Jun-Meng Yang

Bicycle Traffic in China

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published in TRANSPORTATION QUARTERLY
Vol. 39, No.1, January 1985 (93-107)
© 1985 Eno Foundation for Transportation Inc. Westport Conneticut

Excerpt from: Bicycle Reference Manual for Developing Countries. Edited by Barbara Gruehl Kipke, April 1991.


In this section:
About the Author
Introduction / Background Information / Bicycle Travel Characteristics / Problems and concerns / Recommendations / Conclusions / Acknowledgements

About the author

Jun-Meng Yang is a senior research engineer at the Scientific Research Institute of Communication. Chongqing. People's Republic of China. He graduated from the to Xion Highway College in 1964. During 1982-84 he was a visiting scholar at Purdue University working in the area of transportation systems analysis. His current work involves motor vehicle safety research and mixed traffic flow analysis.

Introduction

China not only houses the largest populalion, but also the world's largest fleet of bicycles. Bicycles are the principal and most often used means of private transportation in this eastern Asian nation. In fact, the bicycle plays an important transportation role in all developing countries. Bikes have many advantages: low initial cost, low operaling expense, small space needs for operating and storing, and the flexibility to go where other vehicles cannot. Bicycles are especially advantageous in China where city mass transit systems are often inadequate for meeting urban travel demands.
Used as a primary means of transportation by large numbers of urban inhabitants, bicycles are a mixed blessing, having advantages as well as serious disadvantages. Like some of the adverse impacts of motor vehicle traffic, bicycles contribute to street congestion and noise (bicycle bells), interfere with pedestrian and other vehicular movements, and are the cause of many street accidents. If urban transportation in China is to be improved, the best place to start is with the use and misuse of bicycles. This article describes bicycle traffic in China and suggests measures to improve bicycle use in the overall transportation mix.

Background Information

The tolal number of bicycles in China was about 100 million as of 1979. Comparatively, the nalion's total number of motor vehicles (cars, buses, trucks, and motorcycles) was just over 2 million. The proportion ot bicycies to motor vehicies is therefore considerable if not overwhelming.
In many large and medium size cires there is about one bicycle for every two to three persons. The number of bicycies resistered in some of these large cities is compared to population figures in Table I.

TABLE I - REGISTERED BICYCLES IN RELATION TO POPULATION

City Beijing Shangai Tianjin Guanzhou Chengda Wuhan Tangshan
Number of bicycles* (thousands) 2,8001,6001,250780530380350
Population (millions) 8.7111.327.395.353.853.841.0¹

City Kunming Baotou Changchun Nanjing Hanzhou Fuzhou
Number of bicycles* (thousands) 330330300300250190
Population (millions) 1.931.0¹1.613.551.111.05
* The figures for Beijing, Shanghai and Tianjin are for 1978, the other figures are for 1977.
¹ Rough estimates.

During the last decade, the average rate of growth in the number of bicycles has been about 10 percent in the larger cities, although some areas have increased by 15-20 percent. To keep up with this rise, the annual production of bicycles has also increased rapidly in recent years. The estimate of bicycle manufacturing trends given in Table II implies that production growth rates are rather high and still rising.

TABLE II - BICYCLE MANUFACTURING TRENDS

Year 1949 1952 1978 1979 1980 1981
Number of Bicycles manufactured (thousands) 14808,54010,09513,02217,540
Yearly growth rate (%) ---18.229.034.7

