long-time…
Navigation apps have become pervasive in providing real-time route recommendations to travelers willing to minimize their travel times. However, such technologies introduce new complexities, raising concerns about their overall impact on…