A Study on the Macro Capacity Model of Urban Road Network and Its Application
1/8
A Study on the Macro Capacity Model of
Urban Road Network and Its Application
By Li Shuo1
Abstract How to quantify the macro capacity of an urban road network is a new approach to studying urban total road
network capacity in the recent years. A French scholar Mason(1989) has provided the magnitudes of time and space usage of
city road network occupied by traffic bodies. This theory simply shows the inner effectiveness of various traffic models in
terms of traffic bodies occupation of time of road network space or of space of road network time in the form of quantity, as
well as investigates in convenience the intrinsic potentials of urban road traffic infrastructures (inclusive of static and dynamic
ones), for example, parking, motorway, bikeway, pedestrian and etc. On the other side, it can further prove and compute the
urgent economic costs of time and space usage of road net, and its economic revenues produced by that usage. This paper
amends the concept of time and space usage of road net on the basis of Mason’s, especially taking the density of urban road
network into the consideration, and it mostly represents the reality. Although the model is a little bit complicated, it can be
more effective if the methods provided by this paper are used. This can be verified by the case study of Zhuzhou City, Hunan
province. This paper uses Zhuzhou data given in 1990 as a pilot study city. All the process and results have shown that the
ways given in the paper are useful, rational and efficient.
The Macro Capacity Model of Urban Road Network
The Concepts of Macro Capacity and Space-Time Usage
Macro Capacity
It is the maximum number of pedestrians and vehicles accommodated in a limited road space
during a certain period. Road traffic facilities are stable and limited during a given period, but the
traffic flow is stochastic and dynamic, which will use the space and time of road network. According
to Mason, if C stands for the total capacity of urban road traffic facilities, it can be computed as:
C=A·T
(m2.h)
(1)
where: A = the effective area of urban road facilities, T = the effective traveling time. The space-time
usage of unit traffic body can be converted into the number of total traffic bodies accommodated during a
given period:
Cv=C/Civ=A·T/ Civ
(2)
where: C = total capacity of urban traffic facilities given by equation (1)；
Cv= vehicles accommodated by road facilities；Civ = one vehicle’s normal space-time usage.
Due to the limitation of length, this paper will only discuss the capacity of vehicle that can be
accommodated, while that of pedestrian will be not discussed in the paper.
Space-Time Usage
Space-time usage means road space occupied by unit traffic body during a certain period, in
2
m ·h/v or m2·h/p. It can be defined and evaluated according to the different traffic bodies, types,
periods and situation. To a vehicle, its space-time usage equals the road space needed during travel
multiplied by traveling time, which is:
Civ=Sd·tv
(3)
where: Sd = the road space needed by vehicle, during travelling, Sd=dd·Ld;
dd = lateral safety width needed by vehicle, approximate equaling the width of one lane, (m);
Ld = the minimum safety space headway between vehicles (m);
tv = the average traveling time of vehicle (h).
The Influence of Density (D) of Road Network for Calculating C
The wider isn’t always the better for road. The capacity of a road with 60m wide isn’t larger than
that of two roads with 30m wide. This is because the former road density is smaller than the latter. The
capacity is different among roads with same effective areas and the different densities. So the
influence of density must be considered when C is computed.
1
Assoc. Prof., Dept of Civil Eng., Hunan University, Changsha, HN 410082, China
A Study on the Macro Capacity Model of Urban Road Network and Its Application
2/8
Let us make Do (km/km2) the standard density, and its relevant modified coefficient of road
density kD=1.0;As D>Do, kD>1.0; otherwise, kD<1.0. Here, the modified effective area of road
network is as follow:
A*=KD·A
(4)
In this equation, the total capacity is computed on the base of the concept of “space-time-density
usage”.