Bicycle Travel Characteristics

In addition to the advantages already cited, bicycles also are non-polluting and energy efficient. Their speed is several times faster than walking and they can easily travel on narrow streets and lanes, maneuvering through traffic congestion nearly as well as pedestrians. Bicycles can easily be parked very close to their destinations and they can carry light loads in addition to the weight of the cyclist. Their energy use efficiency is higher than other modes of transportation including pedestrian. A cyclist moving at 10 miles per hour uses only 97 Btu per passenger-mile, while a pedestrian uses 500 Btu per passenger-mile walking at 2.5 mph (1). A person's energy consumption over a given distance while riding a bicycle as compared to walking is about one-fifth of the latter and human transport (bicycling and walking) is 10-40 times as energy efficient as motorized transport. (2)
In China bicycles are used primarily for commuting and shopping. Most workers and professionals use bikes because they are often quicker than transit services or other kinds of private vehicles. For example in the city of Tangshan Hebei province), the average percentage of workers and professionals cycling to work is 70 percent; this figure represents about 80 to 95 percent of those working in state-operated offices and businesses. (3)
Streets are generally congested in the large cities not only because they are narrow but also because of the large number of vehicles operating on them. Consequently transit vehicle speeds are very low, making it difficult for them to keep to schedules, often causing excessive waiting passenger time. As a result of perceived time savings, bicycles are being used increasingly for work trips. In one city, for example, over a million work-trip commuters ride bicycles to work while only 600,000 commute by bus. (4) The number of bicycle trips in Chinese cities generally accounts for 30 to 60 percent of the total number of trips. (5)
In addition to transporting the cyclist, bicycles are used for a number of special purposes. For example, children are frequently carried in bicycle "side cars". In rural areas container attachments on bicycles are used to carry agricultural products to market. These are usually heavy bikes especially designated for this purpose. In some parts of China such as Guangdong province, cyclists sometimes use their bikes as a taxi to carry a paying passenger.

Speed

A bicyclist's speed is dependent on a number of factors. These include geographical characteristics, the age and sex of the cyclist, traffic and roadway conditions, and the cyclist's physical ability among other factors. There are often diurnal variations in cyclists' riding speeds. A recent survey showed that bike travel speeds of about 13-18 km per hour (8-11 mph) are greater in the mornings for work trips than the average speed range of 9-13 km per hour (6-8 mph) in the afternoons for return trips home. After the afternoon commuting peak, average speeds once again return to 13-18 km per hour range(6). In moving traffic, effective bike speeds are about 10 percent lower than average motor vehicle speeds.
Design speeds for bicyles in China are different from those in the United States. In general, a minimum design speed of 20 mph (32 km/h) is used in the States 7). This difference may be due to the types of bicycles used and trip purposes. Americans ride primarily for recreation and sport on multi-geared bicycles as compared to commuter usage and heavier, single-geared bicyles of Chinese cyclists.

TABLE III - ROAD SPACE NEEDED PER BICYCLE

Road space needed per bicycle (m²) Relevant States of bicycle traffic
At Midblocks >10 Very comfortable, can overtake freely, no speed limit pedestrians can cross the road
8 Comfortable, no speed limit, not very hard for pedestrians TO cross the road
6 Cannot overtake, have to concentrate attention, very hard TO cross the road
4.5 Speed under about 10 km/h, more dense bicycle flow, cannot CRoss the road
Near Intersections 4 Speed under 8 km/h, one bicycle falling over may cause the NEarby bicycles to do so
2.5 Speed under 5 km/h, cyclists have to prepare to get off THe bicycles near the intersections
2.2 Speed of 3-4 km/h, most cyclists walk bicycles

Travel Time and Trip Length

When bicycle travel time is perceived to be about equal to that of a transit trip, most cyclists still prefer using a bicycle because it is cheaper and more convenient. The choice is also influenced by the waiting time for transit vehicle arrivals, the walking time to transit stops, and weather conditions.
For commuting, the average bicycle trip length is generally about 9 km (5.6 mi) for males and 5 km (3.1 mi) for females. (8) Of course, if there is no easily accessible transit route or the walking distance to transit stops is very long, the action radius of the bicycle will be larger. Very long bicycle trip lengths are mainly incurred during recreational rides or when attending cultural events. Long trip lengths are also incurred by farmers carrying agricultural products to markets in relatively flat farming areas where this is feasible.

Road Space Needs

The road space needed for bicycle traffic varies with road conditions and traffic volumes. Space needs for the relevant bicycle traffic conditions are summarized in Table III. When planning for bicycle traffic, road areas of 10-12 square meters (108-129 square meters) are usually allocated for each bicycle at a design speed of 10-20 km per hour (6-12 mph). More space is needed as vehicular volumes increase causing uneven traffic flows and more opportunity for cross traffic interference(9). (See Table III.)

