Review of Fuzzy Model

ASSIGNMENT ON
ADVANCED TRAFFIC ENGINEERING (CIV8331)
REVIEW OF FUZZY MICROSCOPIC TRAFFIC FLOW
MODEL
COURSE LECTURER:
PROF. HASHIM M. ALHASSAN
PRESENTED BY:
NURUDEEN ISHAQ
SPS/17/MCE/00052
MAY, 2018
REVIEWOF FUZZY MICROSCOPIC TRAFFIC FLOWMODEL

 With rapid growth in motorway traffic, driver behaviour is becoming of increasing
importance to safety and capacity. The design and assessment of potential measures to
address these issues must be developed off-line because of the cost and risks of
potential field trials. Simulation is a crucial tool in this process, although such techniques
depend for their validity on the quality of the underlying models of driver behaviour.
 Fuzzy logic [2] allows the introduction of a quantifiable degree of uncertainty into the
modelled process in order to reflect 'natural' or subjective perception of real variables
and these can include measures of degrees of 'desire' and 'confidence' in each
information source.
 This is accomplished by dividing the parameter space of real world observables (eg.
speed, headway) into a number of overlapping sets and associating each one with a
particular concept (eg. 'close'), hence allowing one term to be classified in a number of
ways, each with differing degrees of confidence (or membership) as one would in real
life.
INTRODUCTION

Introduction cont…..

 The application of fuzzy numbers helps to deal with imprecise traffic data and to
describe uncertainty of the simulation results. In fact, it is impossible to predict
unambiguously the evolution of a traffic stream. Moreover, the current traffic state
also cannot be usually identified precisely on the basis of the available
measurement data.
 Fuzzy numbers are used in the traffic simulation algorithm to:
 Describe the uncertainty and imprecision of the simulation inputs & outputs
 Allows a single simulation to take into account many potential scenarios (traffic
state evolutions)
 Be suitable for real-time applications in traffic control systems.

STATEMENT OF PURPOSE
To understand how Fuzzy model works

AIMANDOBJECTIVES
Aim
The aim of this review is to understand how fuzzy microscopic model
work.
1.3.2 Objectives:
The objectives of this review are:
To do a review on Fuzzy microscopic model
To Understanding the various types of Fuzzy Microscopic model
To know the state of ark of Fuzzy Model at now

LITERATURE REVIEW
 Over more than half a century, traffic flow theories have been pursuing two goals; simple and
efficient models to abstract vehicular traffic flow models fit and relate to each other (J. Wang, et.al
2013). Continuing these efforts, there are many literatures of traffic flow theories and models that
have been developed but researchers generally agree that modelling has not yet reached a
satisfying level.
 Car-following models have been developed since the 1950s (e.g., Pipes, 1953). Many models
describe the accelerative behavior of a driver as a function of inter-vehicle separation and relative
speed.
 Among many works on CA applications in the field of road traffic modelling, there are also studies
that use CA for simulation and optimisation of a signal traffic control. In a traffic simulation tool
for urban road networks was proposed which is based on the NagelSchreckenberg (NaSch)
stochastic CA. An intersection model was considered in this work including traffic regulations
(priority rules, signs, and signalisation). It was also suggested that for appropriate setting of a
deceleration probability parameter the model yields realistic time headways between vehicles
crossing a stop line at a signalised intersection.

LITERATURE REVIEWCONT……..
 Schadschneider et al. have presented a CA model of a vehicular traffic in signalised urban
networks by combining ideas borrowed from the Biham-Middleton-Levine model of city
traffic [20] and the NaSch model of a single lane traffic stream. A similar model was
adopted to calculate optimal parameters of a traffic signal coordination plan that
maximise the flow in a road network.
 The stochastic CA models applied in traffic simulation tools were further extended to
agent-based models that aim at reproducing sophisticated driver behaviours. In this
approach the drivers are represented by autonomous agents able to make complex
decisions about route planning.
 Hybrid systems that combine CA and fuzzy sets are typically referred to as fuzzy cellular
automata (FCA). FCA-based models have found many applications in the field of complex
systems simulation. A road traffic model of this kind has been proposed in [30]. In such
models, the local update rule of a classical CA is usually replaced by a fuzzy logic system
consisting of fuzzy rules, fuzzification, inference, and defuzzification mechanisms.