The Macro Capacity Model of Urban Road Network and Its Algorithm
The macro capacity model of urban road network that based on the concept of "space-timedensity usage" is as follow:
N=A*·T/C
(5)
where: N = macro capacity of road network, in equivalent vehicles;
A* = the modified affective operation areas of road network;
T = the effective operation time of traffic facilities;
C = the average space-time usage of vehicles in traffic flow;
In view of the integrated influence of actual classification, distribution, use frequency, portrait
and lateral disturb, delay of intersections, pedestrian and so on, the actual macro capacity of road
network can be calculated as:
N=(60SnKDK1K2K3K4K8)/(atnK5K6K7)
(6)
where: K1 = the modified coefficient of road grade;
K2 = the average frequency coefficient of road usage;
K3 = lateral disturb coefficient;
K4 = integrated influence coefficient of intersections;
K5 = traffic flow ratio during peak hour;
K6 = unbalance time coefficient during peak hour;
K7= vehicle type coefficent;
K8 = peak hour factor;
a = space occupied dynamically by unit traffic body;
t = average time usage of traveling of unit traffic body;
Sn = modified network areas of road facilities;
Kd = modified density coefficient of road network;
Confirmation of Technique Parameters
Sin = S×αi. "αi " stands for the proportion of road type i, which means motorway if i=1, bikeway if
i=2, and walkway if i=3.To motorway, the arterial road area is defined as standard, and all others
should be converted to it. Consideration of driver familiarity, preference, location and so on, K2 is
generally assumed 0.7~0.8. K3 is generally assumed 0.7~0.85.The effective operation time (T) of
urban road is usually computed in peak hour, while the most serious influence during peak-hour is in
intersections. So a converted coefficient must be taken according to the factors of intersection type,
traffic organization, traffic control, etc. Generally, the coefficient (K4) is assumed 0.7~0.85, and the
effective operation time during peak-hour is computed as:
T = 60K4
(min)
(7)
The space-time usage of unit traffic body during peak-hour is computed as:
C = atnK5K6K7/K8
(8)
where: a = the dynamic occupied area of unit traffic body, which is defined by the size of plane
projection, the speed and the mental need of traffic safety, in m2;
t = the average traveling time usage of traffic body, which needs to be confirmed by survey,
and
relates with the city scale, road network and distribution, etc, in hours;
n = the average travels of unit traffic body in a day, derived by the travel-survey, in trips;
K5 = the flow ratio of peak-hour,derived by the travel-survey;
K6 = unbalance time coefficient during peak hour, assumed 1.1~1.3;
K7 = modified coefficient of vehicle type, in which car is standard; and
A Study on the Macro Capacity Model of Urban Road Network and Its Application
3/8
K8 = peak-hour coefficient, achieved by traffic volume survey.
Analysis and Calculation on Macro Capacity of Road Network of
Zhuzhou
This paper is part of primary study of “the Total Capacity’s Theory and its Application of Urban
Road System” (No: 97SSR2037) worked by the writer. The data applied in the paper are achieved
from Li(1990), which are the road-survey material of Zhuzhou in 1989. The macro capacity
calculation aims at analyzing the total road capacity of the time in Zhuzhou, and pave the ground for
comparing with the present.
The Modified Effective area (A*) of Road Facilities in Zhuzhou
Datum A* is from A-the effective area of road facilities, which is the area that ensures the safety
and natural use of traffic body, in this paper only area used by vehicles is involved. According to
Li(1990), the total road area of Zhuzhou in 1989 is 2,065,843 m2. In which, motorway area is
1,000,309 m2, bikeway area is 639,348 m2, walkway area is 426,186 m2; they occupied 48.42%,
30.95% and 20.63%, respectively.
The Modified Road Class Coefficient K1
To motorway, let the arterial area be standard, and other areas must be converted according to
one lane’s capacity and their proportions are as follows:
K1=ga+(Ns/Na)·gs+(Nl/Na)·gl
(9)
where:Na, Ns, Nl are the possible capacities of arterial road, subarterial road or lateral road
respectively, and ga, gs, gl are the proportion occupied of them, in %.
