Outgoing Roads Research Articles

Output-Feedback PDE Control of Traffic Flow on Cascaded Freeway Segments

We develop in this paper a boundary output feedback control law for an underactuated network of traffic flow on two connected roads; one incoming and one outgoing road connected by a junction. The macroscopic traffic dynamics on each road segment are governed by Aw-Rascle-Zhang (ARZ) model, consisting of second-order nonlinear partial differential equations (PDEs) of traffic density and velocity. The control objective is to stabilize the traffic network system on both roads around a chosen reference system. Using a ramp metering located at the outlet of the outgoing road, we actuate the traffic flux leaving this considered domain. Boundary measurements of traffic flux and velocity are taken at the junction connecting the two road segments. A delay-robust full state feedback control law and a boundary observer are designed for this under-actuated network of two systems interconnected through their boundaries. Each system consists of two hetero-directional linear first-order hyperbolic PDEs. The exponential convergence to the reference system is achieved.

Global Weak Solutions to the Cauchy Problem for a Two-Phase Model at a Node

This paper considers a system of two conservation laws with a Lipschitz continuous flow and deals with solutions to the Cauchy problems at a node. The system considered is the two-phase traffic model, proposed in [R. M. Colombo, F. Marcellini, and M. Rascle, SIAM J. Appl. Math., 70 (2010), pp. 2652--2666]. We are able to provide global in time existence of solutions at a node with a single incoming road and $m$ outgoing roads. Neither assumptions on the smallness of the total variation of initial data are required, as usual in the case of systems, nor on the range of the initial data.

Representation of capacity drop at a road merge via point constraints in a first order traffic model

We reproduce the capacity drop phenomenon at a road merge by implementing a non-local point constraint at the junction in a first order traffic model. We call capacity drop the situation in which the outflow through the junction is lower than the receiving capacity of the outgoing road, as too many vehicles trying to access the junction from the incoming roads hinder each other. In this paper, we first construct an enhanced version of the locally constrained model introduced by Haut et al. (Proceedings 16th IFAC World Congress. Prague, Czech Republic 229 (2005) TuM01TP/3), then we propose its counterpart featuring a non-local constraint and finally we compare numerically the two models by constructing an adapted finite volumes scheme.

A Riemann solver at a junction compatible with a homogenization limit

We consider a junction regulated by a traffic lights, with n incoming roads and only one outgoing road. On each road the Phase Transition traffic model, proposed in [6], describes the evolution of car traffic. Such model is an extension of the classic Lighthill–Whitham–Richards one, obtained by assuming that different drivers may have different maximal speed.By sending to infinity the number of cycles of the traffic lights, we obtain a justification of the Riemann solver introduced in [9] and in particular of the rule for determining the maximal speed in the outgoing road.

The Riemann Problem at a Junction for a Phase Transition Traffic Model

We extend the Phase Transition model for traffic proposed in [8], by Colombo, Marcellini, and Rascle to the network case. More precisely, we consider the Riemann problem for such a system at a general junction with $n$ incoming and $m$ outgoing roads. We propose a Riemann solver at the junction which conserves both the number of cars and the maximal speed of each vehicle, which is a key feature of the Phase Transition model. For special junctions, we prove that the Riemann solver is well defined.

Conservation law models for traffic flow on a network of roads

The paper develops a model of traffic flow near an intersection, where drivers seeking to enter a congested road wait in a buffer of limited capacity. Initial data comprise the vehicle density on each road, together with the percentage of drivers approaching the intersection who wish to turn into each of the outgoing roads. &nbsp If the queue sizes within the buffer are known, then the initial-boundary value problems become decoupled and can be independently solved along each incoming road. Three variational problems are introduced, related to different kind of boundary conditions. From the value functions, one recovers the traffic density along each incoming or outgoing road by a Lax type formula. &nbsp Conversely, if these value functions are known, then the queue sizes can be determined by balancing the boundary fluxes of all incoming and outgoing roads. In this way one obtains a contractive transformation, whose fixed point yields the unique solution of the Cauchy problem for traffic flow in an neighborhood of the intersection. &nbsp The present model accounts for backward propagation of queues along roads leading to a crowded intersection, it achieves well-posedness for general $L^\infty $ data, and continuity w.r.t. weak convergence of the initial densities.

Traffic flow optimization on roundabouts

The aim of this article is to propose an optimization strategy for traffic flowon roundabouts using amacroscopic approach. The roundabout is modeled as a sequence of 2 × 2 junctions with one main lane and secondary incoming and outgoing roads. We consider two cost functionals: the total travel time and the total waiting time, which give an estimate of the time spent by drivers on the network section. These cost functionals areminimized with respect to the right ofway parameter of the incoming roads. For each cost functional, the analytical expression is given for each junction. We then solve numerically the optimization problem and show some numerical results. Copyright © 2014 John Wiley & Sons, Ltd.

Traffic Flow Optimization on Roundabouts

The aim of this paper is to optimize the traffic flow on roundabouts using a macroscopic approach. The roundabout is modeled as a sequence of 2x2 junctions: with one mainline and secondary incoming and outgoing roads. We consider two cost functionals: the total travel time and the total waiting time, which give an estimate of the time spent by drivers on the network section. These cost functionals are minimized analytically for each junction with respect to the right of way parameter of the incoming road. Then, through numerical simulations, the traffic behavior is studied for the whole roundabout. The numerical approximations compare the traffic behavior for an optimized right of way parameter and for a fixed constant parameter.