ELEMENTS OF FUZZY SET THEORY
Fuzzy Sets
 A fuzzy set is a set for which the criterion for belonging to the set is not dichotomous. The
membership of the set is defined by a grade (or degree of compatibility or degree of truth) whose
value is between 0 and 1. A membership function determines the grade and is defined as:
hA(x): X— [0,1]
 where A is a fuzzy set defined on the universal set X.
 The notion of "high speed" or "low speed," for example, can be represented by fuzzy sets whose
membership functions define the perception of high or low in terms of numerical value of speed.
Operations of Fuzzy Sets
Among the set operations relevant to the subsequent discussions are union, intersection, and
complement, defined by Equations 3, 4, and 5, respectively.

 In these equations, ˄ indicates the minimum and V the maximum of the operands [hA(x) and hB(x), in this
case].
 Fuzzy Inference
Under fuzzy logic, the inference process includes fuzzy input and a fuzzy relationship, as follows:
 Input: x is somewhat A (x = A')
 Rule: if x is A then y is B (R:x = A y = B)
 Conclusion: y is somewhat B (y = B') (6)
 where all or some of A, A", B, and B' are fuzzy sets, and the rule represents a fuzzy cause-and-effect
relation between x and y. The first part of the rule, "x is A," is called the premise, and the second, "y is B,"
is called the consequence. The validity of the consequence depends on the compatibility between the
input and the premise of the rule. In other words, the degree to which "y is B" is true is dictated by the
degree of match between "x is somewhat A" and "x is A."
Operations of Fuzzy Sets Cont…….
hAՍB (X) = hA(x) ˅ hG(x) (3)
hAՈB (X) = hA(x) ˄ hB(x) (4)
hÃ(x) = 1 hA(x) (5)

FUZZY CELLULARMODEL
 A fuzzy cellular model of road traffic was developed to overcome the limitations of cellular automata
models. The introduced model combines the main advantages of cellular automata models with a
possibility of realistic traffic simulation at signalized intersections. This 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
of equal length. The traffic state is described in discrete time steps. These two basic
are consistent with those of the Nagel-Schreckenberg cellular automata model. A novel feature in
this approach is that vehicle parameters are modelled using ordered fuzzy numbers. Moreover, the
model transition from one time step (t) to the next (t + 1) is 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 modelling of signalized intersections, the saturation flow S (in
vehicles per hour of green time) was also taken into account as a parameter of the traffic stream. All
the above quantities are expressed by triangular ordered fuzzy numbers.

FUZZY CELLULARMODEL CONT……
 The triangular fuzzy numbers are represented by three components. Fig. 1 shows a membership
function of a fuzzy number Z = (z(1), z(2), z(3)).
Fig.1. Triangular fuzzy number
 The aim of the introduced approach is to provide a road traffic simulation algorithm, which can
accept a fuzzy number S = (s(1), s(2), s(3)) as an input parameter specifying the level of the
saturation flow. Therefore, the method discussed above was extended to take into account the
three components that are necessary for representation of the triangular fuzzy numbers.
According to this modification, velocities and positions of vehicles are described by fuzzy
numbers.

FUZZY LOGICCAR-FOLLOWINGMODEL
 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).
 On urban roads, parking on kerb side can be generally observed at many places. Because of
this, partial lane change process may occur on the links as shown in the Figure 2.

