Observations from two freeway bottlenecks in and near Toronto, Canada indicate that the average rate vehicles discharge from a queue can be 10 % lower than the flow measured prior to the queue’s formation. Absent any influences from downstream, the queue discharge flows exhibited nearly stationary patterns that alternated between higher and lower rates. These alternating flow patterns were especially evident at one of the two sites, although the feature occurred at both sites during periods that immediately followed the onset of upstream queueing; i.e. a queue’s formation was always accompanied by a relatively low discharge rate followed later by a temporary surge in the discharge flow. When plotted cumulatively over time, however, the counts of discharging vehicles generally did not deviate by more than about 50 vehicles from a trend line of constant slope. Thus, the discharge flows are described as being ‘nearly’ constant; i.e. they varied (slightly) about a fixed rate. At each site, this average discharge rate exhibited little deviation from day to day. The present findings came by visually comparing transformed curves of cumulative vehicle arrival number vs time and cumulative occupancy vs time measured at neighboring loop detectors. This treatment of the data provided clear presentations of some important trac features and this facili-

Nowadays traffic flow and congestion is one of the main societal and economical problems related to transportation in industrialised countries. In this respect, managing traffic in congested networks re-quires a clear understanding of traffic flow operations. That is, insights into what causes congestion, what determines the time and location of traffic breakdown, how does the congestion propagate through the network, etc., are essential. For this purpose, during the past fifty years, a wide range of traffic flow theories and models have been developed to answer these research questions. This paper presents a overview of some fifty years of modelling vehicular traffic flow. A rich variety of modelling approaches developed so far and in use today will be discussed and compared. The considered models are classified based on the level-of-detail with which the vehicular flow is described. For each of the categories, issues like modelling accuracy, applicability, generalisability, and model calibration and validation, are dis-cussed.

Optimal coordination of variable speed limits to suppress shock waves∗

In this paper and in part II, we give the theory of a distinctive type of wave motion, which arises in any one-dimensional flow problem when there is an approximate functional relation at each point between the flow q (quantity passing a given point in unit time) and concentration k (quantity per unit distance). The wave property then follows directly from the equation of continuity satisfied by q and k. In view of this, these waves are described as 'kinematic', as distinct from the classical wave motions, which depend also on Newton's second law of motion and are therefore called 'dynamic'. Kinematic waves travel with the velocity aq/ak, and the flow q remains constant on each kirematic wave. Since the velocity of propagation of each wave depends upon the value of q carried by it, successive waves may coalesce to form 'kinematic shock waves'. From the point of view of kinematic wave theory, there is a discontinuous increase in q at a shock, but in reality a shock wave is a relatively narrow region in which (owing to the rapid increase of q) terms neglected by the flowconcentration relation become important. The general properties of kinematic waves and shock waves are discussed in detail in? 1. One example included in? 1 is the interpretation of the group-velocity phenomenon in a dispersive medium as a particular case of the kinematic

Abstract not found

This paper deals with the early results of a new model of pedestrian flow, conceived within a measure-theoretical framework. The modeling approach consists in a discrete-time Eulerian macroscopic representation of the system via a family of measures which, pushed forward by some motion mappings, provide an estimate of the space occupancy by pedestrians at successive time steps. From the modeling point of view, this setting is particularly suitable to treat nonlocal interactions among pedestrians, obstacles, and wall boundary conditions. In addition, analysis and numerical approximation of the resulting mathematical structures, which is the main target of this work, follow more easily and straightforwardly than in case of standard hyperbolic conservation laws, also used in the specialized literature by some Authors to address analogous problems.

Based on fluid-dynamic and many-particle (car-following) simulations of traffic flows in (urban) networks, we study the problem of coordinating incompatible traffic flows at intersections. Inspired by the observation of self-organized oscillations of pedestrian flows at bottlenecks [D. Helbing and P. Molnár, Phys. Rev. E 51 (1995) 4282–4286], we propose a self-organization approach to traffic light control. The problem can be treated as multi-agent problem with interactions between vehicles and traffic lights. Specifically, our approach assumes a priority-based control of traffic lights by the vehicle flows themselves, taking into account short-sighted anticipation of vehicle flows and platoons. The considered local interactions lead to emergent coordination patterns such as “green waves ” and achieve an efficient, decentralized traffic light control. While the proposed self-control adapts flexibly to local flow conditions and often leads to non-cyclical switching patterns with changing service sequences of different traffic flows, an almost periodic service may evolve under certain conditions and suggests the existence of a spontaneous synchronization of traffic lights despite the varying delays due to variable vehicle queues and travel times. The self-organized traffic light control is based on an optimization and a stabilization rule, each of which performs poorly at high utilizations of the road network, while their proper combination reaches a superior performance. The result is a considerable reduction not only in the average travel times, but also of their variation. Similar control approaches could be applied to the coordination of logistic and production processes.

Abstract. We establish sharp pointwise Green’s function bounds and consequent linearized stability for smooth traveling front solutions, or relaxation shocks, of general hyperbolic relaxation systems of dissipative type, under the necessary assumptions ([G,Z.1,Z.4]) of spectral stability, i.e., stable point spectrum of the linearized operator about the wave, and hyperbolic stability of the corresponding ideal shock of the associated equilibrium system, with no additional assumptions on the structure or strength of the shock. Restricting to Lax type shocks, we establish the further result of nonlinear stability with respect to small L 1 ∩ H 2 perturbations, with sharp rates of decay in L p, 2 ≤ p ≤ ∞, for weak shocks of general simultaneously symmetrizable systems; for discrete kinetic models, and initial perturbation small in W 3,1 ∩ W 3, ∞, we obtain sharp rates of decay in L p, 1 ≤ p ≤ ∞, for (Lax type) shocks of arbitrary strength. This yields, in particular, nonlinear stability of weak relaxation shocks of the discrete kinetic Jin–Xin and Broadwell models, for which spectral stability has been established in [HL,JH] and [KM], respectively. Our analysis follows the basic pointwise semigroup approach introduced by Zumbrun and Howard [ZH] for the study of traveling waves of parabolic systems; however, significant extensions are required to deal with the nonsectorial generator and more singular short-time behavior of the associated (hyperbolic) linearized equations. Our main technical innovation is a systematic method for refining large-frequency (shorttime) estimates on the resolvent kernel, suitable in the absence of parabolic smoothing. This seems particularly interesting from the viewpoint of general linear theory, replacing the zero-order estimates of existing theory with a series expansion to arbitrary order. The techniques of this paper should have further application in the closely related case of traveling waves of systems with partial viscosity, for example in compressible gas dynamics or MHD. Section

We present a model for the flow of pedestrians that describes features typical of this flow, such as the fall due to panic in the outflow of people through a door. The mathematical techniques essentially depend on the use of nonclassical shocks in scalar conservation laws.

Recent research has investigated various means of measuring link travel times on freeways. This search has been motivated in part by the fact that travel time is considered to be more informative to users than local velocity measurements at a detector station. But direct travel time measurement requires the correlation of vehicle observations at multiple locations, which in turn requires new communications infrastructure and/or new detector hardware. This paper presents a method for estimating link travel time using data from an individual dual loop detector, without requiring any new hardware. The estimation technique exploits basic traffic flow theory to extrapolate local conditions to an extended link. In the process of estimating travel times, the algorithm also estimates vehicle trajectories. The work demonstrates that the travel time estimates are very good provided there are no sources of delay, such as an incident, within a link.