The motorway area of arterial road, subarterial road, and lateral in road system of Zhuzhou is
520583m2, 120850 m2, and 358876 m2 respectively, while the proportion of them is 52.04%, 12.08%
and 35.88% respectively. The calculation of Ns/Na and Nl/Na is related with lane width, lateral
clearance, grade, sight distance, disturb alongside, and the influence from bike. Most of the width of
arterial road of Zhuzhou is more than 3.65m。Provided the standard width is more than 3.65m, all
that less than 3.65m must be converted (as table 1 shows). The average weighted width of Zhuzhou’s
arterial road (Wa) equals 3.398m, the Table 1 giving the converted coefficientδwa= 0.8992; while
Ws=3.295m, δws=0.8691 and δwl=0.9268.
Table 1. The Converted Coefficient [δ] of Lane-width
Lane width (m)
2.75
3.00
3.35
3.65
0.76
0.81
0.88
1.00
δ
The road network of Zhuzhou appears as belt-shape and center-radiation. Most road can meet the
sight distance. It has basically been urbanized alongside, and the roads are comparatively smooth. So
it hasn’t been done to modify lateral clearance, grade and sight distance. Part segment of three arterial
road out of eight are equipped the division-facilities. By the actual observation of above mentioned
during peak hours, half motorway areas are occupied by bike, and these arterial road without divisionfacilities occupied 22.3% of total. So the influence coefficient on arterial road by bike can be
computed as:
δna=1-22.3%·1/2=0.8885
(10)
Most type of eight subarterial roads is one-board cross-section. The observation to them shows that
half motorway area is occupied by bike, and the influence coefficient on subarterial road of bike is
computed as:
δns=1-1/2=0.5
In this city, there are 50 lateral roads. There exists serious mixed traffic, and pedestrian produce a lot
of disturbs, 2/3 motorways being occupied, So δnl=1-2/3=0.3333.According to all above:
A Study on the Macro Capacity Model of Urban Road Network and Its Application
4/8
Ns/Na = (δns·δws)/(δna·δwa)=(0.5/0.8691)/(0.8992·0.8885)=0.5439
Nl/Na = (δnl·δwl)/(δna·δwa) =(1/3·0.9268)/ (0.8992·0.8885)=0.3867
From equation (9), the road class influence coefficient (K1) can be computed as:
K1=52.04%+0.5339·12.08%+0.3867·35.88%=0.7249
To bikeway, K1 is given 1.0.
(11)
(12)
(13)
The Average Frequency Coefficient of Road Usage (K2)
This paper describes the average frequency coefficient of road usage with unbalanced quality of
load-degree of network, which means if distribution and arrangement of road is reasonable, its loaddegree will be balanced, and so is the average road usage. But the traffic volume of Zhuzhou has
almost centralized in arterial roads like Xinhua and Honggang Road (east-west orientation), Jianshe,
Hongqi, Renming and Lusong Road (south-north orientation). According to the data of 1990,the
volume of south-north orientation is obviously larger than that of east-west orientation. Let the load2
degree (V/C) of arterial i be xi, the average x =∑xi/n, and its difference S  ( ( x1  x ) ) /( n  1) .
Substituted with the data given (Li,1990), S/ x =0.515. The result reflects the unbalance of frequency
of used road. So K2=1-S/ x =1-0.515=0.485.K2 stands for the reasonability of distribution and
arrangement of road network and unbalanced quality of volume distribution.
The Lateral Disturb Coefficient K3
Market is the most important factor that results in road occupied. The whole Zhuzhou has 17
markets, which occupied 23076 m2 of walkway and 9719 m2 of motorway. They also occupied 4681
m of road, while total length of road of Zhuzhou in 1989 is 89287 m. So K3=1-4681/89287=0.9476
The Effective Operation Area (A) of Road Facilities
From: Ai=Sin·Ki1·Ki1·Ki2·Ki3, (i=1 means vehicles, and i=2 means bikes) ,we get
A1=2065843·48.42%·0.72448·0.485·0.9476=333064 (m2)
A2=2065843*30.945%*1.0*0.485*0.9476=293836 (m2)
The Modified Effective Area of Road Facilities of Zhuzhou A*
It is essential to define the density of road network correctly to modify A. Ten large Chinese
city’s relative data have been shown as table 2. The writer thinks that the density of road network is
decided by the number of vehicles and bikes possessed. Provided a duality linear regression formula
with latter two independent variables namely x1and x2 and the density of road network variable
namely y, and y=a+b1x1+b2x2. A duality linear regression formula (the standard density function) can
be resulted as:
y=5.8864347+0.008564671x1-0.0060753964x2
(2-13)
The plural relative coefficient of formula above R=0.90642587, residual standard differentce
S=0.7336519. Data of Zhuzhou in 1990 shows that there are 9625 vehicles possessed. And
x1=9625/89.3=101.79, while x2=786.0694. So the standard road density of Zhuzhou is computed
as:D0=5.886435+0.00856467 · 107.79-0.006753 · 786.069=2.034016 (km/km2). The actual road
density of Zhuzhou (D) is 1.83 km/km2. And its modified coefficient is computed as:
KD1=D/D0=1.83/2.034=0.899705
*
1
Therefore: A1 =A1·KD =333064·0.899705=299659.35(m2); A2*=A2=293836 (m2).
