Published at : 31 Oct 2017
Volume : IJtech
Vol 8, No 5 (2017)
DOI : https://doi.org/10.14716/ijtech.v8i5.864
Srikanth, S., Mehar, A., 2017. Estimation of Equivalency Units for Vehicle Types under Mixed Traffic Conditions: Multiple NonLinear Regression Approach. International Journal of Technology. Volume 8(5), pp. 820829
Seelam Srikanth  Department of Civil engineering, National Institute of Technology, Warangal, Telangana, 506004, India 
Arpan Mehar  Department of Civil engineering, National Institute of Technology, Warangal, Telangana, 506004, India 
The accuracy of measured traffic flow on a
roadway largely depends on the correctness of the PCU factors used for
converting traffic counts. PCU is the number of passenger cars that are
displaced by a single heavy vehicle of a particular type under prevailing
roadway, traffic and control conditions. The aim of the present study is to
develop more appropriate models for estimating the equivalency units of
different vehicle types on multilane highways, considering the limitations of
available methods. Estimation of equivalency units for vehicle types is
described by developing speed models based on multiple nonlinear regression
approaches. The equivalency units estimated by using models are found to be
realistic and logical under heterogeneous traffic flow conditions. The PCU
values estimated by the multiple nonlinear regression method are compared with
and found to be relatively higher values than the values obtained by the dynamic
PCU. The accuracy of the models is checked by comparing the observed values of
speed with estimated speeds. The multiple nonlinear regression approach is
also used for estimating the equivalency units on sixlane divided highways.
Results indicate that the proposed methodology can be used for estimation of
equivalency units for vehicle types under mixed traffic conditions.
Equivalency units; Multiple nonlinear regression; PCU; Speed
Classical
macroscopic models, which were developed for the modelling of traffic flow,
considered traffic to be homogeneous and lanebased. In a homogeneous and
lanebased traffic system, all vehicles are of the same type, moving strictly
in lanes and at nearly the same speed, a pattern which is more prevalent in
developed countries. However, in developing countries like India, the traffic
conditions are heterogeneous and nonlanebased in nature. In heterogeneous and
nonlanebased traffic conditions, multiple types of vehicles with different
static and dynamic characteristics share the same carriageway without any
physical separation between them. Because of these complexities, the variations
in traffic stream behavior are very high. In order to examine the heterogeneous
traffic flow, researchers proposed different techniques and models. One of the
most widely used techniques at the macroscopic level is to homogenize the
traffic before modelling the traffic flow. Passenger Car Unit (PCU) has been
proposed by various researchers for different classes of vehicles to homogenize
the heterogeneous traffic.
The idea of PCU was
first introduced in the Highway Capacity Manual (HCM) in 1965 to
account for the effect of trucks and buses
in the traffic stream. The HCM is a publication of the Transportation Research Board of
the National Academies of Science in
the United States. It contains concepts,
guidelines, and computational procedures for computing the
capacity and quality of service of various highway facilities including
freeways, highways, arterial roads, roundabouts, signalized intersections and
unsignalized intersections.
Subsequently, PCU values of vehicle type and estimation have been a
subject of interest all over the world. The accuracy of measured traffic flow
on a roadway largely depends on the correctness of PCU factors used for
converting traffic counts. The PCU of a vehicle type depends on vehicular
characteristics, stream characteristics, roadway characteristics, environmental
factors, climate conditions, and control conditions (Chandra et al., 1995;
Karim et al., 1999).
Several
methods were developed for determining PCU values such as modified density
method, speed, and area ratio method, the method based on relative delay,
headway method, multiple linear regression method, and simulation method.
However, most of the methods are unsuitable under highly heterogeneous traffic
conditions. As per the literature review (Chandra et al., 1995), the dynamic
PCU method and homogenization coefficient method are commonly used for
estimating PCU values of various vehicle types under mixed traffic conditions.
In the homogenization coefficient method, PCU values are estimated by the ratio
of the average speed and length of vehicle type. However, Indian traffic
follows a disordered lane system, so using the speed of the vehicle type with
length alone may not be appropriate, as the width of vehicle types also varies.