Parking

Although there is a shortage of bicycle parking space in some areas of the larger cities, bicycle parking is not a serious problem in China. Free bicycle parking spaces are available at every office and factory. Inhabitants of residential areas keep their bicycles in their apartments or in adjacent public parking spaces. Many of the bicycle parking areas are roofed and some have walls. Such facilities are provided on the wider sidewalks or in lightly used small streets or lanes. Some parking services employ custodians to look after the parked bicycles. Bicycle parking fees are generally RMB 2 fen or about one U.S cent (RMB is the official term for Chinese currency whose basic unit is the yuan, which equals 100 fen). Traffic regulations mandate that bicycles be parked in designated parking areas. At recreational facilities like cinemas, theaters, gymnasiums, and stadiums, there frequently is a shortage of legal bicycle parking and some bicycles end up parked on sidewalks or in vehicle parking lanes.
Some parking areas are equipped with bike racks. However, most bicycles are parked on their own kickstands. Since most Chinese bicycles have 28" wheels, this is the slandard for designing bicycle parking spaces. Urban planners use a parking area of 1.4-1.8 square meters (15-19.4 square feet) per bicycle to estimate the amount of space needed for parking areas, including aisles and maneuvering space (10).

Registration

In China all bicycles must be registered with the authorities and must display license plates. However, cyclists are not required to have drivers licenses. When the ownership of a bicycle changes or the bicycle owner moves from one city to another, the bike must he reregistered. As a result it is very difficult to resell stolen bicycles. Bicycle theft is not a major problem in China.

Bikeways

Bikeways are generally arranged on both sides of the road between motor vehicle lanes and adjacent sidewalks. Bikeways are marked with painted lines or separated from motor vehicle lanes by barriers. In the absence of marked bikeways, bicycles must keep to the right side of the road.
The standard width for a bicycle lane is the total of the bicycle's handle bar width plus a deviation width of 0.4 meters (1.3 feet). The total value is generally 0.9-1.0 meters (3.0-3.3 feet). The width of two bicycle lanes is 2.5 (8.2 feet); for each additional lane 1.0 meter in width is added (11). The maximum bikeway width is limited to 2 or 3 lanes in each direction. Experience has shown that cyclists tend to divide into two bicycle flows (in the same direction) regardless of how many additional lanes are provided.
The minimum radius of curvature for a bikeway in China is 10 meters; in special cases, it may be as short as 3 meters but then the safe speed will decrease to under 10 km/h (6 mph).
According to observation, bicycle speed is not significantly influenced when the gradient is below 1 percent. The speed will begin to decrease as the gradient increases to 2 percent; it will be reduced further to 7-8 km/h (4-5 mph) by a 3 percent gradient (12). So it is preferable that the gradient be below 2 percent. On the other hand, the speed can become dangerously high when the downgrade is 3 percent. Of course, the resulting speeds also depend on the length of grade.

Use in Various Weather Conditions

Cyclists are sometimes faced with severe weather conditions. When it is raining they usually wear special raincoats, designed to cover the bicycles' handle bars. Since speeds are relatively slow, it is normally not a major problem if the streets are wet and the bicycle does not stop easily when the brakes are applied.
However, in the northern part of China during the wintertime when the streets are covered with ice, cycling is very dangerous. Thus, under icy conditions many bicyclists turn to transit vehicles instead for commuting, shopping, and other trip purposes.

Some Flow Characteristics

Bicycle traffic flows in China are quite large and rapidly increas ing. In 1965 the largest rate of flow for bicycles was measured at 8,600 bicycles/hr at Beijing's busiest intersection during morning peak hours. By 1977 28 intersections were experiencing bicycle flow rates of over 10,000 bicycles/hr, the largest of them being more than 20,000 bicycles/hr. An intersection in Tianjing was once measured at more than 50,000 bicycles/hr. In Tangshan after the great earthquake of 1976, 8 intersections had bicycle flow rates of about 10,000 bicycles/ hr(13).
The peak flows, of course, are much higher than the average flows. For example, 1977 traffic flow statistics on 10 arterial streets in Shanghai show that the average bicycle flow rate was 1.6 times as large as the motor vehicle flow rate and ranged up to 6.5 times as large during peak hours. (14)
The rates of flow for bicycles moving in opposite directions vary greatly during the day. Because most businesses are located in the suburbs, the flow of bicycles towards the suburbs is several times higher than towards the urban districts in the mornings and just the opposite in the afternoons.

Bicycle Servicing

There are numerous bicycle repair shops in China, scattered all throughout the cities, towns, and countrysides. It is very easy to replace parts, add air to tires, and perform other such repair/ maintenance services on a bike. There are rental shops that lease bikes to anyone producing appropriate identification. Rental fees are about RMB 0.1-0.15 yuan/hr (5-8 cents/hr); the daily rate is much cheaper.

