Fuzzy microscopic traffic model

AN ASSIGNMENT ON
REVIEW OF FUZZY MICROSCOPIC TRAFFIC MODEL
CIV8331 ADVANCE TRAFFIC ENGINEERING
MUJAHID TIJJANI TASHI
SPS/17/MCE/00034
mujahidtashi@gmail.com
Course Lecturer: Prof. H M Alhassan
May 2018.

INTRODUCTION
Definitions
A branch of logic designed to allow degrees of
imprecision in reasoning and knowledge, typified by
terms such as 'very', 'quite possibly', and 'unlikely', to
be represented in such a way that the information can
be processed by computer(Collins English dictionary).
Logic used in computers and other electronic devices
for processing imprecise or variable data in place of the
traditional binary values (Webster’s New World
College Dictionary).

.
Fuzzy logic was suggested by Zadeh as a method for
mimicking the ability of human reasoning using a small
number of rules and still is producing a smooth output
via a process of interpolation.
For example a person of height 1.79 would belong to
both tall and not tall sets with a particular degree of
membership. As the height of a person increases the
membership grade within the tall set would increase
whilst the membership grade within the not tall set
would decrease.
Fuzzy logic is simply the extension of conventional logic
to the case where partial set membership can exist. Rule
condition can be satisfied partially and system outputs
are calculated by interpolation and therefore have
output smoothness over the equivalent binary-valued
rule base.

AIM AND OBJECTIVES
AIM
To understand how fuzzy microscopic model works.
OBJECTIVES
 To predict the reaction of the driver of the following
vehicle (acceleration and deceleration rate) given the
action of the leading vehicle.
 To determine the efficiency of fuzzy microscopic
model

STATEMENT OF PROBLEM
For the past several decades traffic flow has been generally
analyzed under the assumption that all drivers behave in a
similar manner in a traffic stream, studies have shown that a
deterministic relationship exists between the action of a
vehicle and the reaction of the vehicles that follow. The
reaction of drivers to the action of other drivers are perhaps
not base on the deterministic one-to-one relationship, but on
a set of vague driving rule developed through experience, the
difference in the reaction of leading vehicle to the action of
following vehicle resulted in vague decision made by drivers.
A model known as fuzzy microscopic traffic model was
created to incorporate difference in driver response and the
vagueness in driving rule.

BRIEF REVIEW OF CAR-FOLLOWING
BEHAVIOR
 Car-following is a control process in which the driver
of the following vehicle attempts to maintain a safe
distance between his/her car and the vehicle ahead by
accelerating or decelerating in response to the actions
of the vehicle ahead.
 Five distinctive features of car following behavior was
proposed as a framework to evaluate different car
following model.

CONTD.
 These features are:
1. The car-following behavior is approximate in nature.
2. Response to stimuli in car-following is asymmetric.
3. Phenomena of closing-in and shying-away are
observed in car-following.
4. Phenomenon of drift is observed in car-following.
5. Car-following is locally and asymptotically stable.

CAR-FOLLOWING MODELS
The following are representative car-following models.
Stopping-Distance Model:
This Model assumes that a following vehicle always
maintains a safe following distance in order to bring the
vehicle to a safe stop if the leading vehicle suddenly
stops. (Kometani & Sasaki, 1959)

CONTD.
 Where Δx is the relative distance between the lead and
following vehicles
 vL is the speed of the lead vehicle
 vF is the speed of the following vehicle
 T is the driver’s reaction time; and
 α, β, β1, and b0 are calibration constants.

CONTD.
Action-Point Model
The Action-Point Model is the first car-following model
to incorporate human perception of motion. The model
developed by Michaels suggests that the dominant
perceptual factor is changes in the apparent size of the
vehicle (i.e., the changing rate of visual angle) (Michaels,
1963):

CONTD.
Where WL is the width of the lead vehicle.
This model assumes that a driver appropriately accelerates or
decelerates if the angular velocity exceeds a certain threshold.
Once the threshold is exceeded, the driver chooses to
decelerate until he/she can no longer perceive any relative
velocity.

CONTD.
General Motors Model:
The fundamental concept behind the General Motors
Model is the stimulus-response theory (Chandler et al.,
1958). Equation (1) presents a representative
formulation.