 The speed would be reduced as the vehicle slightly use adjacent lane and this will make
other vehicles traveling on adjacent lane also slow down in presence of parked vehicles
along road side and some times vehicles try to change lane to avoid this area. In that
case, it is assumed that vehicle movement would also be influenced by lateral obstructing
distance in case of parked vehicle presence as shown in Figure 3.
Figure 2: Vehicle Behavior under Partial Lane Change Process
 It is essential to consider lateral obstructing distance as a input variable to describe the
above said partial lane change behaviour. In the present model, another three important
input parameters have been considered comparing to existing models to account for the
description of other possible urban situations.
FUZZY LOGIC CAR-FOLLOWING MODEL CONT…..
Partial Lane Change
Condition
(reduced speeds,
unwanted lane changes etc.)
Lateral obstructing distance
On-Street Parking occurring area
Path of vehicle

ROUTE CHOICE MODELWITH FUZZY LOGIC
 In the present simulation model, it is assumed that route travel time is a fuzzy number and
driver choose his route based on possibility index, which represents possibility of choosing
route. To compare the possibility indexes of all available routes, it is necessary to have a fuzzy
goal, G (Akiyama and Nomura, 1999 and Akiyama, 2000).
 All the available routes would be compared with goal function and routes would be ranked
based on possibility indexes.
 In general, fuzzy goal and route travel time are considered as triangular fuzzy numbers and
G, A and B are fuzzy membership functions for fuzzy goal, travel time for route A and route
B respectively as shown in Figure 3.
 The possibility measure, POS(GA) which means possibility that G is greater or equal to A, has
been defined by considering membership functions, G(x) and A(x) of fuzzy sets G and A, as
sup min {G(x), A(x)} (Dubios and Prade, 1980 and 1983).
 In other words, highest point of minimum values of G(x) and A(x) functions and also referred
as intersecting point of fuzzy goal and route travel time curves as shown in Figure 3. The more
explanations can be found in the literature (Zadeh, 1983 and Dubios and Prade, 1980 and
1983).

ROUTE CHOICE MODELWITH FUZZY LOGICCONT…..
Figure 3: Fuzzy Goal and Possibility Index for a Route
 Possibility indexes for the available routes would be separately calculated using the
fuzzy goal as shown in Figure 3.
 From the figure, it can be observed that possibility index is high for route B compared
to route A, even though the travel time of route A is shorter than route B (tA tB) as the
fuzziness of route B is comparatively more than route A.
 Based on the possibility measure approach, the possibility indexes for all the available
routes have been calculated and finally driver selects the route, which has the
maximum possibility index. More details can be found in the previous publication of
the authors (Errampalli et al, 2005a and 2005b).
Route A Route BFuzzy Goal
tA tB Route Travel Time
Membership
Level
0
1
Possibility Index for
Route B
Route A
G A B
x
Route A Route BFuzzy Goal
tA tB Route Travel Time
Membership
Level
0
1
Route B
Route A
G A B
x

 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 (fuzzy sets described by membership functions) as the formula for the input-output
relationship. Figure 4 depicts the structure of the fuzzy logic car-following model.
 Input membership Output membership function function
Fig. 4. Structure of the fuzzy inference system in the fuzzy logic car-following model
FUZZY INFERENCE SYSTEM
DSSD
Relative
Velocity
Acceleration
Rule 1
Rule 2
Rule 3
Rule 4
Rule 5
Rule 6
Rule 8
Rule 7
Rule 9
Rule 10
Rule 11
Rule 12
Rule 13
Rule 14
Rule 15
Headway distance
the desired headway
=
Velocity of leading
vehicle – velocity
of driver’s vehicle
=