In the dynamic PCU method, a rectangular projected area is used instead of
using the length of vehicle types. The method provides excellent results under
all kinds of roadway and traffic conditions. Hence, the dynamic method of
estimating PCUs is considered useful for all types of vehicles under various
traffic conditions. The dynamic method considers the speed ratio and an area
ratio of vehicle types but ignores the effect of headways maintained by
vehicles. Traffic composition is another variable which influences the PCU values
under heterogeneous traffic conditions. Therefore, it is necessary to develop a
more appropriate model for estimating PCU values of different types of vehicles
on multilane highways, such as those prevailing in India.
Following
the introduction of the term PCU in the HCM, considerable research effort has
been made toward the estimation of PCU values under various roadway conditions.
For example, John and Kobett (1978) developed a nonlinear
relationship for deriving PCU values by using the mean speed as the measure of
equivalence, and concluded that PCU values vary not only with different
roadways conditions but also with different traffic control conditions. Huber
(1982) introduced the concept of
equal density to relate mixed traffic flow rate and base flow rate in a
calculation of PCU. The observations were made with two different traffic
streams, one that had trucks mixed with passenger cars and the other that had
passenger cars only, and the impedance was measured as a function of traffic
flow. Three measures of impedance were considered, each of which generate a
separate PCU value for a truck of given physical and operational
characteristics. The PCU values are related to the ratio between the volumes of
the two streams at common levels of impedance. Cunagin and Messer (1982)
developed an analytical method to estimate PCU values for 14 different vehicle
types under different traffic conditions on both twolane and rural fourlane
highways in several states. In this study, relative delays were used to estimate
the PCUs.
Chandra
et al. (1995) proposed a method for estimating PCU values of different vehicle
types under mixed traffic conditions. The basic concept used in this method is
that the PCU value of a subject vehicle is directly proportional to the speed
ratio and inversely proportional to the projected area ratio of the standard
car to the subject vehicle type. Chandra et al. (1995) also developed speed
models for vehicle types under heterogeneous traffic conditions by considering
the average speed of vehicles and the traffic volume as independent variables.
Chandra and Kumar (2003) further studied the effect of road width on PCU values
estimated on twolane highways and observed that the PCU of a vehicle type
increases with the increase in carriageway width as they get more freedom on
the wider roads.
Cao
and Sano (2012) investigated an accurate methodology for estimating motorcycle
equivalency units (MEUs) under mixed traffic flow conditions by considering
speed, the physical size of the subject vehicle, and the surrounding
motorcycles. Field data was collected in Hanoi, capital of Vietnam and Equation
1 was proposed. The results indicate that the MEU values of vehicle types car,
bus, minibus, and bicycle are estimated as 3.4, 10.5, 8.3, and 1.4, respectively.
MEU_{k} = (V_{mc}/V_{k})*(S_{k}/S_{mc}) (1)
where, MEU_{k} is the MEU of vehicle type k, V_{mc} and
V_{k} are the mean speed of the motorcycles and vehicle type k,
respectively (m/s), and S_{mc} and S_{k} are the mean effective
spacing (m^{2}) of motorcycles and vehicle type k, respectively.
Webster and
Elefteriadou (1999) conducted a
simulation study to develop a method for estimating truckpassenger car
equivalents on freeways. This research developed truckpassenger car
equivalents using traffic flow simulation based on traffic density. Arasan and
Arkatkar (2010) also analyzed the effects of traffic volume and road width on
the PCU of vehicles under heterogeneous conditions using the microscopic
simulation technique. Simulation model HETEROSIM was used to study the PCU over
a wide range of traffic volumes.
The objective of the present study is to
develop more appropriate models for estimating equivalency units of different
vehicle types on multilane highways under heterogeneous traffic conditions by
moving beyond the limitations of available methods.