Table 2 Chinese Ten Large Cities’ Roadnet Density(1985)
City
Name
Road net
Density
(km/km2)
VehicleRoad
Density
(Vehicle/
km)
Density
(Bikes/
km)
Beijing
Shanhai
Tianjin
Shenyang
Wuhan
Guangzhou
Harbin
Chongching
Nanjing
Xi’an
Average
6.93
5.62
3.94
5.95
6.91
2.45
4.56
3.52
5.60
3.52
4.90
56.32
84.51
75.24
45.37
19.30
19.30
53.67
112.10
61.26
79.44
79.82
183.90
240.78
392.10
179.32
634.65
634.65
113
15.80
98.04
190.0
195.07
A Study on the Macro Capacity Model of Urban Road Network and Its Application
5/8
Effective Operation Time of Road Network of Zhuzhou
The intersection influence coefficient of effective time during peak hours can be measured in two
methods.
Saturation Flow Rate Modify Coefficient
This method computes modified coefficient with the usage of intersection as:
K4=fw·fHV·fg·fa·fRT·fLT·fn; Where: fw = lane width modified coefficient;
fHV = modified coefficient of heavy vehicles in traffic flow;
fg = grade modified coefficient of entrance lane;
fa = region type modified coefficient;fRT = right-turn vehicles modify coefficient;
fLT = left-turn vehicles modify coefficient;fn = modified coefficient of disturb on motor of bike.
Take the intersection of Jianshe Road and Chezhan Road for example. It is an important one of arterial
road and subarterial road. Its traffic flow during peak-hour is showed as table 3.
Table 3
The Flow of Jianshe Road and Chezhan Road Intersection
east entrance
left
Motor
67
Bike
114
Pedestrian
south entrance
west entrance
straigh right subtotal left straight right subtotal
t
63
117
234
383
7700
364
614
0
0
663
721
145
379
360
808
1100
north entrance
left straigh right subtotal left straight right subtotal
t
33
78
167
213
52
256
1400
252
547
219
256
874
737
29
63
825
1122
1056
Impedance Factor, p
According to the relative Tables in Li(1990), Xu(1992), and HCM (1984), the modified coefficient of
north entrance in table 3 was as follows:fw=0.81, fHV=0.93, fg=1.00, fa=0.9, fRT=0.98, fLT=0.864. At
last, fn was computed in two instances:
1) Bikes and motors used one lane, and the former occupied part of capacity
2) Conflict happened among bikes, pedestrians and turning.motors fn=1.0, for there are not mixed
traffic volume. This resulted :K4n=0.81·0.93·1.00·0.90·0.98·0.864·1.00=0.574.
And the other three entrances’ K4 was 0.598, 0.5029, 0.661, respectively. Accept the average of them:
K4=0.584. The other type is intersections without signals, which mainly consideration of the
impedance factor of minor direction and related to the load degree (in %) arousing block flow, seeing
fig 1.
