International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 6, June 2014)
Estimation of the Passenger Car Equivalent: A Review
Kanakabandi Shalini1, Brind Kumar2
1
Research scholar, 2Assistant professor, Department of Civil Engineering, Indian Institute of Technology (BHU), Varanasi,
Varanasi-221005, U.P, India
PCE value is the numerical value that are given to a
device to convert a mixed vehicle traffic stream into an
equivalent traffic stream composed exclusively of
passenger cars or basic vehicles. Two basic principles
should be applied to estimate of PCE values for any of the
roadway type identified in capacity analysis procedures.
The first principle links the concept passenger car
equivalency to the level of service (LOS) concept. The
second principle emphasizes the consideration of all factors
that contribute to the overall effect of concern vehicle
(other than passenger cars) on traffic stream performance
(Rahman and Nakamura, 2005).
The present review article describes the different
methods to estimate Passenger Car Unit (PCU) or
Passenger Car Equivalent (PCE).
Abstract--Passenger Car Equivalent (PCE) or Passenger
Car Unit (PCU) value is very important for any traffic flow
studies of vehicles. Passenger car equivalents (PCE) are used
as factors to convert a traffic stream composed of different
vehicle types into an equivalent traffic stream composed
exclusively of passenger cars (reference vehicles). In the
literature there are different measures of impedance (speed,
density, vehicle-hours etc.) reported based on which PCE
values are calculated for different types of vehicles. Present
study reviews the various methods have been used to calculate
PCE.
Keywords-- Passenger Car Equivalent, Flow parameters,
Traffic flow studies, Vehicles
I. INTRODUCTION
The travel characteristics, road networks and local
constraints are very different in the cities of developing
countries than those of developed countries. It is therefore
necessary to determine the different parameters of traffic
movements which are suitable for local urban transport
system characteristics. To assess the different types of
vehicles on common basis, a passenger car unit or
passenger car equivalent (PCE) was developed (Saha et
al., 2009). A Passenger Car Unit is a measure of the impact
that a mode of transport has on traffic variables (such as
headway, speed, density) compared to a single standard
passenger car.
The term “Passenger car equivalent” was first introduced
in HCM 1965 to define the effect of trucks and buses in the
traffic stream. It was defined as “the number of passenger
cars displaced in the traffic flow by a truck or a bus, under
the prevailing roadway and traffic conditions”. Highway
Capacity Manual (HCM) 1950 used a single factor of 2.0 to
account for the impact of heavy vehicles on multi-lane
highways. However the most recent definition of PCE is in
Highway Capacity Manual (HCM) 2000 and which is
defined as “the number of passenger cars that are displaced
by a single heavy vehicle of a particular type under
prevailing roadway, traffic and control conditions” (AlKaisy et al., 2005). Passenger Car Equivalents (PCEs)
have important used in freeway design and operations
analysis.
II. LITERATURE ON EXISTING METHODS T O DETERMINE
P ASSENGER C AR EQUIVALENT (PCE)
A. PCEs Based on Flow Rates and Density
In transportation engineering, the term traffic flow rate is
used to indicate the equivalent hourly rate of vehicles
passing a point per unit of time. PCE is computed based on
percentage of grade, mixed vehicle flow, and truck volume
to capacity ratio (John and Glauz, 1976):
Where, = equivalent passenger car only flow rate for a
given v/c ratio, = mixed flow rate,
= truck proportion
in the mixed traffic flow
Huber (1982) suggested a model for estimating PCEvalues for vehicles multilane conditions, under freeflowing. PCE-values are related to the ratio between the
volumes of two streams at some common level of
impedance. He has given equation to calculate PCE value
is
(
97
)
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 6, June 2014)
(Rahman and Nakamura, 2005) used A deterministic
model of traffic flow to estimate the impedance-flow
relationship. They also suggested that PCE-values are
related to speed and length of subject vehicles and to vary
with the proportion of trucks in the traffic stream. Sumner
et al., (1984) further developed Huber’s method by
including more than one truck type in the traffic stream.