The methodology for estimation of PCU is to
develop a speed model consisting of multiple independent variables based on the
nonlinear regression method. The equation consists of variables like the
proportion of all vehicle types, an average speed of vehicle types other than
small car (CS), where CS is consider as standard vehicle, and area ratios of CS
to all other vehicle types. These are considered independent variables that
influence the average speed of the CS. The product of the area ratio of CS to
subject vehicle type, proportion share of subject vehicle type, and average
speed of subject vehicle type are used as a multiplicative components, whereas
a proportional share of CS is used as an additive component in the proposed
equation. The proposed regression model was developed to predict the speed of
standard vehicle types, whose coefficients are estimated as equivalency units
of all subject vehicle types. Equation 2 is provided by the basic equation for
predicting the average speed of standard car.
(2)
where V_{CS} is the_{ }average speed of small car
(km/h), a_{j} and a_{i} are the regression
coefficients, k is total number of
vehicle types in the traffic stream, V_{j}
is average speed of vehicle type j (km/h), n_{j}
is the proportion of vehicle type j, n_{cs}
is proportion of small cars, A_{j}
is the rectangular projected area of subject vehicle type j, and A_{cs} is the rectangular
projected area of a small car (m^{2}).
The intercept term in the equation was not kept
because the speed of the small car type must be fully explained by the chosen
variables. The PCU value of vehicle type j is the regression coefficient of
corresponding vehicle type (a_{j}). Similarly, the Equations 3 and 4
are also proposed in case of twowheeler (TW) and heavy commercial (HCV)
vehicle types, in order to obtain their average speeds and to estimate
equivalency units in their respective term.
(3)
where V_{TW }is the average speed of
twowheelers (km/h), b_{j} and
b_{i }are the regression
coefficients, k is total number of
vehicle types in the traffic stream, V_{j}
is average speed of vehicle type j in km/h, n_{j}
is the proportion of vehicle type j, n_{TW}
is the proportion of twowheelers, A_{j
}is the rectangular projected area of subject vehicle type j, and A_{TW} is the rectangular
projected area of the twowheelers.
(4)
where V_{HCV }is the average speed of HCV (km/h), c_{j} and c_{i}_{ }are the regression coefficients, k is the total number of vehicle types
in the traffic stream, V_{j}
is the average speed of vehicle type j (Km/h), n_{j} is the proportion of vehicle category j, n_{HCV} is proportion of HCV, A_{j} is the rectangular
projected area of subject vehicle type j, and A_{HCV} is the rectangular projected area of HCV.
Field data was
collected at different midblock sections of multilane divided intercity
highways with plain terrains and straight alignments. Different sections of
divided highway were identified and field investigations were performed.
SectionI and SectionII were selected on National Highway (NH) 163, and both
have 1.5 m shoulders in each direction of travel. The SectionIII was selected
from NH 16, a sixlane divided intercity highway that has 1.8 m paved
shoulders. The video graphic
method was used for collecting speed and volume data. A trap length of 50 m was
marked on highway sections to estimate the speed of vehicles by noting the
travel time. The duration of data collection, traffic volume, and posted speed
limits on different highway sections are given in Table 1. Vehicle type surveys
were also carried out to obtain the clear dimensions of different vehicle types
and are given in Table 2. Traffic volume and speed data were extracted manually
from the video recordings playing on a big screen monitor in the traffic
engineering laboratory.
Table 1 Duration,
traffic volume, and free speed of different sections
Section 
Duration 
Traffic
Volume (Veh/hr) 
Posted
Speed Limit (km/h) 

Maximum 
Minimum 

SectionI 
9:00 AM
to 12:00 PM and 3:00 PM
to 6:00 PM 
1512 
576 
80 
SectionII 
9:00 AM
to 12:00 PM and 3:00 PM
to 6:00 PM 
1400 
600 
80 
SectionIII 
9:00 AM
to 12:00 PM and 3:00 PM
to 6:00 PM 
1776 
900 
90 
Table 2 Clear
dimensions of vehicle types and projected area
Vehicle Type 
Length (m) 
Width (m) 
Area (m^{2}) 
Standard
Car (CS) 
3.72 
1.44 
5.36 
Big Car
(CB) 
4.58 
1.77 
8.11 
Light
Commercial Vehicles (LCV) 
4.30 
1.56 
6.71 
High
Commercial Vehicles (HCV) 
6.70 
2.30 
15.41 
Multi
Axle Vehicles (MAV) 
11.50 
2.42 
27.83 
TwoWheeler
(TW) 
1.97 
0.74 
1.46 
Auto (3W) 
3.20 
1.30 
4.16 
Bus (B) 
10.60 
2.40 
25.44 
3.1. Field
Data Analysis
The field data collected at different
highway sections was analyzed by measuring classified volume count and speed at
each 5 minute interval. The traffic composition and average speed of all
vehicle types on all sections are given in Table 3. Field data collected at
SectionI was used for the development of multiple nonlinear regression (MNLR)
speed models and SectionII and SectionIII data was used for the validation of
the developed model.
