Understanding and Modeling Driver Behavior in Dense
Traffic Flow
Principal
Investigator:
H. Michael
Zhang
Dept. of
Civil and Environmental Engineering
University
of California at Davis
Davis, CA
95616
Ph:
530-754-9203
Fax:
(530)-752-7872
Funded by
a UCTC Year 13 grant.
This research will examine
drivers’ car-following behavior in dense traffic flow and identify the critical
behavioral elements and parameters that control traffic flow phase
transitions. Such an understanding will
aid the development of more sound microscopic traffic models that are the
central building blocks of popular traffic simulation packages such as CORSIM,
TRANSIMS and PARAMICS. The main task of
this research concerns the development of a car-following model that reproduce
the capacity gap and hysteresis observed in traffic flow.
Regardless of the cause of
congestion, congested traffic usually exhibits two prominent features: 1) an
initial front that induces sharp flow/density/speed changes, and 2) a prolonged
period of stop-and-go motion across the congested region after the front
passes. Viewed in the phase plane,
these features translate into flow-density or speed-density or flow-speed jumps
near a critical density/speed/flow region and periodic orbits, or hysteresis
loops, in the high density or low speed
region. Eddie (1961) from Lincoln Tunnel
data, first noticed the existence of jumps in the density-speed scatter plot
and hypothesized that speed-density or flow-density phase plots have two
disjoint branches––one for free-flow traffic and the other for congested
traffic, with the maximum flow of free-flow branch considerably higher than
that of the congested branch, hence the name ``capacity drop''. Eddie noted that this jump in flow/speed
could be an intrinsic property of vehicular traffic flow. Drake,
Schofer and May (1967) applied the two-regime hypothesis to traffic
data and found that it produced the
best fit with lowest standard error.
Other experimental evidence of the existence of the ``capacity
drop'' is from Japanese and German
highways. Koshi, Iwasaki, and Ohkura
(1983) analyzed traffic data from the Tokyo Expressway and found that their flow-density
plots resembles the mirror image of a reversed
lambda, with data points
scattered more widely near the right
leg of the reversed lambda. Kerner and Rehborn (1998), on the other hand, have shown that in
German data the flow rate out of a wide jam is considerably lower than the
maximal possible flow rate in free flow and a multitude of homogeneous states
of synchronized flow covers a broad region around the characteristic line J.
The first clear experimental evidence of traffic hysteresis was provided by
Treiterer and Myers (1974). These authors studied a platoon of vehicles and estimated their average flow, density and
travel speed. They found that both the flow-density and speed-density plots
have loop structures. Other experimental evidence of traffic hysteresis include
the observations of Maes (1979) on Belgian
highways and Zhang (1999) on
California highways. Zhang (1999) also
noted the linkage between hysteresis and stop-start waves and provided a
traffic theory to model it. The first exploitation of traffic hysteresis,
however, is by Newell (1965), who hypothesized that drivers respond
to stimulus differently in acceleration and deceleration and developed a model
that contains hysteresis loops. Newell's hypothesis on driver behavior was
corroborated by experimental observations of Forbes (1963), who observed that a
sudden change in drivers' response time occurs before and after a sudden
deceleration. Forbes further suggested that this sudden change of response time
explains the jumps found on various phase diagrams and proposed flow-density
diagrams with multiple branches.
Conventional traffic stream models
(i.e., flow-density or speed-density diagrams or formulas), however, are
usually described by continuous or even smooth functions that contain neither
jumps nor hysteresis loops. A common
property of these models is that most of these functions can be derived from
one car-following model or another under steady-state traffic conditions, which
provides them a behavioral and theoretical foundation. The fact that these
car-following models lead to smooth flow-density or speed-density relations
attest, to a certain degree, their inadequacy to model complex traffic flow
patterns that exhibit capacity drops and hysteresis loops. This is not
surprising if one considers that conventional car-following models treat both
drivers and roads as homogeneous entities---that is, they are modeling
identical drivers who travel on homogeneous roads. The traffic that produces capacity drops and hysteresis loops, on
the other hand, comprise diverse groups of drivers who travel on inhomogeneous
roads and may behave differently under different driving conditions. A
plausible car-following theory that explains these nonlinear phenomena must
consider these inhomogeneities.