Accepted Capacity, %
Fig 1 The Relationship between the Impedance Factor and Traffic Congestion
Take T-shape intersection without signals of Jianshe Road and Park Road for example: there are
178pcu/h vehicles left turn on Jianshe Road (main stream), speeding at average of 31km/h; and
613pcu/h vehicles left turn on Park Road, with four-lane. Further more, bikes’ influence must be taken
A Study on the Macro Capacity Model of Urban Road Network and Its Application
6/8
into consideration, with converted coefficient of 0.2. So the number of main road’s left-turn vehicles
converted is 178+334·0.2=245pcu, while that of minor road’s is 613+275·0.2=668puc. The critical
intermission is 5.26s given by the relative tables in HCM(1984), while the capacity of main road’s
left-turn is 600pcu/h. The load degreeV/C=244/600=0.4083, and the impedance factor is 0.67 by
checking up Fig.1. So K4=(0.67+1.00)/2=0.83 The cross intersections can be analogized like this.
When it was used in roundabout intersections, the exit flow is regarded as the main one, while enter
one the minor. After calculated all main intersections, their K4 are between 0.5 and 0.93, and the
average one is 0.754.
Calculating K4 of Intersection with Average Delay
It’s unreasonable to assume that there is not any impedance on main stream of no-signal
intersections. This paper suggests a simple method to calculate K4. Delay is a crucial indicator of
intersection, almost relating with all factors of intersection. Vehicle’s delay is caused by the factors of
geometry condition, signal time assignment, linkage response, mixed traffic, etc. Operation efficiency
of intersections was showed in table 4. Take the Jianshe-Chezhan Roads intersection for example, its
average delay is 24s, and
Table 4 The Relationship Between Average Delay and Service Level of Intersections
Service level
Average delay(s/v)
K4 computed in the method of
saturation flow ratio
A
<10
0.9
B
10~15
0.8
C
15~20
0.7
D
20~30
0.6
E
>30
0.5
K4=0.6, which is closely to the K4=0.5840 computed in the method of saturation flow ratio modified
coefficient. The average converted coefficient (K4) of all intersections in Zhuzhou is 0.7310 with this
method. Because of the difference of time-period peak-hour appears, the time-period that has the most
frequency of appearance was chosen as the standard peak-hour period. Generally, its between 8:45
and 9:45am, and its effective operation time T=60·0.7310=43.86(min).
The Analyses on Space-Time Usage of Unit Traffic Body of
Zhuzhou during Peak-Hour
Vehicle’s Space-Time Usage
Provided car as standard type. Its static width is 1.8m, while its dynamic width is 1.8+2·0.25
=2.3m. The average speed given is 30km/h; then its minimum safety portrait space headway is
computed as:
L0=V/3.6b+V2/254∮+5+2=30/(3.6·1)+302/(254·0.44)+7=23.39
And the average dynamic space usage of vehicle av=2.3·23.39=53.797 (m2). The survey shows that
average trips time of vehicle in Zhuzhou is 25.8 min/t, and average daily trips nv=1.14(times).
Bike’s Space-Time Usage
The static width of bike is 0.6m, and dynamic one is 0.6+2·0.25m. Its minimum safety portrait
space headway is 7.26m, so its dynamic area ab=(0.6+2·0.25)·7.26=7.986(m2). The survey shows
that average traveling time of bike of Zhuzhou is 25.8 min/t, and average daily trips is 1.48(times).
The Modified Space-Time Usage Coefficient
1) The modified flow ratio during peak-hour. Survey provides: K5n=19.7%, K5v=18.9%;
2) The unbalanced time coefficient during peak-hour is 1.2;
3) Vehicle type’s modified coefficient K7. Whole Zhuzhou have 13341 vehicles in 1989, which
corresponds to 20205pcu standard cars. So K7v=20205/13341=1.5145, while K7b=1.0;
4) Peak-hour modified coefficient. The average peak-hour coefficient K8=0.9998.
A Study on the Macro Capacity Model of Urban Road Network and Its Application
7/8
The Calculation of Macro Road Capacity of Zhuzhou
Table 5 shows the result of calculation.