Traffic Regulations

At the present time, China has no formal national traffic regulations. Although each province and city has its own traffic restrictions, they are quite similar except for slight local differences. Generally, the regulations stipulale:

  1. Every bicycle must have a license issued by the proper authorities and display a number plate.
  2. Safety equipment must be in good working order (bell, brake, etc.).
  3. Every moving bicycle must keep to the right side of the road.
  4. Cyclists may not ride two or more abreast.
  5. Cyclists may not participate in any race or endurance contest with any other vehicle on public roads.
  6. Riders must not hold an umbrella up while cycling.
  7. While moving, the cyclist must not remove both hands from the handle bars, cling or attach himself or his bicycle to any other moving vehicle, nor ride on sidewalks.
  8. Operators must not turn suddenly, and they must use a hand signal to indicate the direction of the turn.
  9. Cyclists must not carry passengers when riding bicycles in urban areas.
  10. Public streets or highways are off limits to learners.

Financing

The price of a standard bicycle is about RMB 155 yuan ($83.78). Commuter bicyclists are subsidized RMB 3 yuan ($l.62) per month by the state, or RMB 36 yuan ($19.46) annually. Therefore, a little over four years worth of subsidy is often nearly equal to the price of a bicycle. Because the life expectancy of a new bicycle is at least 10 to 15 years (more than twice the four plus years needed to amorlize the cost), a commuter cyclist will realize a good part of the total subsidy as an actual addition to personal net income. In Beijing there are about 3 million bicycles. About 50 percent of them are state subsidized in the amount of RMB 4.5 million yuan per month, for a total of RMB 55 million yuan per year. (15)
Skeptics argue that the annual 55 million yuan subsidy would be enough to improve the urban transit system and the overall urban traffic conditions. Some major cities outside of China like Pyongyang, the capital of North Korea, have forbidden bicycles to run on the streets. Commuter traffic in those cities is handled mainly by public transit.

Problems and concerns

Although bicycles are an important means of urban passenger transportation, too many can cause problems. Despite the separate lanes for motor vehicles and bicycles along all major arterial streets in China, large bicycle flows often spill over into motor vehicle lanes. This disturbs motor vehicle flows, causing average motor vehicle speeds to decrease. Because the number of bicycles has increased greatly in recent years, motor vehicle speeds have correspondingly decreased year by year. For example, on East and West Changan Streets (the widest streets in Beijing) average motor vehicle speeds in 1959 were 35 km/hr (22 mph). They were further reduced to 27-30 km/hr (17-19 mph) in 1979 and to 25 km/hr (15 mph) in 1980. Heavy bicycle traffic has forced motor vehicle speeds to decrease almost to those of bicycles. In Shanghai, average bicycle speeds are 13.32 km/hr (8.27 mph); average trolley-bus speeds are 14.76 kmihr (9.17 mph); and average bus speeds are 16.56 km/hr (10.29 mph). In Tianjin, average transit vehicle speeds are as low as 11 km/hr (7 mph) during peak hours, and at intersections stopped bicycles often form a "bicycle wall" in front of motor vehicles, obstructing almost all motor vehicle traffic, especially turning movements (16).
Mixed traffic flows cannot be regulated easily or efficiently by traffic signal timing systems. It is very difficult for the green "go" wave of vehicles to move forward because of the great difference between the acceleralion and speed of motor vehicles as opposed to bicycles. Also, the transverse flows of bicycles dramatically interfere with motor vehicle flows and with the effectiveness of automated signal systems.
In addition, transit vehicle speeds are lowered and schedules are thrown off in urban areas by heavy bicycle traffic. Where vehicle numbers are large, a vicious circle of lowered traffic speeds results.
Traffic accidents involving bicycles have risen in proportion to their total traffic volume. Bicycle accidents constitute about 50 percent of the total traffic accidents in the larger cities of China. For example, in Beijing, traffic accidents involving bicycles make up 49 percent of the total number of accidents: collisions between bicycles and motor vehicles account for 25 percent of the total; bicycles alone, 23.26 percent; and mishaps between bicycles and pedestrians, 1.02 percent (17). In Hangzhou, crashes between bicycles and motor vehicles account for 40 percent of the total traffic accidents. In Tangshan, collisions involving bicycles contribute to 75 percent of total traffic accidents, of which 60 percent are between bicycles and motor vehicles (18). Bicycle accidents are evenly divided between the urban areas and the suburbs.
In 1976, the total direct eronomic loss from traffic conditions was several hundred million yuan. If indirect losses are included, the total mounts to several thousand million yuan (19).

