Chapter

4

Traffic
engineering
Takashi Oguchi
Professor, Institute of Industrial Science, The University of Tokyo

Traffic engineering got its start with the popularization of internal combustion vehicles in the early 20th
century, and has developed along with the progress of global motorization that began after World War
II. Traffic engineering traditionally encompasses scientific and technical fields related to reduction of thenegative aspects of automobiles, such as traffic congestion, traffic safety, and pollution (environmentalload). This chapter introduces traffic flow sciences and provides an overview of related technologies.

4.1

Traffic flow fundamentals

The three variables, namely, traffic volume, density, and speed, are fundamental to understand automobile traffic flow on roads.
The term traffic flow rate [vehicles per hour (veh/h)]—or the term traffic volume in general—
describes the number of vehicles passing through a given location per unit time based on the measurement conducted over a duration of 1 h or possibly less. Traffic flow is simply the number of automobiles
passing through a given point, and thus is the traffic demand at the location when there is no traffic congestion. On the other hand, if there is traffic congestion, the traffic volume is equal to the traffic capacityof the downstream bottleneck (see Section 4.2) that causes the traffic congestion.
The term traffic density [veh/km] describes the number of vehicles present at a given time per unit
space length based on measurement conducted over an interval of 1 km or possibly shorter. Unlike traffic volume, direct measurement of traffic density requires simultaneous aerial observation over relatively
long stretches of road and is not very easy.
Traffic speed [km/h] is the representative speed of a traffic flow comprising various vehicles traveling at different speeds. This representative value must be the space mean speed of individual vehicles. It
is calculated by dividing a given space length by the mean of travel times required for individual vehicles
to travel the length. The space mean speed can be estimated by the harmonic mean of the speed of eachvehicle observed at a given location. Using the space mean speed as the traffic speed, Eq. (1) holds.
(Traffic volume Q) = (Traffic density K) × (Traffic speed V)(1)Chapter 4: Traffic engineering｜41

Space
Throughput N1x

V[km/h]Time headway ht

Throughput N2

Measurement distance D

Measurement time T
Traffic flow rate:
Q1 = N1/T [veh/h]Existing count
M1120

Q2 = N2/T

100

100

80

80

60

60

40

40
20

20

0

0
0

20

40

60

40

60

Q[veh/h]Traffic density:
k1 = M1/D [veh/km]

Space headway hs

V[km/h]

120

80

100

80

100

K[veh/km]

0

500

1000

1500

2000

2500

Q[veh/h]

2500
2000
1500
1000
500
0

0

t

Figure 1. Time–space diagram

Time

20

120

K[veh/km]

Figure 2. Example measurement of the relation
between traffic volume, density, and speed

This equation does not generally hold when the simple arithmetic mean is used as the representative
speed of traffic flow. Indeed, Eq. (1) corresponds to the law of conservation of mass in basic physics,
which is universally holds for general flow phenomena, not only traffic flows.
Figure 1 shows time–space trajectories of individual vehicles as well as the relation between traffic
volume and density. As the figure shows, these two variables are in a symmetric relation on the time andspace axes, with the reciprocal of the mean time headway corresponding to the traffic volume, and thereciprocal of the mean space headway corresponding to the traffic density.
Figure 2 shows the mutual relations among the three variables, using actual vehicle detector measurements aggregated in every 5 min and the calculated traffic density obtained by Eq. (1) using themeasured traffic volume and speed. In general, the speed approaches a maximum value (the free speed)
as traffic density approaches zero, and traffic density approaches a maximum value (the saturation density) as speed approaches zero. These two variables are in a monotonically decreasing relation. Furthermore, there exists a maximum traffic volume reached at a certain value of traffic density (the criticaldensity) and a certain value of speed (the critical speed). Densities above the critical density and speeds
below the critical speed indicate a state of traffic congestion; conversely, densities below the critical density and speeds above the critical speed indicate an uncongested traffic state.
Using the monotonic decreasing relationship between density and speed combined with Eq. (1), it
is straightforward to show that the traffic volume–density (volume–speed) relationship is a binary function that has a maximum value of traffic volume. This is the theoretic basis for the existence of a maximum traffic volume (capacity) for road traffic.

