Criterion for traffic phases in single vehicle data and empirical test of a microscopic three-phase traffic theory

A microscopic criterion for distinguishing synchronized flow and wide moving jam phases in single vehicle data measured at a single freeway location is presented. Empirical local congested traffic states in single vehicle data measured on different days are classified into synchronized flow states and states consisting of synchronized flow and wide moving jam(s). Then empirical microscopic characteristics for these different local congested traffic states are studied. Using these characteristics and empirical spatiotemporal macroscopic traffic phenomena, an empirical test of a microscopic three-phase traffic flow theory is performed. Simulations show that the microscopic criterion and macroscopic spatiotemporal objective criteria lead to the same identification of the synchronized flow and wide moving jam phases in congested traffic. It is found that microscopic three-phase traffic models can explain both microscopic and macroscopic empirical congested pattern features. It is obtained that microscopic distributions for vehicle speed difference as well as fundamental diagrams and speed correlation functions can depend on the spatial co-ordinate considerably. It turns out that microscopic optimal velocity (OV) functions and time headway distributions are not necessarily qualitatively different, even if local congested traffic states are qualitatively different. The reason for this is that important spatiotemporal features of congested traffic patterns are it lost in these as well as in many other macroscopic and microscopic traffic characteristics, which are widely used as the empirical basis for a test of traffic flow models, specifically, cellular automata traffic flow models.Comment: 27 pages, 16 figure

A THEORY OF TRAFFIC FLOW FOR CONGESTED CONDITIONS ON URBAN ARTERIAL STREETS II: FOUR ILLUSTRATIVE EXAMPLES

The accompanying theoretical paper by Vaughan and Hurdle proposes an analytical model for simulating traffic conditions along a badly congested arterial street; this paper illustrates the theory by means of four example problems. The examples are all set on the same street, but the time-varying origin-destination patterns differ. The first pattern is deliberately very simple so that the results can be compared to what one would expect. The second is a slightly more complex loading which can be thought of as a disaster evacuation scenario. The third is an idealized journey-from-work scenario and the last is a modified version of the third example in which demand is elastic. These last two examples illustrate the power to deal with dynamic phenomena that the model gains by solving problems in a work space defined by location and trajectory-label axes rather than the usual time-space plane

A theory of traffic flow for congested conditions on urban arterial streets II: Four illustrative examples

The accompanying theoretical paper by Vaughan and Hurdle proposes an analytical model for simulating traffic conditions along a badly congested arterial street; this paper illustrates the theory by means of four example problems. The examples are all set on the same street, but the time-varying origin-destination patterns differ. The first pattern is deliberately very simple so that the results can be compared to what one would expect. The second is a slightly more complex loading which can be thought of as a disaster evacuation scenario. The third is an idealized journey-from-work scenario and the last is a modified version of the third example in which demand is elastic. These last two examples illustrate the power to deal with dynamic phenomena that the model gains by solving problems in a work space defined by location and trajectory-label axes rather than the usual time-space plane.

A THEORY OF TRAFFIC FLOW FOR CONGESTED CONDITIONS ON URBAN ARTERIAL STREETS I: THEORETICAL DEVELOPMENT

In an earlier paper, the authors posed a time-dependent traffic flow problem in which travellers go home from work on a long arterial street. Each traveller enters the street at a particular time and place, bound for some given destination as prescribed by a continuous trip density function, but the time at which his or her trip is completed depends on the traffic conditions en route; hence on the origins, destinations, and departure times of other motorists. A solution was obtained, but a solution that is valid only if no intersection becomes saturated. In this paper, the analysis is extended to cover cases where some key intersection does become saturated. The model is macroscopic and differs from alternative models of traffic flow in two ways. The first and more important is that the impact of the origin destination pattern on the traffic dynamics and vice versa are explicitly recognized and included in the model. This is particularly important when the impact of exit flows on downstream facilities is an issue and in applications involving route choice or elastic demand, since it allows choices based on the travel times that would be experienced by the travellers actually making the decisions. The second difference is that is is explicitly a queueing model: the basic assumption is htat intersections along the roadway have capacities and that when the capacity of some key intersection is exceeded by the arrival flow, the large queue that results will be the dominant element controlling subsequent operation of the system

A theory of traffic flow for congested conditions on urban arterial streets I: Theoretical development

In an earlier paper, Vaughan, Hurdle and Hauer posed a time-dependent traffic flow problem in which travellers go home from work on a long arterial street. Each traveller enters the street at a particular time and place, bound for some given destination as prescribed by a continuous trip density function, but the time at which his or her trip is completed depends on the traffic conditions en route; hence on the origins, destinations, and departure times of other motorists. A solution was obtained, but a solution that is valid only if no intersection becomes saturated. In this paper, the analysis is extended to cover cases where some key intersection does become saturated. The model is macroscopic and differs from alternative models of traffic flow in two ways. The first and more important is that the impact of the origin destination pattern on the traffic dynamics and vice versa are explicitly recognized and included in the model. This is particularly important when the impact of exit flows on downstream facilities is an issue and in applications involving route choice or elastic demand, since it allows choices based on the travel times that would be experienced by the travellers actually making the decisions. The second difference is that it is explicitly a queueing model: the basic assumption is that intersections along the roadway have capacities and that when the capacity of some key intersection is exceeded by the arrival flow, the large queue that results will be the dominant element controlling subsequent operation of the system.

Road test of a freeway model

A few years ago Newell reworked classical traffic wave theory into "A simplified theory of kinematic waves in highway traffic" (Newell, 1993a and Newell, 1993b). The simplifications - use of cumulative count curves instead of flows for most of the calculations and a triangular flow-density relation to describe traffic flows - were sufficient to allow him to apply the theory (Newell, 1993c) to complex situations with multiple bottlenecks and multi-destination flows. This paper tests Newell's model by comparing its predictions with conditions observed at three freeway test sites. The test data from San Francisco Bay Area freeways is old, but extraordinarily detailed, so provides the necessary input and observed densities for comparison. In the tests, the model did a very good job of predicting the growth and decay pattern of large queues and the effect of traffic entering and leaving the roadway within a congested area, but had difficulties dealing with light or sporadic congestion. However, the predicted travel times were quite accurate even for lightly congested roadways. The estimation of roadway capacities needed as input proved to be a major problem. The duration of queuing - both in the model and the real world - is very sensitive to the maximum rate at which vehicles can enter bottlenecks, and neither standard estimation tools nor the data set provided estimates of sufficient precision. This would seem to be a problem for any freeway model, but for many purposes there is no need for the level of accuracy sought here, and for others better data would be available. Overall, the results were very encouraging: the model requires very little calculation time and delivers excellent results for the severely congested freeways that are of the most practical interest.