The LWR traffic model at a junction with multibuffers

We consider the Lighthill-Whitham-Richards traffic flow model on a network composed by a single junction $J$ with $n$ incoming roads, $m$ outgoing roads and $m$ buffers, one for each outgoing road. We introduce a concept solution at $J$, which is compared with that proposed in [14]. Finally we study the Cauchy problem and, in the special case of $n \le 2$ and $m \le 2$, we prove existence of solutions to the Cauchy problem, via the wave-front tracking method.

Vehicular Traffic Flow Dynamics on a Bus Route

We propose a new model in the analysis of car traffic flow phenomena which in particular refers to a bus route, namely, a closed path embedded in the urban network of roads. The model consists in a scalar balance law for the (macroscopic) density of cars, with source terms representing incoming and outgoing roads (with respect to the bus route), and a coupled system of ODEs describing the dynamics of (microscopic) buses along the route. The coupling takes into account both the buses as moving bottlenecks in the car flow and the effect of the car flow on the buses' ODEs as microscopic vehicles. The resulting fully coupled micro--macro model promises to give an appropriate description for the car flow as well as for the buses. Finally, we study the model numerically.

Intersection Modeling using a Convergent Scheme based on Hamilton-Jacobi Equation

This paper presents a convergent scheme for Hamilton-Jacobi (HJ) equations posed on a junction. The general aim of the approach is to develop a framework using similar tools to the variational principle in traffic theory to model intersections taking in account many incoming and outgoing roads. Then a time-explicit numerical scheme is proposed. It is based on the very classical Godunov scheme. The proposed model could be characterized as a pointwise model of intersection without any internal state. Moreover, our model respects the invariance principle. This scheme is applied to the cases of diverge junctions. The goal is to know how to manage the fluxes in order to maximize the flow through the junction.

Optimal distribution of traffic flows in emergency cases

The aim of this work is to present a technique for the optimisation of emergency vehicles travel times on assigned paths when critical situations, such as car accidents, occur. Using a fluid-dynamic model for the description of car density evolution, the attention is focused on a decentralised approach reducing to simple junctions with two incoming roads and two outgoing ones (junctions of 2 × 2 type). We assume the redirection of cars at junctions is possible and choose a cost functional that describes the asymptotic average velocity of emergency vehicles. Fixing an incoming road and an outgoing road for the emergency vehicle, we determine the local distribution coefficients that maximise such functional at a single junction. Then we use the local optimal coefficients at each node of the network. The overall traffic evolution is studied via simulations, both for simple junctions or cascade networks, evaluating global performances when optimal parameters on the network are used.

Connectivity-aware minimum-delay geographic routing with vehicle tracking in VANETs

In this paper, we propose the connectivity-aware minimum-delay geographic routing (CMGR) protocol for vehicular ad hoc networks (VANETs), which adapts well to continuously changing network status in such networks. When the network is sparse, CMGR takes the connectivity of routes into consideration in its route selection logic to maximize the chance of packet reception. On the other hand, in situations with dense network nodes, CMGR determines the routes with adequate connectivity and selects among them the route with the minimum delay. The performance limitations of CMGR in special vehicular networking situations are studied and addressed. These situations, which include the case where the target vehicle has moved away from its expected location and the case where traffic in a road junction is so sparse that no next-hop vehicle can be found on the intended out-going road, are also problematic in most routing protocols for VANETs. Finally, the proposed protocol is compared with two plausible geographic connectivity-aware routing protocols for VANETs, A-STAR and VADD. The obtained results show that CMGR outperforms A-STAR and VADD in terms of both packet delivery ratio and ratio of dropped data packets. For example, under the specific conditions considered in the simulations, when the maximum allowable one-way transmission delay is 1 min and one gateway is deployed in the network, the packet delivery ratio of CMGR is approximately 25% better than VADD and A-STAR for high vehicle densities and goes up to 900% better for low vehicle densities.

Multicommodity flows on road networks

In this paper, we discuss the multicommodity flow for vehicular traffic on road networks. To model the traffic, we use the “Aw-Rascle” multiclass macroscopic model. We describe a solution to the Riemann problem at junctions with a criterion of maximization of the total flux, taking into account the destination path of the vehicles. At such a junction, the actual distribution depends on the demands and the supplies on the incoming and outgoing roads, respectively. Furthermore, this new distribution scheme captures efficiently key merging characteristics of the traffic and in contrast to M. Herty, S. Moutari and M. Rascle, Networks and Heterogeneous Media, 1, 275-294, 2006, leads to an easy computational model to solve approximately the homogenization problem described in M. Herty, S. Moutari and M. Rascle, Networks and Heterogeneous Media, 1, 275-294, 2006, (M. Herty and M. Rascle, SIAM J. Math. Anal., 38(2), 595-616, 2006). Furthermore, we deduce the equivalent distribution scheme for the LWR multiclass model in M. Garavello and B. Piccoli, Commun. Math. Sci., 3, 261-283, 2005, and we compare the results with those obtained with the “Aw-Rascle” multiclass model for the same initial conditions.