FUZZY INFERENCE SYSTEMCONT…..
 The parameter of the fuzzy inference system is estimated using the following combination of back-
propagation and least square methods.
 The initial fuzzy inference system adopts the grid partition method in which the membership
functions of each input are evenly assigned in the range of the training data.
 Next, the membership function parameters are adjusted using the hybrid learning algorithm. The
parameters of output membership functions are updated in a forward pass using the least square
method. The inputs are first propagated forward. The overall output is then a linear combination of
the parameters of output membership functions.
 The parameters of input membership functions are estimated using back propagation in each
iteration, where the differences between model output and training data are propagated backward
and the parameters are updated by gradient descent. The parameter optimization routines are
applied until a given number of iterations or an error reduction threshold is reached.
 The input-output mapping specified by the fuzzy inference system has a three-dimensional structure.
We focus on relative velocity-acceleration mapping in order to analyze the dynamic aspect of car-
following behavior (i.e., drivers’ acceleration controls based on the variation in relative speeds).

The rule base reflects behavioural traits of traffic on 3 lane motorways link sections, forming the two basic
models describing driver behaviour:
 Car following theory (longitudinal speed distance relationship), governing the acceleration of any driver,
circumstances.
 Lane changing (the interaction between adjacent lanes), describing 'lateral' traffic behaviour.
Rulebase For Car Following
 In this formulation the two principle inputs to the decision making process are relative speed (DV) and the
divergence, DSSD, (the ratio of vehicle separation, DX, to the driver’s desired following distance, Sd, (an important
parameter believed to vary significantly between drivers). Table 1 lists the fuzzy sets used for the car following
 A typical fuzzy rule for the car
following model has the form:-
If Distance Divergence, DSSD, is Too Far and relative speed, DV, is Closing
then the driver’s response is No Action (keep current speed).
BEHAVIOURAL RULEBASES
Relative Speed Distance Divergence Driver Response
(Acceleration Rate)
Opening Fast Much Too Far Strong Acceleration
Opening Too Far Light Acceleration
About Zero Satisfied No Action (Keep
Current Speed)
Closing Too Close Light Deceleration
Closing Fast Much Too Close Strong Deceleration

 Rulebase For Lane Changing
 Driver’s motivation to move to the off-side lane is to get some form of speed benefit, while the motivation
move to the near-side lane is to reduce impedance to fast moving vehicles approaching from the rear.
Therefore, two different rule-bases are used for lane changing, LCO (lane change to off-side) and LCN
change to near-side)
 LCO Rule-Base. The LCO rule-base has two input variables, the ‘overtaking benefit’ and ‘opportunity’. The
overtaking benefit is measured by the speed gain when a LCO is carried out.
 The opportunity concerns the safety and comfort of the lane changing measured by the time headway to
nearest approaching vehicle to the rear in the offside lane. Table 2 lists the fuzzy sets of input and output
variables for the LCO model rule-base.
Table 2 Fuzzy Sets for LCO Model
 The typical LCO rule has the form:
If overtaking benefit is high and opportunity is good then intention of LCO is high.
Rulebase For Lane Changing
Overtaking Benefit Opportunity Intention of LCO
High Good High
Medium Moderate Medium
Low Bad Low

Rulebase For Lane Changing CONT…..
Pressure
From Rear
Gap
Satisfaction
Intention of LCN
High Good High
Medium Moderate Medium
Low Bad Low
 LCN Rule-Base.
The LCN rule-base uses the input variables, ‘pressure from rear’ and ‘gap satisfaction’ in the near-side
lane. The variable ‘pressure from rear’ is measured as the time headway of the following vehicle(s),
while ‘gap satisfaction’ is measured by the period of time for which it would be possible for the
simulated vehicle to stay in the gap in the near-side lane, without reducing speed. Table 3 shows the
fuzzy sets of LCN model.
Table 3 Fuzzy Sets for LCN Model
 The typical LCN rule has the form:
If pressure from rear is Low and gap satisfaction is High then intention of LCN is Medium.