(
Werner and Morrall (1976) recommended determining
PCE using headways when the roadway is sufficiently
congested on level terrain:
Where,
= is the average headway for a sample
including all vehicle types,
= is the average headway
for a sample of passenger cars only,
= is the proportion
of cars,
= is the proportion of trucks.
Using the spatial headway methodology, Seguin et al.
(1982) suggested PCE as the ratio of average headway for
vehicle types: average truck headway divided by the
average headway for passenger cars:
)
Where,
=additional subject flow rate,
=
proportion of subject vehicles
Rahman and Nakamura, (2005) reported from the
1985 HCM, density is to be the governing parameter for
LOS, although it is defined both by density and speed. It
explains, density is a measure that quantifies the proximity
of vehicles to each other within the traffic stream and
indicates the degree of maneuverability within the traffic
stream. They stated from McShane and Roess (1990)
density is the primary parameter for LOS and equal density
approach will be more appropriate.
Mallikarjuna and Rao (2000) stated that Chari and
Badarinath (1983) made an attempt to quantify density
under these conditions using areal density. This is the first
study that considered vehicle areas in measuring the
density. Areal density is defined as sum of the total vehicle
area projected on the ground per unit area of road way.
Demarchi and Setti (2003) proposed the PCE’s formula
to eliminate the possible error for mixed heavy vehicles in
the traffic stream, including interaction between multiple
trucks types:
∑
(
Where,
= the PCE of vehicle Type i under
Conditions j,
= average headway for vehicle Type I,
= the average headway for passenger car for
Conditions j.
Cunagin and Chang (1982) determined the effect of the
presence of heavy trucks on freeway traffic streams using
time headway based on headway type, lane width, and
traffic volume. They conclude that the presence of trucks
in the traffic stream is accompanied by an increase in the
mean headway. They suggested the equation for calculating
the PCE.
)
Where,
= the mean lagging headway of vehicle type
i under conditions j,
= the mean lagging headway of
passenger cars.
Krammes and Crowley (1986) derived PCE equation
in terms of variables that reflect the relative importance of
three factors that contribute to the overall effect of trucks
on the roadway type.
Where
= proportion of trucks of type i out of all
trucks n in the mixed traffic flow
B. PCEs Based on Headways
The concept behind using the headways (time or space)
is that headway is a measure of the space occupied by a
vehicle. This is the most commonly used method for
measuring PCE at signalized intersections. Many
researchers have used headway as the basis of estimation.
Greenshields et al., (1947) estimated PCU value by the
following equation. This method is known as basic
headway method.
[
]
Where,
= the lagging headway of trucks following
passenger cars,
the lagging headway of trucks
following trucks,
= the lagging headway of cars
following either vehicle type.
PCUi = Hi / Hc
Where PCUi= passenger car unit of vehicle type, Hi =
average headway of vehicle type, Hc = average headway of
passenger car
98
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 6, June 2014)
The disadvantages of this method are 1. does not account
for the additional delay experienced by vehicles stopped
beyond the eighth position behind the truck; 2) does not
consider through movement; and 3) the computed PCE
values are independent: of traffic volume, heavy vehicle
percentages and multiples heavy vehicles in the queue.
C. PCEs Based on Queue Discharge Flow
Praveen and Arasan (2013) mentioned that Al-Kaisyet
al., (2002) developed a method for passenger car
equivalents (PCEs) using Queue-Discharge Flow (QDF) as
the equivalency criterion. The methodology was based on
the assumption that the fluctuation in QDF capacity
observations would be minimal if the traffic stream was
uniform and consisted of passenger cars only. The vehicle
counts from QDF capacity observations were used to
formulate a nonlinear programming problem, where the
objective function was to minimize the variation in the
QDF capacity. They found that the effect of heavy vehicles
on a freeway is greater when it is operating in oversaturated
conditions. In addition, it was found that PCE both during
dry or rainy days and during the presence of roadside
maintenance work are not significantly different.
