Jam Density Research Articles

New equilibrium function of traffic flow

Using nonlinear stability theory in macroscopic traffic flow model, we proposed a new equilibrium function starting from the existing equilibrium functions. The kinematic wave velocity at jam density yielded by this equilibrium function is consistent with the empirical value, and this equilibrium function is related to the critical stability in higher density interval.

Comparison of System- and User-Optimal Stochastic Dynamic Network Design Models Using Monte Carlo Bounding Techniques

This paper compares the continuous network design problem formulations using system-optimal (SO) and user-optimal (UO) dynamic traffic assignment when the following independent stochastic parameters with known discrete probability distributions are considered: time-dependent origin-destination demands, time-varying saturation flow rates and jam density, and network improvement unit costs. These models propagate traffic according to Daganzo's cell transmission model. Two Monte Carlo bounding techniques, common random numbers (CRN) and independent random numbers (IRN) strategies, are used to solve the stochastic models. The results show that the CRN strategy outperforms IRN on a simple test network resembling a freeway corridor. The network size is sacrificed to gain higher confidence probabilistic behavior and to understand intuitively the effects of different network improvement policies. Although the findings may not necessarily be generalized, they provide interesting and insightful information. First, ...

Comparison of System- and User-Optimal Stochastic Dynamic Network Design Models Using Monte Carlo Bounding Techniques

This paper compares the continuous network design problem formulations using system-optimal (SO) and user-optimal (UO) dynamic traffic assignment when the following independent stochastic parameters with known discrete probability distributions are considered: time-dependent origin–destination demands, time-varying saturation flow rates and jam density, and network improvement unit costs. These models propagate traffic according to Daganzo's cell transmission model. Two Monte Carlo bounding techniques, common random numbers (CRN) and independent random numbers (IRN) strategies, are used to solve the stochastic models. The results show that the CRN strategy outperforms IRN on a simple test network resembling a freeway corridor. The network size is sacrificed to gain higher confidence probabilistic behavior and to understand intuitively the effects of different network improvement policies. Although the findings may not necessarily be generalized, they provide interesting and insightful information. First, the SO and UO models allocate investment differently for certain budgets, and the stochastic models may lead to an erroneous solution (i.e., a bottleneck) for some budgets. Subsequently, the results of three comparison cases are discussed: (a) for the SO models, it should be more valuable to solve the stochastic than the deterministic models, but it is not always the case for the UO models; (b) the SO models appear more desirable than the UO models for single-level analysis; and (c) it should be more valuable to solve the stochastic model accounting for more randomness.

A new approach for modeling of Fundamental Diagrams

According to the intra-vehicle interaction, a traffic flow can generally be divided into three homogeneous states (1) that of free driving, (2) that of bunched driving, and (3) that of standing. The parameter describing the state of free driving is the desired speed, for the state of bunching it is the intra-vehicle gaps (time headway) within the convoy and the mean speed of the convoy, and for the state of standing it is the maximum jam density. These are the most essential parameters which do not depend on the actual traffic situation. This paper introduces a new model which considers the Fundamental Diagram (equilibrium speed–flow–density relationship) as a function of the homogeneous states. All traffic situations in reality can be considered as combinations of the homogeneous states and therefore can be described by the essential parameters mentioned above. The non-congested (fluid) traffic is a combination (superposition) of the states of free driving and bunched driving, the congested (jam, stop, and go) traffic is a combination of the states of bunched driving (go) and standing (stop). The contribution of the traffic states within the differently congested traffic situations can then be easily obtained from the queuing and probability theory. As a result, Fundamental Diagram in all equilibrium traffic situations is derived as simple functions of the essential parameters. According to the new model the capacity of freeways and rural highways can be determined by measuring the essential parameters. This is much easier than measuring the capacity directly. Furthermore, the probabilities of the various traffic states can be obtained from the new model. This leads to new possibilities in real-time controlling and telematics. The new model is verified by comprehensive measurements carried out on freeways and rural highways in Germany.

A Novel Traffic Stream Model Deriving from a Bimodal Kinetic Equilibrium 1

The traffic stream model corresponding to the (bimodal) local equilibrium solution of the kinetic equation of Nelson is presented, and shown to compare favorably, for densities not too near jam density, to several selected classical traffic stream models. It is argued that the bimodal traffic stream model is preferable, in that all of its parameters are related to a microscopic model of driver behavior (and road characteristics). Some operational consequences (i.e., pertaining to measurements) of the kinetic equilibrium interpretation of traffic stream models are discussed.

On deterministic developments of traffic stream models

Classical deterministic (or “mechanical”) developments of traffic stream models from car-following models are criticized on the following basis. The evaluation of the constant of integration for initial conditions corresponding to speed zero and headway equal to the reciprocal of jam density ignores large numbers of possibly relevant solutions of the underlying car-following model. Some undesirable consequences, particularly the restriction to temporally and spatially constant flow conditions, of viewing traffic stream models as being deterministic consequences of car-following models are also noted. It is suggested that an approach to traffic stream models via kinetic models possibly would be more appropriate and useful.

Traffic dynamics

Previous descriptions of traffic flow under changing conditions are shown to be untenable. Deterministic relationships between traffic speed and density do not allow for observed scatter and imply that traffic can lock up spontaneously. Equilibrium relationships between speed and density allow impossibly high traffic densities and provide unrealistically slow responses to changes in roadway and traffic conditions. A qualitatively superior representation of traffic flow is developed. Traffic is described as a fluid that cannot be compressed beyond a certain density, k jam. The equations of state are: (1) Volume = speed x density. (2) Continuity of vehicles. (3) Traffic speed “relaxes” to the free-flow speed of the roadway, independent of density except that volume cannot exceed roadway capacity and flow is incompressible when traffic density is equal to the jam density. The representation is innovative in two respects: (1) Traffic flowing with density = k jam is explicitly recognized as being incompressible. (2) No speed-density relationship is contained in or implied by the traffic formulation. The new traffic formulation models both interrupted and uninterrupted traffic flow. It has been tested by simulating several traffic flow situations. The reproductions of light to moderate flows are equal to those of the best previous traffic formulation, and the representations of congested and bottleneck flow are superior. The new traffic formulation also reproduces the general qualities of observed speed/ volume curves and provides interpretation of those curves in terms of upstream and downstream bottlenecks.

High Density Vehicular Flow-Density Relationships

Experimental research was conducted on vehicular flow-density-speed relationships for conditions ranging from maximum flow to jam density. Investigation was made of the applicability of the Greenshields and Greenberg models for vehicular flow to the experiments which were based on the halting of a high-volume stream of traffic by a traffic signal. Photographic observations provided speeds, densities, and flows for successive pairs of vehicles brought to a halt. After analyzing the material in accordance with the principles of macroscopic car-following, it was concluded that both the Greenshields and Greenberg models provided a good indication of the relationship between speed, density, and flow within the range of densities studied.