A study on motorcycle equivalent unit
and capacity estimation in urban streets
Doan Thanh Tan
Supervisor: Dr. Kazushi Sano
1. INTRODUCTION
The growth of urban traffic is recognized as problem inmetropolitan areas in the country, with significant
effects on economy, travel behavior, land use and causeof discomfort for millions of motorists. Vietnam likes
most developing countries which have to face withmany serious traffic problems in over the world. Various
vehicle classes in a running lane, lack of traffic law
understanding and unconscious of road user, etc.
Besides, almost urban streets have two lanes that aresmaller than 7.5 m, citizen tends to concentrate in centerof cities for working and living. Backwardness inplanning is parameter that makes traffic more
complicated. For a decade, Hanoi in particular andVietnam in general try to find a best solution for current
traffic problem, included developing a public transportsystem by bus, improving parking system, expanding
arterial streets and main street…but the effectiveness
isn’t very attractive because they can’t catch up with thefast rising of private vehicles, especially motorcycle andcar. Furthermore, traffic volume estimation business
isn’t very good. It leads to the ineffectiveness of roadand to be short of planning vision. As regards traffic
flow estimation, many studies have been done but mostof them use passenger car unit as a vehicles conversion
standard to estimate highway capacity, etc. Generally,
this method isn’t very good because traffic flow ischiefly dominated by two-wheel motorcycles. In
Hochiminh city, 98% households own motorcycle, 400
motorcycles/1000 population. In Hanoi, 1000 population
have 296 motorcycles. At present, car ratio per year isrising but amount of cars are still very small incomparison with amount of motorcycles. That’s why
traffic condition in Vietnam doesn’t like other countries
that traffic is dominated by car. As a result, a vehicle
conversion solution using motorcycle equivalent unit
should be mentioned, replaced the passenger car unit
and it’s useful for the capacity estimation

3. LITERATURE REVIEW
According to Highway Capacity Manual 2000, PCU or
passenger-car equivalent is “the number of passenger
cars displaced by a single heavy vehicle of a particular
type under specified roadway, traffic, and control
conditions.”
Cuthbert (1983) has promoted an analytical approach todefine PCUs factors on surveys of traffic flows at
selected locations (in Indonesia) which offer thefollowing conditions: saturated flow for significant
periods; no end constraints on the link under survey; mixof vehicle types. His approach represents the traffic
under saturated conditions and number of stops, but it’sdifficult to find the situations at every road in every
Vietnam city.
“Projected area method” is one of methods thatconcerning to projected area of vehicles. In thisapproach, Chandra & Sikdar (1999) have developed apassenger car unit factor for a vehicle class based on
dynamic and static vehicle performance and geometricvariables. The adjustment factor for the presence ofvehicles other than cars is based on PCUs. Thisadjustment factor correlates with the flow rates ofpassenger cars only and mixed traffic streams that areequivalent in terms of drivers’ perception of the level ofservice (LOS). LOS on a segment of highway is definedin terms of two variables: speed and volume. These twovariables alone should be able to explain the relative
effect of individual vehicles on traffic stream in terms of
PCUs.

Vc

Ac

Vi
Ai

2. RESEARCH OBJECTIVES
Figure 1: PCU estimation by Chandra & Sikdar

This study focuses on building a new approach of MEU
and capacity estimation that used car following modeland statistical concept as basis. Main objectives of thestudy are listed here below:

The PCUs of a vehicle class are taken as given by

PCU i =

(1) Investigate the traffic performance at roadsegments under mixed traffic conditions, e.g. speed,flow.

Vc / ViAc / Ai(1)

Where
VC : Mean speeds of cars (c) in traffic stream (km/h)
Vi : Mean speeds of vehicles type i in traffic stream(km/h)
AC : respective projected rectangular areas of cars(m2) on road(2) Investigate parameters that can be used todescribe MEU.
(3) Develop new procedures of MEU measurement
which take into account mixed traffic flow at roadsegments.

1

flow characteristics. Each of the segments has 2
physical separated lanes. Survey time was selectedduring peak hours in working days and good conditionof weather (From 06h30 AM– 08h00 AM and 5h00 PM– 7h00PM). Camcorders were placed at about 10 - 15
meter high at the edge of streets, from these points the
traffic movement is observed very clearly and wasn’t
obstructed by anything. Four collected vehicle
categories are motorcycle, car (sedan), bus, van. In
these, motorcycle was chosen as equivalent unit
because motorcycle is main private vehicle ofVietnamese and it dominates every urban streets. The
samples are collected from recorded clips to ensure
random condition, the location of vehicle is placed into
Decartes coordinate grid in Avistep software to
calculate speed and other parameters in proposed model.