Al-Kaisyet al., (2002) given optimization procedure to
determine PCE:
Objective function: Minimize Z(C*) (Z =Coefficient of
Variation=Standard Deviation/Mean)
Design variable: PCE factor
Constraints: C* >=X1 (X1 =1600 pcphpl at site 1, X1 =
1400 pcphpl at site 2)
C* <=X2 (X2 =2800 pcphpl at site 1, X2 =
2600 pcphpl at site 2)
PCE >=X3 (X3 = 1.0)
PCE <=X4 (X4 = 10.0)
Where,
= the coefficients of speed reductions
for each vehicle type
Using the speed reduction coefficients, the PCE for a
vehicle type n is calculated as:
Where,
= speed reduction coefficient for vehicle type
= speed reduction coefficient for passenger cars
Chandra and Sikdar (2000) proposed a methodology
to estimate PCE values for mixed traffic conditions. They
have estimated the PCE values as a function of vehicle area
and speed. According to their methodology PCE of any
particular vehicle is formulated as follows:
n,
⁄
⁄
Where,
= mean speeds of car and type i
vehicle respectively, in the traffic stream; and
= their respective projected rectangular areas
(length * width) on the road.
Rahman and Nakamura, (2005) estimated the
passenger car equivalent of non-motorized vehicles at midblock section along urban arterial based on the speed
difference of mixed flow and basic flow of passenger cars.
PCE value for non-motorized vehicles was estimated with
equation given below.
D. PCEs Based on Speed
This is another method used to determine PCE as the
rate of motion of vehicles in a distance per unit of time or
speed. Van Aerde and Yagar (1983) developed a
methodology to estimate PCE based on the relative rates of
speed for each type of vehicle traveling in the main
direction and for all vehicles combined traveling in the
opposing direction. They found that PCE decreases for
higher speed percentiles. The speed analysis using the
linear regression model structure is
= Passenger car equivalents of non-motorized
vehicles, = Average speed of passenger car in the basic
flow (km/hr),
= Average speed of passenger car in the
mixed flow (km/hr)
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E. PCEs Based on Delays
This method based on the relative capacity reducing
effect of heavy vehicle is directly related to the additional
delay caused by such vehicle when compared to the all
passenger car case. Werner and Morrall, (1976) used
Walker method to determine PCE values. A basic
assumption in the Walker method is that faster vehicles are
not hindered in passing as they overtake slower vehicles, so
queues do not form.
⁄
⁄
Where, = PCE of vehicle Type i under Conditions j,
= delay to passenger cars due to vehicle Type i under
Conditions j,
= delay to standard passenger cars due
to slower passenger cars.
Zhao (1998) proposed a delay-based passenger car
equivalents method for heavy vehicles at signalized
intersections. The author used the headway data and
estimate PCE value by following equation.
[ ⁄
] [ ⁄
]
[ ⁄
] [ ⁄
]
Where,
= delay-based PCE for vehicle type i,
= additional delay caused by a vehicle type i,
=
average delay of passenger car queue
Where,
= the number of overtaking of vehicle type i
by passenger cars,
= the volume of vehicle type I,
= the number of overtaking of lower performance
passenger cars by passenger cars,
= the volume of
lower performance passenger cars,
= the mean speed
of the mixed traffic stream,
= the mean speed of the
base traffic stream with only high performance passenger
car,
= the mean speed of the traffic stream with only
passenger cars.
In the equivalent-delay method, it assumed that faster
vehicles are always hindered by slower vehicles, such that
queues form. Using that premise, PCE values calculated
using a linear combination of the Walker and equivalentdelay in each intermediate volume level yields.