4.2

Features of traffic congestion

4.2.1 Bottlenecks and the definition of traffic congestion
Traffic congestion is defined as a traffic state (a waiting queue) in which queued traffic (congested vehicles)

42｜Theory

develops upstream from a traffic capacity bottleneck that occurs when traffic demand exceeding the bottleneck traffic capacity attempts to enter the bottleneck. A bottleneck is a road section in which traffic
capacity is relatively low in comparison with upstream and downstream road segments. Traffic congestion on inter-city expressways in Japan is generally triggered at sag sections (road sections with longitudinal slope changes from downward to upward) or at tunnel entrances.1) On the other hand, major bottlenecks on European or American expressways are merging or diverging sections and weaving sections.
Major bottlenecks on surface streets are key signalized intersections with heavy traffic, queues formingat parking garages of large shopping centers, and on-street parked cars. From the definition of traffic
congestion, it is obvious that there is no fixed speed threshold to distinguish congested traffic conditions
from uncongested traffic conditions. For simplicity, 40 km/h on inter-city expressways and 20 km/h onurban expressways are used as the thresholds to identify traffic congestion for practical use in Japan.
4.2.2 Calculating traffic congestion
Figure 3 shows a simplified assumption of the volume–density relationship per lane based on the data
shown in Fig. 2. Figure 4 schematically shows the change in traffic congestion caused by a bottleneck on
a time–space diagram. Point a (traffic volume A, traffic density k1, velocity v) in Fig. 3 represents the
traffic conditions of traffic demand A attempting to pass through a bottleneck with capacity Cb (location
BN in Fig. 4). Here, in the case where A > Cb, traffic congestion occurs upstream of the bottleneck (pointb in Fig. 3; traffic volume Cb, traffic density k2, velocity vb), and the tail of the congestion queue moves
upstream. The shock wave speed uab is given by the following Eq. (2) according to shock wave theory:2)
uab = ( A − Cb ) / ( k1 − k2 )(2)
The shock wave speed uab is the slope of the line connecting a and b in Fig. 3. The slope in Fig. 3 isobviously negative, which indicates that the shock wave moves upstream. The boundary between
demand traffic condition a and traffic congestion b moves at speed uab in Fig. 4. If the traffic demandchanges to point c in Fig. 3 (traffic volume A', traffic density k3, velocity v) and A' < Cb holds at time T1,then ucb is positive, meaning that the tail of the congestion queue shortens until it vanishes at time T2.
For example, when traffic demand A=1800 veh/h arrives at a bottleneck with capacity Cb=1600
Q [veh/h]
2000
A
Cb
A'

Space

a

uab

b'
c

Status b'

v

BN

vb

b

ucb

uab

Statusb
ucb

Status a

v vb
k3 k1
k2' 25k2[veh/km]K
125

Figure 3. A model of traffic volume–density relation

Status cv
0T1

T2 TimeFigure 4. Expansion and reduction shock wave of traffic congestion

Chapter 4: Traffic engineering｜43

veh/h, the tail of traffic congestion moves upstream at a speed of uab = (1800−1600) / (22.5−50) ≈ –7
km/h, so if T1 = 2 h, the traffic congestion length L ≈ 14 km. If the traffic demand decreases to A' = 1500
veh/h at time T1, then ucb = (1500−1600) / (18.75−50) = 3.2 km/h and time T2 is T1 + L/ucb ≈ 6.5 h.
It is generally known that the excess of traffic demand over the bottleneck capacity is at mostapproximately 12–15% (in the case of this example, it is 12.5%, as given by 1800/1600 = 1.125) evenwhen traffic congestion occurs due to an increase in traffic demand. It is also known that the duration of
traffic congestion (6.5 h in this case) greatly exceeds the duration of traffic demand exceeding the capacity (2 h).3)
4.2.3 Features of traffic congestion on ordinary expressway sections
It was recently found that on inter-city expressways in Japan, bottlenecks at sag and tunnel entrance sections together account for 80% of all bottleneck sections.4) There is no merging or traffic signals at suchsections, but slight speed perturbations due to slight changes in slope cause speed reduction shock waves
that propagate upstream, causing traffic congestion. The level of traffic demand causing such phenomena varies widely in the range of 75–90% of the normal capacity for ordinary expressway sections. Thisvariation is thought to be due to the differences between individual drivers and between vehicle types in
car-following behavior.5)
Furthermore, once traffic becomes to traffic congestion, the bottleneck capacity declines further, toaround 60% of the normal capacity for ordinary expressway sections. This is because drivers’ carfollowing behavior becomes sluggish due to driver boredom and fatigue caused by the low speed in traffic congestion.5) Assume traffic demand is 1800 veh/h per lane as shown in Fig. 3, and the reduced bottleneck capacity is 1600 veh/h per lane, which is equivalent to 80% of an ordinary expressway section’s
normal capacity of 2000 veh/h per lane. The speed of extension of the traffic congestion tail is calculated
to be approximately 7 km/h (see Section 4.2.2). If the reduced traffic capacity after formation of traffic
congestion is 1200 veh/h per lane, which is equivalent to 60% of the normal capacity of an ordinary
expressway section, the speed of extension of the traffic congestion tail doubles, to approximately 14
km/h based on Fig. 3 and Eq. (2). At a sag section, the traffic capacity is further lowered after formationof traffic congestion, and causes a rapid increase in the length of the traffic congestion queue. Furthermore, even when the traffic demand is reduced, the duration of traffic congestion is prolonged because
the traffic congestion queue shortens at a lower speed. These are the reasons why congestion on expressways easily grows and persists.