Recommendations

Though bicycles have certainly caused many urban truffic problems in China, they are and will continue to be an important means of private transportation. Their impact cannot be ignored or neglected. The principal reasons for their cominued use are:

  1. Bicycle traffic can adapt well to road condilions in older cities because bicycle traffic is flexible and can better serve the needs of door-to-door passenger and small goods transportation than larger vehicles.
  2. Initial costs and operational expenses for bicycles are very low, making them the most economically feasible private means of transportation now and in the foreseeahle future.
  3. Cycling does not require any passenger waiting time.
  4. Road conditions in the older cities are not amenable to the efficient use of rapid public transit system networks.
  5. In mixed vehicle traffic flows, average bicycle speeds are barely below the speeds of buses and trolleys for medium to long distance trips.
  6. A bike can make full use of the space on busy streets and still maintain speeds of 12-13 km/hr (7-8 mph) without causing traffic congestion. A bikeway lane width of one meter is sufficient.
Chinese bicycle transportation is currently an important supplement to urban mass transit systems. The control and management of bicycle traffic, however, needs much improvement. The principal measures recommended for improving and administering bicycle traiffic are listed below.

Active Development and Improvement of Urban Transit Systems

In China both the population and land area are very large but, because of the topography, the amount of usable land is small, causing urban population densities to be high in order to reserve enough land for agriculture. The road area occupied by each bicycle passenger is much larger than that for a transit vehicle passenger (see Table IV). Consequently, it is urgent that mass transit systems be more extensively developed and used in order to relieve urban traffic congestion. If those who cycle are to be encouraged to change to transit, then the qualify of service delivered by urban transit systems must be improved. Therefore, the effective speed of transit vehicles must increase, passenger waiting times must decrease, passenger walking distances need to be shortened, and vehicles must be kept on schedule. Rapid transit systems should be established in all large cities so bicycle trip lengths and travel times can be decreased along with bicycle traffic flows.
Much more attention should be given to the planning of circulation patterns in residential areas. At present, China's city residential blocks tend to be too large for setting up convenient transit routes. Some blocks are as long as 1-1.5 km (0.62-0.93 mi), requiring local residents to ride bicycles in order to avoid long walks to transit stops.

TABLE IV - COMPARISON OF CHARACTERISTICS OF SOME PASSENGER TRANSPORT MODES IN CHINA

Characteristics Bus Passenger Car Bicycle
Operating speed (km/h) 16-1830-4010-15
Capacity of vehicle (person/vehicle) 90-1603-51
Road area per person (m²/person) 1-210-206-10
Parking area per person(m²/person) 1.5-24-61.5
Relative fuel consumption 16-
Relative transportation costs 110-12-

Spreading Out Bicycle Traffic Flows Over Time

Peak bicycle traffic flows could be decreased if trips were spread over time. In Beijing, passenger flows were 9 percent greater during the peak hours in winter 1979 than in 1978. When about 700 of the larger enterprises staggered their working hours, the flow of passengers decreased by 4 percent-13 percent less then peak flows estimated for 1979 (19). As expected, peak bicycle flows fell off greatly, too.

Spatial Segregation of Bicycle Traffic Flows

Spatial segregation of bicycles would reduce the marginal friction between bicycles, motor vehicles, and pedestrians.

