Steady-state traffic flow on a ring road with up- and down-slopes

Abstract

This paper studies steady-state traffic flow on a ring road with up-and down-slopes using a semi-discrete model. By exploiting the relations between the semi-discrete and the continuum models, a steady-state solution is uniquely determined for a given total number of vehicles on the ring road. The solution is exact and always stable with respect to the first-order continuum model, whereas it is a good approximation with respect to the semi-discrete model provided that the involved equilibrium constant states are linearly stable. In an otherwise case, the instability of one or more equilibria could trigger stop-and-go waves propagating in certain road sections or throughout the ring road. The indicated results are reasonable and thus physically significant for a better understanding of real traffic flow on an inhomogeneous road.

A geometric Brownian motion car-following model: towards a better understanding of capacity drop

“…It is noted that in simulations, the initial state is the state in the last simulation instant rather than the traffic condition at the beginning of the simulation. That is, as shown in Zhang, Wu, and Wong (2012) and Wu et al (2014), similar to the many existing car-following models, the car-following model in this paper takes the current traffic states into account. SDE (3) indicates that the stochastic process S(t) follows a Geometric Brownian motion, and therefore, under Itō's interpretation of SDEs (Øksendal 2010), obeys a log-normal distribution with expected value E[S(t)] = S 0 e −βt and variance Var[S(t)] = S 2 0 e −2βt (e σ 2 t − 1).…”

A macroscopic flow model for mixed bicycle–car traffic

“…Although the Eulerian method is most commonly used, the Lagrangian method has been successfully applied to numerically solve the kinematic wave model as well. This has been done for homogeneous traffic (Leclercq 2007;Wu et al 2014), as well as mixed traffic including trucks (van Wageningen-Kessels et al 2011) and motor cyclists (Gashaw, Harri, and Goatin 2018). Examples of the Lagrangian method applied to second-order flow models are Greenberg (2001Greenberg ( , 2004; Zhang, Wu, and Wong (2012).…”

Topology-based control design for congested areas in urban networks

“…By (11), the steady-state ρ * (ξ, η) implies space-independence of φ * (η), and can be achieved only for stationary D in (η) and S out (η). The steady-state flow can be obtained in analogy with [15] who analysed it for a single ring road with bottlenecks, i.e., ∀η ∈ D the following holds…”