CALIBRATIONDATA
 Two types of data are required for model calibration. Firstly the membership functions of the fuzzy sets for a range of drivers
need to be measured, in order to estimate where sets such as 'closing' are perceived as starting and finishing. Secondly, we
need to obtain dynamic traces of car following behaviour in a range of circumstances, against which the model can be fine
tuned to produce the correct performance. This data has been collected by using an instrumented vehicle, which has been
fitted with speed and acceleration measuring equipment, and a forward facing radar unit in order to monitor the behaviour of a
test driver in relation to the preceding vehicle [9].
 2.7.1 Data Collection
Each of six subjects drove the test vehicle for a total of 2 hours on local 2 and 3 lane motorways, with each test run being split
into five sections:
 The subjects follow a target vehicle at their 'minimum safe distance' in order to collect a number of time series traces on
following behaviour.
 The driver is asked by an observer to give spontaneous subjective assessments of their following distance/ relative speed
using the verbal terms used to describe the fuzzy sets .
 The driver of the target vehicle performed a number of acceleration/ braking manoeuvres (typically at differing rates
between 50 and 70 mph) in order to collect data on how drivers adjust and perceive relatively large changes in speed and
distance.
 The driver was instructed to pass the target vehicle, find a slower vehicle and approach from over 100m until his desired
headway was reached. This set of data allows us to examine the approach phase of car following.
 Lastly, and still in 'free mode' the driver was again questioned regarding their closing speed. This last phase is necessary to
ensure that a range of distances were used in the collection of relative speed perception data, as in phase ii), all the data
was collected from a small window of close following distances.

CALIBRATION DATACONT…..
 Membership Sets
 Data from the six subjects for the distance and relative speed sets were compiled and fitted to a
triangular distribution. For relative speed, DV, the surveyed results were very similar for all six
subjects. However, significant differences were found for the following distance (in time
headway) sets, DS. For example, the minimum desired following distance within the subjects
found to be 0.61 seconds while the maximum was 1.92 seconds, three times as great. This
difference indicates the wide differences between driver’s desired following distances. The
calibrated fuzzy sets DSSD and DV are listed in Table 4.
Table 4 The Ranges of the Calibrated Fuzzy Sets
Number of Set Calibrated Ranges of the Fuzzy Sets
DSSD DV (m/s)
Set1 < 0.73 < -1.56
Set2 0.46 to 1.0 -3.34 to 0.20
Set3 0.73 to 1.34 -1.56 to 1.27
Set4 1.0 to 1.68 0.20 to 2.31
Set5 > 1.34 > 1.27

CALIBRATION DATACONT….. Fuzzy Rule Base Calibration
 The fuzzy rule base (or fuzzy inference system) for the following model, determines how the driver reacts to DSSD and DV. To
calibrate the car following fuzzy rule base, more than 10,000 records (each record includes the DS, DV, acceleration rate, etc.)
from each subject were examined and a two step method used:
 Creating a Response Table, which contains the average acceleration rate calculated from the surveyed data for each DSSD
set and DV set combination.
 Determining the fuzzy rule base for each possible combination of DSSD and DV by referring the Response Table (step 1).
The following two equations were used for this purpose.
X + Y = 1 (7)
AS(i) X + AS(j) Y = AS(ij) (8)
 where AS(i) is the average acceleration rate corresponding to DSSD and DV in set(i) as determined in step 1; AS(j) is the average
acceleration rate corresponding to DSSD and DV in set(j) as determined in step 1; and AS(ij) is the average acceleration rate
corresponding to the situation when DSSD is in set(i) and DV in set(j). X and Y are the parameters determining the percentages
the base acceleration rate sets AS(i) and AS(j) will fire when DSSD is in set(i) and DV is in Set(j).
 TESTING OF THE CAR FOLLOWING MODEL
 In order to test the validity of the calibrated fuzzy rule base, a range of performance tests were undertaken by implementing
the rule-base in a microscopic simulation. The basis of these tests was the replication of the observed accelerations, speeds
and relative speeds and headways measured during phases i) and iii) of data collection through the rule based model. The lead
vehicle in each test was programmed with the speed profile of the target vehicle, and the simulated following vehicle provided
with three parameters:-