CONTD.
Where
 aF(t+T) is the acceleration or deceleration rate of the FV at time t+T
 VL(t) is the speed of the lead vehicle at time t
 VF(t) is the speed of the following vehicle at time t
 XL(t) is the spacing of the lead vehicle at time t
 XF(t) is the spacing of the following vehicle at time t
 T is the perception-reaction time of the driver; and
 m, l, and α are constants to be determined.

 Basically, the response is the acceleration
(deceleration) rate of the following vehicle. This is
a function of driver sensitivity and the stimulus.
The stimulus is assumed to be the difference
between the speed of the lead vehicle and that of
the following vehicle. Driver sensitivity is a
function of the spacing between the lead and
following vehicles and the speed of the following
vehicle.
 However, one weakness of the General Motors
Model is that the response of the following vehicle
is determined by one stimulus, speed relative to
the leading vehicle. When the relative speed
between the two vehicles is zero, the acceleration
or deceleration response is zero.

FUZZY LOGIC CAR-FOLLOWING MODEL
 The car-following models discussed above have
established a unique interpretation of drivers’ car-
following behaviors. A driver in a car-following
situation is described as a safe distance keeper in
the Stopping-Distance Model, a state monitor who
wants to keep perceptions below the threshold in
the Action-Point Model and a stimuli-responder in
the General Motors Model,
 constraints such as: symmetry between
acceleration and deceleration, the “safe headway”
concept, and constant acceleration or deceleration
above the threshold are non-realistic.

Fuzzy microscopic traffic model

TYPES OF FUZZY MODEL
 Linguistic fuzzy model
 The linguistic fuzzy model (Zadeh, 1973; Mamdani, 1977)
has been introduced as a way to capture available (semi-
)qualitative knowledge in the form of if–then rules:
 Example: Consider a simple fuzzy model which
qualitatively describes how the heating power of a gas
burner depends on the oxygen supply (assuming a constant
gas supply). We have a scalar input, the oxygen flow rate
(x), and a scalar output, the heating power (y). Define the
set of antecedent linguistic terms: A = {Low, OK, High},
and the set of consequent linguistic terms: B = {Low, High}.
The qualitative relationship between the model input and
output can be expressed by the following rules:

CONTD.
 R1: If O2 flow rate is Low then heating power is
Low:
 R2: If O2 flow rate is OK then heating power is
High:
 R3: If O2 flow rate is High then heating power is
Low:

CONTD.
 Takagi–Sugeno model
 The Takagi–Sugeno (TS) fuzzy model (Takagi and Sugeno,
1985), uses crisp functions in the consequents. It can be
seen as a combination of linguistic and mathematical
regression modeling in the sense that the antecedents
describe fuzzy regions in the input space in which
consequent functions are valid.

CONCLUSION
Fuzzy logic car-following model including a comparison with
other car following models were described in this
assignment. This model can determine the degree to which a
driver controls longitudinal acceleration according to the
relationship between the preceding vehicle and his/her
vehicle. The fuzzy logic model evaluates the driver’s
acceleration and deceleration rates using a rule base in
natural language.

RECOMMENDATION
It can be seen that fuzzy microscopic traffic model
incorporated both the vehicle factor as well as the factors that
drive drivers to making vague decision in a traffic stream.
Fuzzy microscopic model should be adopted by car
producing companies to incorporate it in their design
because fuzzy microscopic traffic model when incorporated
in a car will greatly improve the safety level of the car as well
as the safety level of the occupant.

REFERENCES
 Collins English Dictionary
 Kometani, E. & Sasaki, T.; (1959). Dynamic behaviour of traffic with a
nonlinear spacing speed relationhip. Proceedings of the Symposium of
Theory of Traffic Flow, pp. 105-119, New York, USA, 1959
 Mamdani, E.H. (1977). Application of fuzzy logic to approximate
reasoning using linguistic systems. Fuzzy Sets and Systems 26, 1182–
1191.
 Takagi, T. andM. Sugeno (1985). Fuzzy identification of systems and its
application to modeling and control. IEEE Trans. Systems, Man and
Cybernetics 15(1), 116–132.
 Webster’s New World College Dictionary, 4th Edition.
 Zadeh, L.A. (1973). Outline of a new approach to the analysis of
complex systems and decision processes. IEEE Trans. Systems, Man,
and Cybernetics 1, 28–44.

Fuzzy microscopic traffic model

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