Table 3 Average
speed and percentage share of vehicles at study sections
Vehicle Type 
SectionI 
SectionII 
SectionIII 

Average Speed (km/h) 
Proportional Share 
Average Speed (km/h) 
Proportional Share 
Average Speed (km/h) 
Proportional Share 

CS 
66.59 
0.32 
64.5 
0.20 
83.3 
0.22 
CB 
69.80 
0.07 
67.0 
0.06 
75.1 
0.10 
LCV 
49.80 
0.03 
47.6 
0.07 
60.1 
0.04 
HCV 
46.70 
0.04 
42.1 
0.07 
51.9 
0.08 
TW 
50.02 
0.45 
45.1 
0.45 
56.5 
0.49 
3W 
39.50 
0.05 
40.8 
0.12 
49.4 
0.02 
B 
50.47 
0.04 
45.2 
0.03 
66.1 
0.05 
3.2. Development
of Speed Equations and Estimation of Equivalency Units
The MNLR equation predicts the speed of a
vehicle type within a heterogeneous traffic stream. Initially, the speed of
vehicle types and their proportional shares are aggregated in 5 minute
intervals, establishing a relationship to estimate average speed of the CS. The
PCU values of subject vehicle types are identified as regression coefficients
of the proposed regression model, as shown in Table 4. The coefficient a_{1}
was estimated as the average speed of CS, which is also affected by its own
proportional share. The value of coefficient a_{1} was 63 km/h. The
value of R^{2} for the model is 0.77. The high R^{2} value indicates the strength of the model in
predicting the speed of CS.
(5)
where, a_{2}=PCU
of CB, a_{3}=PCU of LCV, a_{4}=PCU of HCV, a_{5}=PCU of TW, a_{6}=PCU of 3W, a_{7}=PCU of B.
Table 4 Regression
coefficient as PCU value of subject vehicle types
Vehicle Type 
Coefficients 
PCU Values 
Standard Error 
BC 
a_{2} 
1.56 
0.15 
LCV 
a_{3} 
2.69 
0.42 
HCV 
a_{4} 
3.83 
0.65 
TW 
a_{5} 
0.28 
0.02 
3W 
a_{6} 
0.85 
0.12 
B 
a_{7} 
6.80 
1.12 
Similarly, Equations 6 and 7 for vehicle
types TW and HV were established by using the same set of field data. High R^{2}
values indicate the strength of the models in predicting the speed.

(6)

(7)
3.3. Validation
of MNLR Speed Models
Validation of the MNLR speed models was
performed using another set of field data obtained from SectionII. The average
speed of vehicle types observed on the field section was used validate the
values obtained from the models. First, estimated average speeds of CS were
compared with the field observed values at varying compositions and volume
levels. The two average speeds were plotted against the 45° line chart, with the
comparison shown in Figure 1. The test of significance was performed for
comparison and the Pvalue was obtained and found to be higher than the
critical value at 5% level of significance, which shows no difference between
observed and estimated speeds.
Figure 1 Comparison of average speed of CS between estimated and field data
Similarly, Equation 6 and Equation 7 were also
validated using the same set of field data. The two average speeds of TW and
HCV were plotted against the 45° line chart, with the comparisons shown in
Figure 2 and Figure 3, respectively. The test of significance was also
performed between observed and estimated average speeds of TW and HCV, and also
showed no difference between observed and estimated speeds of TW and HCV.