Craus et al. (1980) in their equivalent delay method
considered the difference between delay caused by heavy
vehicle to standard passenger cars and delay caused by
slower passenger car to standard passenger cars. The
following equation reflects the actual disturbance and delay
caused by trucks to other traffic:
F. PCEs Based on V/C Ratio
Fan (1989) studied PCE for expressways in Singapore
using volume-to-capacity (V/C) ratio instead of density or
level of service because these freeways operate at LOS E.
The study focused on congested flow conditions or V/C
ratio above 0.67 and mentioned that it is unnecessary to
calculate PCEs at uncongested flow conditions. Using
multiple linear regressions by multiplying the observed
flow by the V/C ratios, he found that commercial vehicles
such as light and heavy trucks, buses, and trailers generally
have higher PCE values compared with the PCEs used in
US and UK for the level terrain.
G. PCEs Based on Vehicle-Hours
Hourly traffic volumes are used for determining the
length and magnitude of peak periods, evaluating capacity,
and assessing geometric design and traffic control.
Metkari et al. (2012) mentioned that Sumner et al. (1984)
suggested a method for calculating PCE values between
consecutive signalized intersections on urban arterial roads
using microscopic simulation, NETSIM. The values are
derived from the vehicle-hours of road utilization that are
added when large vehicles are introduced to the traffic
stream.
Sumner et al. (1984) developed an approach to compute
PCE values between consecutive signalized intersections
on urban arterial roads.
The resulted values were
cumulative over a length of road between intersections, and
PCE computations were expressed in terms of additional
vehicles-hours. Values were generated for a diverse
number of vehicle types under different flow conditions for
various classes of urban arterial roads in US.
Where,
= average delay time caused by one truck,
= average delay time caused by one passenger car
Cunagin and Messer (1983) developed PCE estimation
based on speed distribution, traffic volumes, and vehicle
types. The PCE values were determined by using Walker
spatial-headway and equivalent-delay methods. Their
method estimates PCEs using the ratio of delay
experienced by a passenger car due to non-passenger
vehicles to the delay experienced by a passenger car due to
other passenger cars:
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PCE resulted from the combination of: 1) the
pronounced effect of a queued truck on vehicles queued
behind the truck, and 2) small additional vehicles-hour
values due to the small differences on speed when slower
vehicles were traveling along the link.
Anand et al., (1999) reported that he following are some
of the many factors on which the PCE values of different
vehicle classes depend; dimensions, power, speed,
acceleration and braking characteristics of the vehicle, road
characteristics such as geometric characteristics including
gradients, curves, access controls, type of road: rural or
urban, and presence and type of intersection.
H. PCEs Based on Travel Time
Keller & Saklas (1984) suggested a PCE for heavy
vehicles on an urban arterial network; the estimated PCEs
are functions of traffic volume, vehicle classification, and
signal settings. The method is based on the premise “that
reduction in capacity is directly related to the additional
delay caused by large vehicles in the traffic stream”. PCE
is measured as the ratio of the total travel times of heavy
vehicles and passenger cars traveling through an urban
network. This can be expressed mathematically as
IV. CONCLUSION
A brief insight into various methods for calculating
Passenger Car Equivalent has been provided. Out of the
various methods discussed, headway ratio method is
currently the most commonly used method for PCE
estimation. Chandra’s Method is only method that can be
applied to the Indian condition of heterogeneous traffic that
is characterized by loose lane discipline. All the other
methods are primarily based on homogeneous traffic
conditions mainly prevailing in developed countries. Some
of the studies resulted in non-constant PCE, they did not
establish direct relationships among PCE, traffic volume
and percentage of heavy vehicles.
Where,
= total travel time of vehicle type i over the
network in hours and
= total travel time of the base
vehicle over the network in hours.
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not take into account the differences in operational
characteristics of buses and trucks.
Benekohal and Zhao (2006) applied a heavy vehicle
adjustment factor
to reduce the ideal saturation flow
rate at intersections using the HCM (TRB, 1985, 1994,
1997). The
is computed from the following equation:
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International Journal of Emerging Technology and Advanced Engineering
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