Ai : Respective projected rectangular area of vehicle
class i (m2)
The mean velocity is defined as :K

Vi = ∑ a ij (n jVj )+d i (
j =1

1
)
N

(2)

Where
- Vi : Mean speed of vehicle i (km/h)- aij : Regression coefficients- di : Regression coefficient- K : Total number of vehicle categories in traffic
stream- nj : Number of vehicles of j category passing
through the observation point per unit time (veh)K

N = ∑ nj(3)

5. METHODOLOGY
5.1 Situation

j =1

Consider a real situation of a running vehicle on a road(figure 2) in mix traffic condition, most people think that,the more space between vehicle and adjacent vehicles,
the faster it can run. This argument isn’t wrong but it
isn’t enough. Sometime, we see that, vehicles run at thesame speed with different surrounding areas which are
resulted by those vehicles and adjacent ones. Of course,
if the space between vehicles is too small, the vehicle
must reduce its speed to avoid collision.

Henk van Zuylen & Ning Wu (2007) estimated PCU
as equation of speed and effective area that based on 2
modal – flow (car and truck) at any given level ofservice (LOS) in combination with Greenshields model.
Zuylen model is improved from St.John model (1976).
Y et al (2006) have same idea with Henk van Zuylen &Ning Wu but they have different viewpoint in approach.
From Chandra model, they expanded the projected area
and called effective area. They explained that, vehicles
need an effective area among surrounding vehicles, theproduct of longitudinal space and latitudinal space iseffective area.

This phenomenon denotes that, there is a “best effective
distance” between the concerned vehicle and adjacentvehicles for stabilizing motorcycle speed. If the space
between the concerned vehicle and adjacent vehicles are
smaller than “the best effective distance”, the concerned
vehicle might slow down. In the case of the opposite
situation, according to field survey, the concerned
vehicle trends to maintain initial speed and trajectory.
Some vehicles might accelerate and change theirtrajectory to overtake front vehicle. This study will not
mention these situations because they aren’t general.
Wherefore, there are unnecessary spaces for stabilizing
the speed of the concerned vehicle and they should be
cut off.

Vb
Vi

S bi
Si

Figure 2.2: PCU estimation by Zuyen & Ning Wu

Vb
Vi
PCU =
Lb .Wb
Li .Wi(4)
Safe space

2

3
Where
- Vb: Optimal speed of basic vehicles (car or
motorcycle) within mixed traffic stream (km/h)- Vi: Optimal speed of vehicle class i within mixed
traffic stream (km/h)- LB : Effective length of basic vehicles (m)- WB : Effective width of basic vehicles (m)- Li : Effective length of vehicle class i (m)- Wi : Effective width of vehicle class i (m)1v

Figure 2: Safe space for avoiding collision
5.2 “Optimal effective distance” in latitude
a. Best effective distance in latitude

4. DATA COLLECTION

In general conditions, the trajectory of a running vehicle(vehicle 1) on a road is considered as a line. It maintains
a safe space for adjacent vehicles (see figure 2).

The study has investigated 5 main road segments in
Hanoi, Vietnam. 5 road segments have typical traffic2Assuming that, safe space of vehicle 1 is the maximum
distance in latitude which vehicle 1 can shift to avoid
collision with vehicle 2, when vehicle 2 suddenly shifts
towards vehicle 1 because of some certain reasons.
According to the safety theory, at speed v, the trajectoryof leading wheels (dash curve) and safe space areillustrated in figure 3.