4.3

Traffic performance-oriented planning and design of road networks

Expressways are the main arteries for high-volume, high-speed automobile transportation. They include
long-distance nationwide expressways that form the backbone of the national transportation network,
expressways that constitute major networks within regional areas, and urban expressways within large
cities. For surface roads accepting more variety of transportation modes including pedestrians and44｜Theory

cyclists, there are different functional classifications according to connectivity scale. Roads in cities furthermore perform various non-transportation functions, such as providing space for infrastructure likesewage and gas lines and performing disaster prevention functions to prevent the spread of fire. This
makes such roads within cities (streets and avenues) quite different from inter-city roads (expressways
and highways). In recent research activities in Japan, focus has been placed on such difference in transportation functions in hierarchical road classifications the concept of “performance-oriented” road planning and design has been promoted with the goal of attaining a road network that provides a certain
level of traffic service functionality.6)
Junctions, the crossing points ofroads, are key locations for transPhase 1

Phase 1

Phase 2Phase 2Phase 3Phase 3Phase 4Phase 4

Figure 5. Example of traffic control improvement at a key signalizedintersection

portation and are one of the mostimportant elements for ensuring
hierarchical road functionality.
Many traffic capacity bottlenecks areat junctions, especially at key signalized at-grade intersections of surface
streets. At intersections where traffic
demand is concentrated, there areneeds for proper geometric design(a sufficient number of lanes, grade
separation, traffic islands, etc.) andfor traffic signal phasing plan andoptimization of signal control parameters (cycle, green split, and offset) to prevent the occurrence oftraffic congestion (Fig. 5).
There are many intersections where the capacity (Cb) is high enough so that they are free from traffic congestion and capacity bottleneck. Even when the traffic demand D is extremely low (0 to D ≪ Cb),
waiting time (delay) occurs at signalized intersections corresponding to the signal control parameters.
On the other hand, when traffic demand exceeds a certain volume (D > Q0) at an unsignalized intersection, the delay under unsignalized control may exceed that under signalized control. For intersections
with moderate demand (0 ≪ D to Q0 < Cb), roundabouts have attracted attention in recent years in Japanas a method for both reducing delay and greatly reducing the risk of rear-end collisions and deai-gashiracollisions (collisions that occur when vehicles, bicycles, pedestrians, etc. suddenly enter into an intersection) frequently observed at unsignalized intersections. There has been increasing momentum for the
introduction of roundabouts in Japan.
To ensure a certain level of transportation functionality for arterial roads, it is important that traffic
flow on arterial roads not be inhibited much at minor intersections. Effective means to that end include
techniques concerning road geometric design and traffic operation and control, such as not connecting
minor streets to arterial roads, limiting the allowance of traffic entering/exiting arterial roads by left
turns only, and providing a dedicated auxiliary right turn lane (or pocket) at the median of arterial roads

Chapter 4: Traffic engineering｜45

to separate this exiting right turn traffic from the main traffic stream on the road. The concepts describedabove are called “access management” in the United States7) which aims to establish a systematic
scheme.