Figure 2 Comparison of average speed of TW between estimated and field data
Figure 3 Comparison of average speed of HCV between estimated and field
data
3.4. Estimation
of PCU by Dynamic PCU Method
Chandra et al. (1997) found that the
dynamic PCU method is better for estimating the PCU values of different vehicle
types under heterogeneous traffic conditions. PCU values for different vehicle
types were estimated by taking the speed and area ratios of a CS to subject
vehicle measured in SectionI. Equation 8 estimates the PCU value of an i^{th
}(subject vehicle type) vehicle. This method, proposed by Chandra and
Sikdar, is called dynamic PCU and is effectively used for interrupted and
uninterrupted traffic conditions.
(8)
where PCU_{i} is
PCU of the i^{th} vehicle, is speed ratio of the car to the i^{th} vehicle and is space ratio of the
car to the i^{th} vehicle.
The PCU values estimated by the MNLR method
were compared with the values obtained by the dynamic PCU method and are shown
in Figure 4. The traffic volume data collected at SectionI was converted into
PCU/hr using PCU values obtained by the dynamic PCU method. Figure 5 shows the
observations and flow where flow was converted into PCU/hr using the MNLR and
dynamic PCU methods. The plot shows that the maximum traffic flow is 1728
PCU/hr where flow was converted into PCU/hr using the MNLR method, while the
maximum traffic flow is 1628 PCU/hr where flow was converted into PCU/hr using
the dynamic PCU method. The maximum traffic flow is 1710 PCU/hr where flow was
converted into PCU/hr using PCUs suggested by IRC 641990. The maximum flow
obtained by the MNLR method is almost on par with the maximum flow when PCU
suggested by IRC is used. Hence it is justified that the PCU by MNLR method is
more realistic and logical compared to the dynamic method.
Figure 4 PCU estimated using MNLR method and dynamic method for
subject vehicle types
Figure 5 Comparison of traffic volume using
both methods
3.5. SixLane
Divided Highway
The multiple nonlinear regression approach
can be used for estimating the equivalency units on sixlane and eightlane
divided highways. The PCU values for different vehicle types at SectionIII are
estimated using the MNLR model. The equivalency units of different vehicle
types at SectionIII are shown in Table 5. The obtained equivalency units are
realistic and logical values.
Table 5
Equivalency units of different vehicles at SectionIII
Vehicle
Type 
PCU 
TwU 
HCVU 
CS 
1.000 
2.624 
0.205 
BC 
1.660 
3.246 
0.504 
TW 
0.342 
1.000 
0.086 
LCV 
The unique multiple
nonlinear approach can be used to accurately estimate the equivalency units of
individual vehicle types under heterogeneous traffic conditions. The PCU values
estimated using the MNLR method are found to be realistic and logical under
heterogeneous traffic flow conditions. The dynamic method considers the speed
ratio and an area ratio of vehicle types but ignores the effect of vehicle
composition under heterogeneous traffic conditions. However, the MNLR method
considers the effect of vehicle composition for estimating the PCU values. From
the results, it is concluded that the PCU by MNLR method is more realistic and
logical compared to the dynamic method. The accuracy of the proposed model was
checked by collecting field data at one additional section of fourlane road.
The speeds obtained from the models were found in good agreement with observed
speeds in the field, i.e., both the speeds are along a 45° line. The test of
significance also indicated there was no difference between estimated and
observed speeds at 5% level of significance. These models are useful in estimating the equivalency unit of a vehicle
at a given volume and composition of a traffic stream. The multiple nonlinear
approach was also used for estimating the equivalency units on a sixlane
divided highway. The results showed that the multiple nonlinear approach can
be used for estimation of equivalency units for vehicle types under mixed
traffic conditions. But the present study has practical difficulties related to
field data because the traffic composition of all vehicle types cannot be
obtained under controlled conditions. The study will be continued to observe
the variation in PCU with respect to composition of each vehicle type using a
simulation technique.
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