  1. Where the number of pedestrians is large, physical barriers could be arranged between the bicycle lanes and sidewalks to prevent disturbances from pedestrians crossing suddenly.
  2. Where the volume of traffic flow is not large and the marginal friction between motor vehicle flows and bicycle flows is not really serious, road markings could be used to separate them. In such situations motor vehicles and bicycles would normally run within their own lanes but they still might share when necessary and possible.
  3. Where the volume of bicycle flow is rather large and the roads are wide enough, physical barriers could be used to separate bicycle flows from motor vehicle flows. This strategy would be better than the use of road markings because it completely separates the traffic flows. Under these conditions it would not be possible for bikes and motor vehicles to share with each other, so the roads would have to be wide enough to handle both flows.
  4. Where the flow of bicycles is very large and it is impossible to avoid serious marginal friction by means of road markings alone and where there is not enough room for physical barriers, exclusive bikeways should be established. They separate bicycle flows from motor vehicle flows satisfactorily and increase the capacity of roads for other vehicles and thus greatly reduce traffic accidents. In new cities or new urban quarters, separate bicycle road networks can be built more easily than in existing developed areas, and if very carefully planned and engineered, can be made to work well. However, such systems are almost prohibitively expensive and difficult to introduce into already buil-up areas
  5. In older cities, especially where there are very long blocks, sometimes narrower streets and alleys paralleling main street can be used for arranging separate bicycle rout systems within the appropriate areas. Where the distance between arterial streets is large, there are likely to be many alleys in between and the areas furthest from the arterials may be impossible to serve well with street transit vehicles. With careful planning exclusive bicycle route networks based on such narrower streets and alleys could be set up. Usually pavment improvements and the installation of traffic sighns and signals would be necessary. This kind of bicycle route network would attract much of the overall bicycle traffic, thus lighten the load on principle arterials and improve traffic flows. Urban noise volumes would decrease (in mixed traffic drivers often have to sound their horns to warm cyclists and pedestrians) and traffic accidents would undoubtedly decrease. For example, when the bicycles were forbidden to use Huaihai Road in Shanghai in 1979, motor vehicle flow volumes inreased by 25 percent and their average speed increased by 7.7 percent.

Managing Bicycle Flows Through Intersections

For safety, bicycles must be made to observe the traffic signals just as motor vehicles do. Where intersections are at grade, the stopping areas for both major vehicles and bicycles need to be efficiently arranged. There are two main types of intersection arrangements. The first one has motor vehicles and bikes stopping sepparately, side by side, for left turn and through travel. Right-turning motor vehicels and bikes jointly use the rightmost lane, the advantage being that there is no disturbance between vehicles going straight ahead and those waiting to turn right. However, under this arrangement, the travel delay for lefl-turning bicycles is long. The second arrangement has the bicycle stopping area as close to the intersection as possible and ahead of the motor vehicle stopping area. Motor vehicles will generally have to wait for the bicycles to disperse before they can enter the intersectlion. The advantage here is that the conflict between bicycles and motor vehicles is minimized, but the disadvantage is a relatively longer delay for motor vehicles. Both arrangements involve some weaving section conflicts in the traffic stream before an intersection is reached. Selection of the best arrangement depends on local conditions.
Where traffic flows are extremely high, grade separations for bicycle traffic flows through intersections should be built. Underpasses are better than overpasses for bikes because of the vehicle's smaller vertical clearance and the shorter approach grades required. The latter make for easy grade-climbing given high initial downhill speeds; consequently, cyclists like underpasses better than overpasses.

Road Shoulders

Shoulders are often unpaved or very rough. Thus, pedestrians, bicycles, and other nonmotorized vehicles may be forced to use the motor vehicle lanes. Because the cost of providing motor vehicle lanes is usually much more than for nonmotorized vehicle lanes or paved shoulders, it is only logical that the more expensive pavement should be reserved for motor vehicles as much as possible.

Research Concerning Mixed Traffic Flows and Capacities

Mixed traffic flows contain vehicles having disparate characteristics of size and movement. As a result, mixed flows are uneven and are seriously disturbed by random lateral factors. This makes the development of mixed traffic flow theories very difficult. Although it would be desirable to separate the various classes of traffic flow completely, the high contruction costs discourage this approach. It is likely that mixed traffic flows will continue to exist in China and many other countries for a long time. More research into the characteristics of mixed flows and into cost-effective solutions should be undertaken.

Conclusions

Bicycles play a very important and continuing role as a private means of passenger transportation in China. Along with their distinct benefits have come some serious traffic problems. Today, bicycles are the most important component of nonmotorized vehicles in mixed traffic flows. In order to improve traffic conditions in China's urban areas, the problems of mixed traffic must be studied and soved. The object of such studies should be to make the use of bicycles safe while at the same time improving the quality of all traffic flows both in China and elsewhere.

Acknowledgements

The author gratefully acknowledges the guidance of Prof. K. C. Sinha of Purdue University in preparing this article. The author would also like to express his thanks to Prof. W. William Patterson for his reviewing and editing. The assistance of James Poturalski in reviewing an early version of the manuscript is also acknowledged.

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