This research proposes a
car-following model that captures situation-dependent driving behavior. A
central concept in this model is that the time gap a driver adopts depends on
both the driving condition and the type of motion (acceleration, deceleration, or
coasting) he is in:
(1)
where 
is the time gap adopted by driver n at time t , 
is the space gap
between driver n’s vehicle and the immediate
vehicle ahead of him, and P(t)
indicates the type of motion the driver is in at time t. Fig.1 shows the
definition of variables.
Figure
1. Definitions of time and space gaps
From the definitions of time and space gaps, we have the
following car-following
model
(2)
where 
is the travel speed
of driver n’s vehicle at time t.
From Eq. 2 we can see that driver
behavior is embodied in the time gap variable, which is a function of traffic
condition (captured by space gap, a measure of crowdness) and motion type
(acceleration/deceleration/coasting). By specifying different forms for the
function H, we obtain various specific car-following models, among which
some were discussed earlier in the text and some are brand new models that can
reproduce either the capacity drop or traffic hysteresis or both phenomena. The form of the function H can be depicted graphically, and Figs 2 and 3 show two
specifications of the H function,
which lead to two specific cases of the car-following model, which we shall
refer as Model C and Model D respectively.
The corresponding fundamental diagrams for steady-state traffic for
Models C and D are also shown in Figs 2 and 3 on the right, and as can be seen
from these figures, capacity drop and hysteresis are built into the behavior of
these models. Indeed this can be verified through traffic simulation, which
shows the dynamic evolution of traffic governed by the proposed car-following
model. These results are shown in Figs
4 and 5, respectively. The capacity
drop and hysteresis are evident in these figures (the details of the
theoretical and numerical analysis of these models can be found in Zhang and
Kim , 2001).
In summary, both theoretical analysis
and numerical simulations have demonstrated the potential of the new
car-following model to describe complex traffic flow phenomena. Further
research will be devoted to validate this model with experimental data. It is hoped
that this new model, once validated, can provide a more realistic and powerful
traffic flow model for high fidelity microscopic traffic simulations.
Papers:
References:
Drake, J.S., Schofer, J.L., and May, A.D.,(1967). A Statistical Analysis of Speed Density Hypothesis. Highway Research Record 154, pp. 53-87.
Edie, L. C. (1961). Following and Steady-State Theory for Non-congested Traffic, Operations Research, Vol .9, pp.66-76.
Forbes, T.W. (1963). Human Factor
Considerations in Traffic Flow Theory. Highway research Board, Record 15, pp. 60-66.
Kerner, B.S. (1998) Experimental
features of self-organization in traffic flow, Physical Review Letters Vol. 81, No. 17, pp.3797-3800.
Koshi, M., Iwasaki, M., Ohkura, I.
(1983). Some Findings and an Overview
on Vehicular Flow Characteristics, Proc. 8th
Intl. Symp. On Transportation and Traffic Flow Theory (V. Hurdle, E.
Hauer, G. Stuart ed.) pp. 403-426.
Maes, W. (1979) Traffic data
collection system for the Belgian motorway
Network–measures of effectiveness
aspects. Proceedings of the International Symposium on Traffic Control Systems,
Vol. 2D–Analysis and Evaluation, pp. 45--73.
Newell, G.F.(1961). Nonlinear Effects in the Dynamics of Car Following, Operations
Research, Vol 9, 209-229.
Treiterer, J. and Myers, J.A.
(1974). The Hysteresis Phenomenon in Traffic Flow. Proc. 6th Intl. Symp. on
Transportation and Traffic theory, (D.J. Buckley ed.), pp. 13-38.
Zhang H. M. and T. W. Kim (2001) A
car-following theory for multiphase vehicular traffic flow, pre-print 01-3456,
2001TRB Annual Meeting.
Zhang, H.M.(1999). A mathematical theory of traffic hysteresis, Transportation Research, Part B 33, 1-23.
Figure 2 The H
function and the corresponding fundamental diagram for Model C
Figure 3 The H
function and the corresponding fundamental diagram for Model D
Figure 4 Simulation
results for Model C on a ring road
Figure 5 Simulation
results for Model D on a ring road