-µlati : lateral force coefficient- g: gravitation field acceleration (g9.8 m/s2)

From (5) and (6) we get:⎧v2
v.∆t.90o 2w=4.().(sin(
))
⎪
g
.(
i
)
.
r
±
µ
π
lati
lati
⎨
⎪
2
⎩l = 4.r.w − w(7)b. Optimal effective distance in latitude
In the aspect of theory, the best effective distance inlatitude (w) in the set of equations (7) is a distance that
ensures the safety of vehicle at speed v. However, inpoint of fact, sometimes latitudinal distance between
two neighbour vehicles is smaller than w. There aremany reasons for this problem, such as driver’s sex,
driver’s reaction ability, component of traffic flow,
vehicle class,…When vehicle 1 still runs at speed v in an
unsafe distance to v, this means the area which surroundthe vehicle 1 is large enough for avoiding crash withothers, driver doesn’t care his safety or because of someother reasons. Thus, to estimate the optimal effective
distance in latitude of each sample (vehicle), we have tochoose between 2 values:

Figure 3: The trajectory and safety space of vehicle 1
For manoeuvre, driver has to control the leading wheels
to turn left or turn right for creating possible safe space.
Suppose that the time for manoeuvre is equal to thereaction/perception time (∆t = 1s). Vehicle 2 shifts
toward vehicle 1 on a maximum range. Immediately,
vehicle 1 has to respond in the same direction. The
maximum distance that could create by vehicle 1 when
avoiding collision with vehicle 2 is called best effective
distance in latitude (w)- Theoretical value: w – calculate in item 5.2 a above- Surveyed value: wf – measure on video clip.
There are 2 cases:

In the figure 3, the outside wheel of vehicle 1 moves on- The 1st case: wf < w , we follow reality, and choose
wf . In fact, on the field, vehicle 1 can run well at
speed v and distance wf to vehicle 2.

arc AB of the circle O, radius r.
we have:⎧β 2v.∆t.90 2))⎪ w = 4.r.(sin ) = 4.r.(sin(2π .r⎨⎪l = 4.r.w − w2⎩o- The 2st case: wf ≥ w, vehicle 1 doesn’t need a big
distance like wf to maintain speed v, the residual
should be cut off from wf to w. In this case, w is
optimal choice.

o(5)

Hence, the general equation is:
Optimal effective distance in latitude = min(w, wf ) at
speed v

Where:- w: best effective distance in latitude (m)- l: distance from initial location to farthest locationof vehicle, project on x-axis (m)- v: speed of vehicle 1 (m/s)- r: minimum radius of circle O that made by vehicle
1’s outside wheel. This radius is calculated on theconditions of stability against overturning. (m)5.3 “Optimal effective distance” in longitudedefinitiona. Best effective distance in latitude
Normally, when running on a road, most vehicles don’tcare how many vehicles behind them. Therefore, thespace between a vehicle and rear vehicles won’t bementioned in this study. On the contrary, let’s look at
the figure 4, vehicle 1 cares for vehicle 3– the next
leading vehicle of vehicle 1, because vehicle 3 directly
influences on the safety of vehicle 1. According to carfollowing model, the minimum distance which made byvehicle 1 for keeping safety with vehicle 3 is estimatedas follows:

In the set of equations (5), r is unknown parameter. For
determining r value, we have to deal with the problem of
running vehicle on a horizontal curve. In this case:=> r =v2g.( µlati ± ilati )

(6)

Where
- ilati: cross slope of road3

Where, Lf is the surveyed effective distance in longitude
on a field
Lre/peLbreak1

L Lbreak3o

5.4 Optimal effective area estimation

1

3

2
A

Figure 4: Car following modelA

The safety distance in latitude of vehicle 1 is the
distance caused by its braking action from speed v tozero, in the case of vehicle 3 stops suddenly. Thisdistance is called the best effective distance in latitude(L). We have

4
Previous model

2
A

L= Lre/pe + Lbrake-veh1 + Lo – Lbrake-veh3

4

car , bus , smallvvan

2− k3 .

2 g (ϕ3 ± ilong )

3

C

1

Lo
= 1m
From the car following theory and above assumtion, wehave:
2 g (ϕ1 ± ilong )DHThe previous models like Zuylen & Ningwu or Y et al
defined effective area as a projected rectangularboundary (dash rectangle) made by vehicle 2, 3, 4around vehicle 1. According to the viewpoint of thismodel, previous methodologies have determined
effective area fast and simply but it might be not precise
because when running on a road, in the case vehicle 1
has to maneuver for avoiding collision with vehicle 2 orvehicle 4, it just uses its leading wheels. For moredetails, let’s look at figure 6; maximum maneuver area
looks like the trapezoid AA’D’D (in fact, A’D’DA isn’t
an trapezoid but real shape area of it is close to thetrapezoid A’D’DA. Therefore, for simplicity, theproposed model assumes that the trapezoid A’D’DA is
maximum maneuver area of it). Any vehicle which
overlaps on the trapezoid AA’D’D might influence on
the speed and the movement of vehicle 1. Looking at
vehicle 4 in figure 6, we see it overlap on ABDN at
representative point C, right side of the trapezoid
AA’D’D. Hence, ACPN is the optimal effective area on
the right of vehicle 1. Conversely, we regard thetrapezoid ABDN as the optimal effective area on theright of vehicle 1 if vehicle 4 doesn’t overlap it.

mc

L = v1∆t + k1 .

