This document reviews a fuzzy microscopic traffic model that uses fuzzy logic to simulate traffic streams at signalized intersections. The model represents vehicle parameters like position and velocity as fuzzy numbers. It combines aspects of cellular automata models and fuzzy calculus. Compared to traditional cellular automata models, the fuzzy microscopic model requires fewer simulation runs, stores less data, and estimates output distributions in a single run. Future work could explore a stochastic cellular automata model with fuzzy decision rules to analyze more complex traffic situations.

1. BAYERO UNIVERSITY, KANO
FACULTY OF ENGINEERING
REVIEW OF FUZZY MICROSCOPIC TRAFFIC MODEL.
ASSIGNMENT ON
(CIV8331)ADVANCE TRAFFIC ENGINEERING.
OJIAH ONIMISI KANDIRI
SPS/17/MCE/00027
onimisikandiri@gmail.com
COURSE LECTURER: PROF. H.M ALHASSAN.
MAY, 2018

2. INTRODUCTION
The condensed traffic together with the increasing number of traffic
requires more complex solution of traffic situation including the traffic
signal control, the monitoring and controlling of traffic became a
crucial task. Fuzzy Logic is a form of logic used in some expert
systems and other artificial-intelligence applications in which variables
can have degrees of truthfulness or falsehood represented by a range of
values between 1 (true) and 0 (false). With fuzzy logic, the outcome of
an operation can be expressed as a probability rather than as a certainty.
For example, in addition to being either true or false, an outcome might
have such meanings as probably true, possibly true, possibly false, and
probably false. Microsoft ® Encarta ® 2009.

3. INTRODUCTION CONT.
In this review, a new microscopic traffic model is introduced, which
does not involve the Monte Carlo technique and enables a realistic
simulation of signal controlled traffic streams. The model was
formulated as a hybrid system combining a fuzzy calculus with the
cellular automata approach. The original feature distinguishing this
model from the other cellular models is that vehicle position, its
velocity and other parameters are modeled by fuzzy numbers. The
application of fuzzy calculus helps to deal with imprecise traffic data
and to describe uncertainty of the simulation results of based on fuzzy
definitions of basic arithmetic operations.

4. STATEMENT OF THE REVIEW
To understand the use of fuzzy traffic model in traffic
engineering.
STATEMENT OF PROBLEM
Currently fuzzy Microscopic model is being used in
traffic modeling; this is done in order understand the
current research and the state of art in transportation
engineering .

5. Aim
To proposes a fuzzy rule-based car-following model that assumes
that a decision made by a driver is the result of a fuzzy reasoning
process and then predicts the possibilities of the reaction of the
follower vehicle.
Objectives
 To Understand the driver car-following behavior using a fuzzy
logic car-following model.
 To look at other related works that use the fuzzy model in car
moving theory.

6. LITERATURE REVIEW
Fuzzy logic is a form of many-valued logic in which the truth values of variables
may be any real number between 0 and 1. It is employed to handle the concept of
partial truth, where the truth value may range between completely true and
completely false. By contrast, in Boolean logic, the truth values of variables may
only be the integer values 0 or 1. The term fuzzy logic was introduced with the
1965 proposal of fuzzy set theory by Lotfi Zadeh L.A.(1965). Fuzzy logic had
however been studied since the 1920s, as infinite-valued logic notably by
Łukasiewicz and Tarski (2000). A first attempt to give different degree of truth was
developed by Jan Lukasiewicz and A. Tarski formulating a logic on n truth values
where n ≥ 2 in 1930s. This logic called n-valued logic differs from the classical one
in the sense that it employs more than two truth values. To develop an n-valued
logic, where 2 ≤ n ≤ ∞, Zadeh modified the Lukasiewicz logic and established an
infinite-valued logic by introducing the concept of membership function.

7. Let X be a classical set of objects, called the universe, whose generic elements are
denoted by x. An ordinary subset A of X is determined by its characteristic function
χA from X to {0, 1} such that, χA(x) = 1 if 0 if x x / ∈ ∈ A, A.
In the case that an element has only partial membership of the set, we need to
generalize this characteristic function to describe the membership grade of this
element in the set.
Note that larger values denote higher degrees of the membership. For a fuzzy subset
A of X, this function is defined from X to [0, 1] and called as the membership
function (MF) denoted by µA, and the value µA(x) is called the degree of
membership of x in A. Thus we can characterize A by the set of pairs as following: A
= {(x, µA(x)), x ∈ X}.