4.4Road traffic management-based countermeasures

4.4.1 Fundamental ideas
The basic concepts of countermeasures for traffic congestion reduction or elimination are adjusting traffic demand and increasing bottleneck capacity. The former includes well-known traffic demand management (TDM), as well as additional efforts toward more dynamic adjustment methods in recent years
such as providing traffic information and route guidance. The latter mainly includes physical measures
such as increasing the number of lanes and expanding road networks, and additionally entails the introduction of active traffic management (ATM), which has been popular in Europe in recent years (see Section 4.4.2).
Improving traffic safety requires a more multifaceted approach that includes not only traffic engineering, but also vehicle technologies and the elucidation of human factors. Traffic congestion, particularly on expressways, is a significant cause of rear-end and near collisions of vehicles, and therefore, traffic congestion alleviation measures may also significantly reduce such accidents.8) It is important to let
drivers naturally understand the road geometric structure and conditions by applying proper road alignment, arrangement planning of intersections, and so forth. Appropriate setting of overall traffic restrictions, including signal control planning, may also result in highly safe spaces for expressways, as well as
for surface streets which are shared with pedestrians and cyclists.
Environmental impacts due to road vehicular traffic include noise, air pollution, and greenhousegas emissions. Improvements in automobile performance and fuel quality have resulted in significant
lessening of noise and air pollution problems in Japan in recent years, and improved fuel economy has
reduced carbon dioxide emissions. Nonetheless, traffic congestion and repeated stopping and starting
caused by traffic signals would lead to needless carbon dioxide emissions, 9) and therefore any trafficsmoothing policies to alleviate traffic congestion or to reduce number of stops are effective at reducing
the environmental impact of road vehicular traffic.
4.4.2 Expressway traffic measures
Expressways are motorways (dedicated roads for automobiles) that serve as the main arteries for highvolume, high-speed nationwide and urban transportation. Frequent traffic congestion on expressways isa functional failure of these arteries, and leads to major losses to the country and to regional communities. Reducing congestion, especially on expressways, is thus extremely important. Ramp metering,which controls traffic volume at on-ramps, has become a common measure, and ATM such as lanebased variable speed limits (Fig. 6) and temporary hard shoulder opening has also been popular indeveloped countries except Japan.

46｜Theory

Particularly severe traffic congestion was expected
to be caused by partial opening of the Shizuoka segment of the New Tomei Expressway due to traffic concentration on the Tomei Expressway section between
the Otowa-Gamagori Interchange and Toyota Junction
prior to opening the Aichi segment. Therefore, a policy
was implemented that increased the number of traffic
lanes on the Tomei Expressway by narrowing them asshown in Fig. 7, while keeping road width unchanged.10)
This measure in Japan resulted in a great reduction of

Figure 6. Example of lane-based variable speed
limits (U.K.)

traffic congestion and traffic accidents on the Tomei
Expressway section. An advanced automotive technology that has recently been attracting attention isadaptive cruise control (an advanced form of cruise control, which automatically maintains a constant
speed). Adaptive cruise control adjusts the vehicle’s speed and spacing ahead to conform to the leading
vehicle’s behavior. Because drivers’ car-following behavior is a prime cause of bottlenecks on ordinary
expressway sections (see Section 4.2.3), adaptive cruise control technology is expected to help reduce
traffic congestion.11)

Figure 7. Increase to three lanes between the Otowa-Gamagori Interchange and the Toyota Junction on the Tomei
Expressway (source: NEXCO Central Nippon Expressway Co., Ltd. press release)

4.5

Future trends in traffic management

One issue in traffic engineering is the extreme difficulty of running laboratory experiments. This makes
careful practical observations and investigations in the field important. Small differences and changes intraffic flow, such as 10–20% variations in traffic demand and the emergence of traffic congestion at sag
sections due to individual differences in driver behavior, can have a significant impact on the characteristics of traffic flow: whether it is congested or uncongested. The conventional point observations withvehicle detectors described in Section 4.1 have limitations to describe such temporal and spatial
variations.
Advanced information technology has enabled the establishment of “probe” technology that allows