H

Figure 5: unnecessary area in the previous models

Lo = 0.5m

v3

D

Proposed model

In this situation, we have some assumtions :- Lre/pe = v. ∆t; Where ∆t is reaction/perception timeof driver (normally, ∆t = 1s)- Lo: Safe distance between two vehicles depend on
type of vehicle. In this study:

2

C’

11

A

(8)

Where
- L: the minimum safe distance or the best effective
distance in latitude (m)- Lre/pe : the distance that vehicle 1 passes over inreaction/perception time of driver (m)- Lbrake-veh1 : the distance that vehicle 1 passes over inbraking time of driver 1(m)- Lbrake-veh3 : the distance that vehicle 3 passes over inbraking time of driver 3 (m)- Lo: Safe distance between two vehicles, its value isdepended on vehicle 1’s type (m)

v1

3

11

+ Lo (9)Where:- v1, v3: speed of vehicle 1, vehicle 3 (km/h)- k1, k3: safety coefficient of vehicle 1, vehicle 3- ϕ1,ϕ3: braking coefficient of vehicle 1, vehicle 3- ilong : Longitudinal slope of roadb. Optimal effective distance in longitude
Similar to the case of optimal effective distance inlatitude (item 5.2), in point of fact, sometimes
longitudinal distance between two consecutive vehicles
is smaller than the minimum safe distance of vehicle 1.
We have to find optimal effective distance in longitude
as follows:
Optimal effective distance in longitude = min (L, Lf) at
speed v

4

- Calculate optimal effective area of vehicle 1

Figure 6: The optimal effective area of a vehicle

S optimal = S optimal + S optimal +vehicle 1

The optimal effective distances between vehicle 1 andvehicle 3, vehicle 2, vehicle 4 make the optimal
effective area of it.
From figure 6, We have many situations that the vehicle
1 is influenced by surrounding vehicles.
Assuming that every surveyed vehicle parallels withroadside, we set a Cartesian coordinates on video clip
and get the speed and surrounding coordinates ofvehicles 1: A’(xA’,yA’), N’(xN’,yN’), N(xN, yN), A(xA, yA),
C’(xC’,yC’), C(xC, yC), K(xK, yK),
Where
C, C’ is representative point of vehicle 4 andvehicle 2
A’, A, N, N’ - Top left, bottom left, top right,
bottom right coordinates of vehicle 1 respectively
K is representative point of vehicle 3
From these coordinates, we can estimate the function oflines: A’B’, A’N, N’N’, B’D’ , AB, AN, BD.
Assuming that the equation of line AB and A’B’ are:y = ax+b (equation of line AB)
y= cx+d (equation of line A’B’)right veh 1[ min(w, w ) + ( x − x ) + min(w, w ) ] .[ min( L, L ) ] (10)
f2

N′

N

f4

f

5.5 Motorcycle equivalent unit estimation
As defined above, MEU value helps us to know that acertain vehicle can be replaced by how many
motorcycles. MEU of a stopping vehicle is equal to areaof that vehicle divided by area of a motorcycle. This
area is called static areas. According to this reason, if
we know the necessary areas of a certain running vehicle
and a running motorcycle, we can estimate MEU of thatrunning vehicle and this area is called dynamic area.
We know that dynamic areas have high impacts on
speed of running vehicles. Dynamic area isrepresentative face of other parameters as density, traffic
component, environmental parameters, etc. It affects
directly and powerfully on vehicles speed. This researchaims to estimate regression functions of dynamic areas
by speed of vehicles i and motorcycles. From
motorcycle’s regression functions, the model sets
the motorcycle’s speed at the mean speed of vehicles ito estimate MEUi. Above argument is interpreted
hereafter:

Generally, we have algorithm for this:- Check the effective distance conditions of vehicle 1
in latitude by both side
+ Left side, check the conditions of C’ inside
A’B’D’N’- Step 1: Collect data of vehicles from video clips tocalculate “the optimal effective area” and speed foreach vehicle⎧ yC ′ − d≤ xC ′ < xN ′⎪left veh1
if ⎨ cthen Soptimal= S A′C ′PN ′⎪⎩ y N ′ < yC ′ < yN ′ + w- Step 2: Estimate regression function of Optimal
effective area (S) by speed (V). For simple, Si and Smc
function will be estimated as cubic functions

S k = f k (vk ) = aVi 3 + bVi 2 + cVi + dleft veh1= S A′B′D′N ′else Soptimal

Smc = f mc (vmc ) = a1Vmc3 + b1Vmc2 + c1Vmc + d 1+ Right side, check the conditions of C’ inside
ABDN

Where, i is vehicle class i (motorcycle, car, bus, van,…)⎧ yC − b< xC < xN⎪
right veh1
if ⎨ athen Soptimal= S ACPN⎪⎩ yN - w < yC < y N- Step 3: Motorcycle equivalent unit of vehicle class i atmean speed vi of them on traffic flow is estimated asfollowing:f k (vi )aVi 3 + bVi 2 + cVi + d(11)
MEU i ==
f mc (vi ) a1Vi 3 + b1Vi 2 + c1Vi + d1

right veh1
else Soptimal= S ABDN- Check the optimal effective distance in longitude

6. RESULTS

Llongitude
optimal = min( L, L f )whereleft veh 1

The results show high confidence of S(v) function incomparison with other models. An example of S(v) isfigured below.

L f = xK − x N

5REFERENCES
1. Chandra, S. and Sikdar, P.K. (2000), Factors
affecting PCU in mixed traffic situations in urban
roads, Road and Transport Research, Vol. 9(3),Australian Road Research Board.
2. Chandra, S., and Kumar, U. (2003) Effect ofLane Width on Capacity under Mixed Traffic
Condition in India, Journal of Transportation
Engineering, Mar. Apr., pp. 155 – 160.
3. Dr. Henk van Zuylen, Capacity and traffic
performance of unsignalized intersections undermixed traffic conditions, Bochum, August 2007.
4. Highway
Capacity
Manual2000,
Transportation research board. Washington D.C,
1999

Figure 7: Optimum effective area – the comparisonof 3 models

5.

This leads to the fluctuation of MEUs on streets arerather low. Streets have same lane width also have same
MEU value, reflected good stability of proposed model.
StreetModel

Proposal
Kim Zuylen & Ning Wu
ma and Y et al
Chandra&Sikdar
Proposal
Tay Zuylen & Ning Wu
son and Y et al
Chandra&Sikdar
Proposal
Giai Zuylen & Ning Wu
phong and Y et al
Chandra&Sikdar
Proposal
Tay Zuylen & Ning Wu
son 2 and Y et al
Chandra&Sikdar
ProposalThai Zuylen & Ning Wu
ha and Y et al
Chandra&Sikdar

MEU
Sedan
2.97
2.41

MEU
Van
3.45
2.97

MEU
Bus
8.28
6.76

6.02
3.51
3.16

7.72
3.75
3.09

23.45
8.96
6.06

6.02
3.03
2.80

7.72
3.44
3.19

23.45
8.24
7.68

6.02
3.26
3.78

7.72
3.64
4.01

23.45
8.36
9.29

6.02
3.41
3.94

7.72
3.84
4.56

23.45
9
8.70

6.02

7.72

23.45

Indonesian highway capacity manual

6. Kimber, R.M, McDonald, M. and Hounsell, N.
(1985), Passenger Car Units in Saturation Flows:
Concept, Definition, Derivation, Transportation
Research – B, Volume 198, No. 1, pp. 39 – 61.
7. Nguyen Cao Y et al., Motorcycle equivalent
units at road segments and signalizedintersections in urban roads, Nagaoka Universityof Technology, School of Civil and Environmental
Engineering, Japan, July 2008.
8. Zhow Wei, A Method for Capacity Analysis
Basedon
TheoreticalandPractical
Considerations, TRB 82nd Annual Meeting and
TRR, 2003

7. CONCLUSIONS
Proposed models of MEU have some difference incomparison with previous models as follow:
Proposed model of MEU is more flexible thanthe others because it deals well with traffic situations.
Moreover, it can be applied for many kinds of segmentseven intersection.
MEU results in proposed model are quite
stable. This also demonstrates that proposed model isbetter than the others.

6