8. FUZZY SYSTEM MODELING
A fuzzy system is a system where inputs and outputs of the system are modeled as fuzzy
sets or their interactions are represented by fuzzy relations. A fuzzy system can be
described either as a set of fuzzy logical rules or a set of fuzzy equations. Several
situations may be encountered from which a fuzzy model can be derived: a set of fuzzy
logical rules can be built directly; there are known equations that can describe the
behavior of the process, but parameters cannot be precisely identified; too complex
equations are known to hold for the process and are interpreted in a fuzzy way to build,
for instance a linguistic model; input-output data are used to estimate fuzzy logical rules
of behavior. The basic unit for capturing knowledge in many fuzzy systems is a fuzzy
IF-THEN rule. A fuzzy rule has two components: an IF-part (referred to as the
antecedent) and a THEN-part (referred to as the consequent). The antecedent and the
consequent are both fuzzy propositions. The antecedent describes a condition, and the
consequent describes a conclusion that can be drawn when the condition holds.

9. CURRENT RESEARCH IN THE AREAS
Fuzzy rule-based models for the car-following problem:
In the car-following situation, one follows a set of driving rules built over
time through experience. Examples of the rules that the FV might apply are
as follows:
Accelerate if the lead vehicle (LV) accelerates, decelerate and keep longer
distance if the LV decelerates and the distance between cars is short.
Understanding driver car-following behavior using a fuzzy logic car -
following model
The fuzzy logic car-following model was developed by the Transportation
Research Group (TRG) at the University of Southampton (Wu et al., 2000).
McDonald et al., 1999. collected car-following behavior data on real roads
and developed and validated the proposed fuzzy logic car-following model
based on the real-world data. The fuzzy logic model uses relative velocity and
distance divergence (DSSD) (the ratio of headway distance to a desired
headway) as input variables. The output variable is the acceleration-
deceleration rate. The DSSD is the average of the headway distance that is
observed when the relative speeds between vehicles are close to zero. This
model adopts fuzzy functions as the formula for the input-output relationship.

10. INPUT VARIABLE VALIDATION
The following eight conditions were applied to the fuzzy inference system estimation
in order to obtain satisfactory performance of the fuzzy logic model. - Velocity of the
driver’s own vehicle (Vd)
Headway distance to the lead vehicle (HD)
Relative velocity between the lead vehicle and the driver’s vehicle (RV = d(HD)/dt)
Velocity of the lead vehicle (Vl = Vd+RV)
Time headway (THW = HD /Vd)
Inverse of time to collision (1/TTC, TTC = HD/RV, where the value is infinite when RV
= 0.)
Angular velocity (This value is calculated using the following approximate formula:
(width*RV)/HD2, where the width of the lead vehicle is assumed to be 2.5m.)
Distance divergence (DSSD, calculated from HD divided by the desired headway. The
desired headway was chosen to be the average of the headway observed when the
relative speeds between vehicles were close to zero.)
The performance of the fuzzy logic model was evaluated by the Root Mean Square
Error (RMSE) of the model prediction.

11. MODEL VALIDATION
The fuzzy logic car-following model describes driving operations under car-following
conditions using linguistic terms and associated rules, instead of deterministic
mathematical functions. Car-following behavior can be described in a natural manner
that reflects the imprecise and incomplete sensory data presented by human sensory
modalities. The fuzzy logic car-following model treats a driver as a decision-maker
who decides the controls based on sensory inputs using a fuzzy reasoning. There are
two types of fuzzy inference system that uses fuzzy reasoning to map an input space
to an output space, Mandani-type and Sugeno-type. The main difference between the
Mamdani and Sugeno types is that the output membership functions are only linear or
constant for Sugeno-type fuzzy inference. A typical rule in the Sugeno-type fuzzy
inference (Sugeno, 1985) is: If input x is A and input y is B then output z is
x*p+y*q+r;where A and B are fuzzy sets and p, q, and r are constants.The constant
output membership function is obtained from a singleton spike (p=q=0).