Table 5 The Calculation Results
ITEMS
VEHICLES
BIKES
Total areas of road network , S(m2)
2065843
2065843
Proportion of motor v.s. bike way, 
48.42
30.95
Road class modified coefficient, K1
0.7249
1
Average usage frequency of road , K2
0.485
0.485
Lateral disturb coefficient , K3
0.9476
0.9476
Net Road areas Sn (m2)
1000309
639348
Effective areas of road facilities, Ai (m2)
333064
293836
Modified coefficient of Ai ,KD
0.8998
1
The modified effective areas of road facilities, Ai*(m2)
299659
293836
The integrated converted coefficient of intersections, K4
0.731
0.731
The effective operation time during peak-hour, T(min)
43.86
43.86
Average dynamic areas of unit traffic body , a(m2)
53.797
7.986
Average time usage of unit traffic body (min/t)
25.8
17.68
Average daily travels of unit traffic body (t/v)
1.14
1.48
Flow ratio during peak-hour , K5
0.189
0.197
1.2
1.2
Vehicle type modified coefficient, K7
1.5145
1
Peak-hour factor, K8
0.9998
0.9998
Average space-time usage of unit traffic body during peak-hour,
Ci(m2.min/v)
543.926
49.4092
13143044
12887647
Macro capacity of road network, N(standard car)
24163
260835
Actual vehicles possessed (standard-car)
20205
262191
Load degree of road network (v/c, %)
83.62
100.52
Unbalanced time coefficient during peak-hour, K6
Space-time capacity of network during peak-hour, C(m2.min)
The fact can be found from table 5 that the bike traffic is in over saturation state, especially in
peak-hour. The vehicle traffic is near saturation, where the through traffic hasn’t included. There are
six main exits and entrances as table 6.
This table shows that the net increase of traffic during peak-hour is 170 vehicles. If this number is
added, the load degree is 84.32%, closer to saturation. As mainly traffic mean of dwellers, bike traffic
is in over saturation. And there aren’t special bikeway system and independent bikeway. There is
serious mixed traffic in most road, which makes the vehicle traffic jam worse. Further more, there are
many factors resulting in traffic difficult like complex composition, narrow pavement, lower standard,
A Study on the Macro Capacity Model of Urban Road Network and Its Application
8/8
unreasonable plane layout of intersection and so on. So transportation planning, construction and
management must accord to the macro capacity.
Table 6 The Peak-Hour Flow of Exits and Entrances of Zhuzhou
Exit and entrance
In flow
Out flow
zhuyi road
479
273
zhuchang road
149
164
zhulu road
185
211
zhuli road
201
190
Zhuliu road
108
107
zhuheng road
88
95
Total
1210
1040
Conclusions:
This paper tries to study macro capacity of road network primarily. The calculation example
proved that the method suggested in the paper is feasible. It can be used to calculate and analyze the
total capacity of road network in the macro view, and provide a mathematics tool for transportation
planning and assessment. It’s sure that the method is cursory, and needs amending a lot. Combined
with the item of science commission of Hunan province, the writer will calculate the macro capacity
of road networks of Changsha and Zhuzhou carefully. A more reasonable method will be suggested to
improve the theory of space-time usage through calculating the standard density of road classes and
macro capacity of jam and unjam regions, and so on.
APPENDIX. REFERENCES
Luis Mason, A Generalized Concept-the space and Time usage of a City, Translated by Tianjin
Institute of Comprehensive Transportation Study, 1996.6.6, Tianjin.
Yan Tao, Xujiqian, The Roadnet’s Total Capacity Under the Space and Time usage, Proc. Of
China Civil Eng. Annual Meeting, Tianjin Unv. Press, 1990, Tianjin;
Li Shuo , The Comprehensive Transportation Planning Report of Zhuzhou City, 1990, Zhuzhou;
Li Shuo, The Subereport of (3), 1990, Zhuzhou;
Li Shuo, The Data of Zhuzhou Transportation Study, 1990, Zhuzhou;
Xu Jiqian, Traffic Englineering, Chinese Communication press, 1992, Bejing;
Ministry of Construction of China, The Basic Data Complilation for the Transportation of
Domestic and Overseas’ Cities, 1985, Beijing;
Highway and Intersection’s Capacity, The Soceity of Highway of China, 1987, Beijing;