 Driver’s desired following distance, Sd, (in time headway)
 Vehicle initial speed, and
 Initial headway.
 Surveyed data for four subjects (each with differing desired following distances) was used in the microscopic validation
process. Table 5 lists the desired following distance, Sd, of the four subjects.
Table 5 Different Desired Following Distance for four subjects used in validation
 The microscopic validation results produced by these tests have shown a very good agreement between the surveyed
simulated data for all the four subjects.
FUTURE DEVELOPMENTS
 With a generally satisfactory performance being obtained for the car following model, attention is now focusing on the
collection of data collection for the lane changing model with attempts being made to quantify perception of speed
advantage and gap satisfaction. Each subject is again asked to drive the test vehicle for one and a half hours and
asked to give their judgement of the factors used in the rulebase. Although only preliminary data is currently available on
this stage, it is already clear that gap acceptance (and rejection) are ‘highly fuzzy’ processes, with the sets demonstrating
high degrees of overlap, and producing widely varying output.
CALIBRATIONDATACONT…..
Subject Desired following Distance, Sd,
Subject 1 0.61 seconds

VALIDATION TEST RESULT
Figure 5 Validation Test: Comparison of Accelerations
Figure 6 Validation Test: Comparison of Speeds

CURRENTRESEARCH
 Some recent researches carried out on fuzzy traffic models are given below:
 Critical Infrastructure Renewal: A framework for fuzzy logic-based risk assessment and micro
simulation-based traffic modelling for assessing the traffic impacts due to construction related
bridge opening delay. (The research was conducted at Halifax, Canada in 2016).
 Driver Car-following Behavior Simulation using Fuzzy Rule-based Neural Network (Virginia
Polytechnic Institute and State University).
 A New Approach for Fuzzy Traffic Signal Control (Pamukkale University, Civil Engineering
Department Denizli / TURKEY).
PROBLEM RESEARCH IN THE AREA
 The capability of traffic simulation to emulate the time variability of traffic events makes it
matchless facility for capturing complexity of traffic systems.
 Taha and Ibrahim (2012) stated that, "there are may researches which implement fuzzy but to
specific problems and there are many traffic simulation applications but with no support for
fuzzy logic".

Conclusion and recommendation
CONCLUSIONS
 This review has presented a preliminary report on the state of development of a new microscopic simulation model
on the use of fuzzy logic reasoning to describe driver behavioural processes.
 The fuzzy numbers are used in order to describe the uncertainty and precision of the simulation inputs and outputs.
 The basic sets/concepts used to describe these models have been presented along with results obtained in their
calibration, using time series data and subjective judgements of the real physical meaning of the terms used, collected
using an instrumented vehicle.
 Initial results obtained from comparing such data with simulated tests have been very encouraging with the most
important parameter proving to be DSSD, the deviation from the desired time-headway following distance.
 Work thus far has shown that fuzzy logic can be successfully be used to describe human behaviour in a situation where
inputs are well defined (car following).
RECOMMENDATION
 The review of Fuzzy microscopic model have a number of applications, including control of vehicle separation under the
lVHS. for the traffic flow analysis the model can be extended to derive a possibility-based speed-volume relationship.
a relationship would allow capacity analysis as a fuzzy number and to recognize tile level of service as the fuzzy
traffic conditions, instead of as the traditional rigidly bounded measure.

REFERENCES
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 Algers, S., Bernauer, E., Boero, M., Breheret, L., Di Taranto, C., Dougherty, M., Fox, K., and Gabard, J. (1997) ‘Review of micro-simulation models’.
Smartest Project deliverable D3. Leeds, UK.
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Japan, August 2002.
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 Muller, R. and G. Nocker. Intelligent Cruise Control with Fuzzy Logic. Intelligent Vehicles Symposium, Paris, Oct., 1992. pps 173-178. IEEE.
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 Driver Behaviour. In preparation.
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0001-4575

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