12. FUZZY MICROSCOPIC CELLULAR MODEL
Fuzzy microscopic model of road traffic was developed to overcome the
limitations of cellular automata models. This model combines the main
advantages of cellular automata models with a possibility of realistic
traffic simulation at signalized intersections. The proposed method allows
the traffic model to be calibrated in order to reflect real values and
uncertainties of measured saturation flows. A traffic lane in the fuzzy
cellular model is divided into cells that correspond to the road segments of
equal length. The traffic state is described in discrete time steps. These
two basic assumptions are consistent with those of the Nagel-
Schreckenberg cellular automata model.

13. Thus, a novel feature in this approach is that vehicle parameters are
modeled using ordered fuzzy numbers. The model transition from one
time step (t) to the next (t + 1) is also based on fuzzy definitions of basic
arithmetic operations. The road traffic stream is represented in the fuzzy
cellular model as a set of vehicles. Each vehicle (i) is described by its
position Xi,t (defined on the set of cells indexes) and velocity Vi,t (in
cells per time step). Maximal velocity Vmax is a parameter, which is
assigned to the traffic stream (a set of vehicles). In order to
enable appropriate modeling of signalize intersections, the
saturation flow S (in vehicles per hour of green time) was also
taken into account as a parameter of the traffic stream.

14. Algorithm 1. Traffic simulation with fuzzy cellular model.
For t = 1 to T do
Update traffic signals.
For all vehicles (i = 1 to N) do
Compute using rule RL
For m=1 to 3 do
If
then compute using rule RH
else compute using rule RL,
compute using rule RH.
Source:Bartlomeij placzec, 2014

15. Comparison with Nagel-Schreckenberg cellular automata model
This section compared the simulation performed with the fuzzy
cellular model and the Nagel-Schreckenberg (NaSch) cellular
automata model. The proposed model can be precisely calibrated by
adjusting its parameters. Moreover, the uncertainty of model
parameters can be taken into account as the parameters are
represented by fuzzy numbers. Secondly, the fuzzy cellular model
does not need multiple simulations because it uses the fuzzy numbers
to estimate the distributions of traffic performance measures (travel
time, the number of vehicles in a given region, delays, queue lengths,
etc.) during a single run of the traffic simulation.

16. The implementation of the NaSch model requires multiple traffic
simulation runs (see Algorithm 2). At each run, the simulation results
have to be stored. After K runs, the stored results are used to calculate
distributions of the traffic performance measures. The number of
simulation runs K has to be appropriately high in order to obtain
meaningful estimates .The velocity in the NSL rule is calculated
according to the following formula:
The randomisation step of the NaSch model was implemented in the
simulation algorithm by introducing a selection of the deterministic rule
(NSL or NSH). The selection is based on a random number ξ ∈ [0;1) ,
which is drawn from a uniform distribution.
 1),,1min(,0max max,1,,   vgvv tititi

17. Algorithm 2. Traffic simulation with the NaSch model
For simulation run 1 to K do
For t = 1 to T do
Update traffic signals.
For all vehicles (i = 1 to N) do
Generate random number ξ
If ξ <p then compute using rule NSL,
else compute using rule NSH.
Store simulation results.
Source:Bartlomeij placzec, 2014
Let us assume that the basic operation in the traffic simulation
algorithm is the execution of the computation of the position and
velocity for a single vehicle.

18. simulation with the NaSch model requires K•T•N basic operations
whereas during the simulation with the fuzzy cellular model the
basic operation is executed 5•T•N times. It was assumed that the
number of vehicles N is constant in the analysed simulation period.
The computational cost of traffic simulation is considerably reduced
for the fuzzy cellular model because the number of simulation runs
K is always much greater than 5 (usually amounts to several hundred
runs). Moreover, the traffic simulation with the fuzzy cellular model
does not need to store partial results, thus it requires less memory
space than the simulation with the NaSch cellular automata.

19. The fuzzy cellular model of signal controlled traffic stream eliminate
the main drawbacks in the application of other cellular automata
models in traffic control system. It also considerably reduces the
computational cost of traffic simulation. These findings are of vital
importance for real-time applications of microscopic models in the
road traffic control.
FUTURE RESEARCH
A Stochastic cellular automata traffic model with fuzzy decision rules,
the experiments should involves on-and off – ramps and loop detectors
that will help to analyze different and more realistic situations such as
city roads with many intersections traffic lights.
CONCLUSIONS

20. REFERENCES
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Łukasiewicz and Tarski, infinite-valued Fuzzy logic, 1920s.
Zadeh, Concept of membership function, 1967.
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