Chapter 4: Traffic engineering｜47

temporally and spatially continuous measurement and monitoring of traffic status via automobilemounted navigation systems or drivers’ smartphones. Complete knowledge of the overall quantitative
features of traffic flow, however, remains difficult because such techniques provide only sampled data.
An estimation method of the overall traffic state in combination with data from vehicle detectors
and probe data has recently been developed by applying the traffic flow theory described in Section
4.2.12) It is expected that the accumulation of large amounts of detector and probe data and the application of recent data mining technologies will provide dramatic increases in our knowledge of overall traffic states. Based on knowledge derived from such accumulated data, real-time use of sensor and probe
data will allow the establishment of “nowcast” technology13) to estimate the current traffic state throughthe application of theory-based traffic simulation models. The dynamic flexible application of nowcast
technology applied to traffic information provision, route guidance systems, and ramp metering and
TDM measures should result in minimization of daily recurrent traffic congestion. The nowcast technology is also considered to allow for prompt planning and execution of countermeasures against bad
weather, large events, traffic accidents, and other incidents that are difficult to predict.
For example, Fig. 8 shows the state of extraordinarily massive traffic congestion that occurred on
major arterial roads in the Tokyo Metropolitan Area
immediately after the Great East Japan Earthquake
on March 11, 2011.14) Gridlock, which is the phenomenon where an entire road traffic network becomesparalyzed, emerged on that day. Gridlock can be
defined as the traffic state where the throughput of abottleneck is reduced to a value lower than the original bottleneck capacity by the tail of a traffic congestion formed upstream of the bottleneck extending to
Figure 8. Gridlock of arterial roads in Tokyo
the bottleneck location on a loop-shaped road network. Gridlock is a serious traffic congestion phenomenon that is extremely difficult to resolve once it
starts. It is believed that the development of a system for real-time detection of gridlock, or the establishment of traffic control methods for predicting and avoiding it, would be a significant contribution
leading to increased stability and reliability of road transportation systems.
References
1) Koshi, M. 1985. “Traffic Flow Phenomena in Expressway Tunnels.” IATSS Research Vol. 9: 50–56.
2) Lighthill, M. J., G. B. Whitham. 1955. “On Kinematic Waves: 2. A Theory of Traffic Flow on Long Crowded Roads.” Proceedings of the Royal Society of London A Vol. 229: 317–345.
3) Koshi, M., H. Akahane, and M. Kuwahara. 1989. “Explanation of and Countermeasures against Traffic Congestion.” IATSS
Research Vol. 13, No. 2: 53–63.
4) http://www.mlit.go.jp/road/ir/ir-council/autopilot/pdf/05/6.pdf.
5) Koshi, M., M. Kuwahara, and H. Akahane. 1992. “Capacity of Sags and Tunnels on Japanese Motorways.” ITE Journal Vol.
62, No. 5: 17–22.
6) Oguchi, T. 2008. “Redesign of Transport Systems on Highways, Streets and Avenues.” IATSS Research Vol. 32, No. 1: 6–13.

48｜Theory

7) Transportation Research Board. 2003. Access Management Manual.
8) Oguchi T., H. Akahane and Y. Yamada. 2004. “Analysis of Accident Rate in Critical Condition of Traffic Flow on Expressways.” Traffic Engineering Vol.39, No.3: 41-46. (in Japanese)
9) Oguchi T. and M. Katakura. 2000. “New Conceptual Evaluation Method of Amount of Exhaust Emission Gas on VehicularRoad Traffic.” Advances in Transport (Urban Transport VI) Vol.6: 383-392.
10) http://media2.c-nexco.co.jp/images/press_conference/78/2918114934ea7888494e01.pdf11) Kanazawa, F., K. Suzuki, K. Sakai, and K. Iwatate. 2013. “Conducting the FOT to Evaluate the Driving Practice for Smooth
Traffic to Mitigate Traffic Congestion at Sag Sections on Expressways. ” In Proceedings of 20th World Congress on ITS.
CD-ROM.
12) Mehran, B., M. Kuwahara, and F. Naznin. 2012. “Implementing Kinematic Wave Theory to Reconstruct Vehicle Trajectories
from Fixed and Probe Sensor Data.” Transportation Research Part C Vol. 20: 144–163.
13) Hanabusa, H., M. Kobayashi, K. Koide, R. Horiguchi, and T. Oguchi. 2013. “Development of the Nowcast Traffic Simulation
System for Road Traffic in Urban Area.” In Proceedings of 20th World Congress on ITS. CD-ROM.
14) Oguchi, T., M. Ito, R. Mizuta, R. Horiguchi and M. Iijima. 2013. “Analysis with Traffic Simulation and Evaluation of Traffic
Congestion Mitigation Measures for the Tokyo 23-wards at a Great Earthquake Disaster. ” Proceedings of Traffic Engineering
Meeting, Vol. 33: 273-278. (in Japanese)
Recommended Reading
1) May, A. D. 1990. Traffic Flow Fundamentals. Prentice Hall.
2) Daganzo, C. F. 1997. Fundamentals of Transportation and Traffic Operations. Elsevier Science.
Practical application projects for reference
Practical optimal signal control emphasizing pedestrian road crossing realities: 144–147
Significant reduction of cycle length via a two-stage crossing system: 148–151
A study on the practical deployment and promotion of safe and ecological roundabouts: 152–155
A study on the role and limitations of motorcycles as a means of urban transport in Southeast Asia: 156–159