# Quantitative Analysis

The data of the annual ridership from 1971 to 2011 within the Beijing subway system was obtained from the official website of Beijing subway[1]and is shown in Table 1. The life cycle phases are shown in Figure 1, from which we can see, the fast growing ridership indicates that the Beijing subway system is still in its growth phase now. But the existing data is plotted along with first half of the S-curve very well. Even though, the future development may not exactly follow the S-curve’s second half, it can provide a reference for the government when planning for the future, such as designing the network, station capacity and related policies.

Figure 1 S-curve of the Beijing Subway Ridership.

### Equations:

The data was then used to estimate a three-parameter logistic function of the form:

S(t) = K/[1+exp(-b(t-to)] (1)

Where:

S(t) is the predicted annual ridership; to is the inflection point at which ½ K is achieved.

The S(t) formula can be transformed to get a the following linear relationship:

Y = LN(Ridership/(K - Ridership))=c+b×t (2)

Where:

b from the S-curve

c = -b * to (3)

### Determine the Value of K:

Here, K, is the saturation level of ridership, which has not been achieved for Beijing subway, so different K values were tested.

The “Golden Section Search” is used to coordinate with the “Least Squares method” to find the best K in the fastest way.

Before using the “Golden Section Search”, four initial K values of 2,200, 2,500, 2,700 and 2,900 are tested. The results show that values of 2,500 and 2,700 are better than of 2,200 and 2,900, based on the strength of the R-square and t-stat numbers. So, the best value of K must lie in the interval [2,500, 2,700].

Then we use the “Golden Section Search”, and the R(x) is used to represent the R-square number when the value of K is x.

• Set xl=2,500 and xr=2,700;
• Set xl’= xl+ (xr-xl)×0.382 and xr’= xl+ (xr-xl)×0.618;
• If R(xl)＞R(xl’) or both R(xl)＜R(xl’) and R(xr’)＜R(xl), then the best K must lie in the interval [xl, xl’], so set xr= xl’;
• If R(xr)＞R(xr’) or both R(xr)＜R(xr’) and R(xl’)＜R(xr), then the best K must lie in the interval [xr’, xr], so set xl= xr’;
• Otherwise, the best K must lie in the interval [xl’, xr’], so set xr= xl’, so set xl= xl’ and xr= xr’;
• If xr- xl＜5, we are done; otherwise, go to step 1.

The result of the test of different K values are shown in Table2. After the test of K, a value of 2558.367 was used for it has the biggest R-square and t-stat numbers. The results of its analysis is shown in Tables 3.

Table 2 Determine the value of K

### Summary output:

Table 3 Regression results when K=2558.367

It can be seen that the R square is 0.925593 which is close to 1 and t-statistics is higher than 2, which means the results were statistically significant at the 95% confidence interval. Overall, this model seems to reflect the actual data.

This analysis gives the intercept of the predicted model.

In this case, the intercept was -275.882.

b, was estimated to be 0.137371.

to = Intercept / -b=2008.299881.

With all the variables were found to solve for S (t), predicted ridership could be determined for each year. The resulting data is plotted in red in Figure 1. It forms an S-curve that fits the actual data as accurately as possible.

In this case, there are some outliers in the data that affect the R-square value. It can be seen that the actual data itself does not perfectly follow an S-curve shape.

### Some Factors Affect the Trend of the Ridership:

Some data did not follow the curve very well, but it does not mean the curve is incorrect. Some extension of the two existing lines were done in 1989 which attracted some ridership, and the ridership continued to grow rapidly to reach an all-time high level in 1995[1]. However, the ridership fell from 558 million in 1995 to 444 million in 1996, when fares rose from ¥0.50 to ¥2.00[1]. After fares rose again to ¥3.00 in 2000, annual ridership fell to 434 million from 481 million in 1999. In the summer of 2001, the city won the bid to host the 2008 Summer Olympics and accelerated plans to expand the subway. 7 new lines were opened from 2002 to 2008, including the Olympic Branch Line and the Airport Express. What is more, subway fares were reduced from between ¥3 and ¥7 per trip, depending on the line and number of transfers, to a single flat fare of ¥2 with unlimited transfers in 2007[1]. The annual ridership reached 1.2 billion in 2008. After the 2008 Olympic, rapid extensions to suburban districts which attracted large number of commuters who live in the suburban but work in the central city[1].

# Qualitative Analysis

## Birth of the Beijing Subway

Figure 2 Development of Beijing Subway.

The first line began to construct in July, 1965 and trial operated in October, 1969.The system was opened to the general public in 1977 and to foreign visitors in 1980. It ran 21 km from the army barracks at Fushouling to the Beijing Railway Station and had 16 stations. This line forms parts of present day Lines 1 and 2.

### Technological

• Learn technology from the Soviet and Moscow Metro : The Beijing Metro was the country’s first subway. For the lack of expertise in building subways, the Beijing subway was originally planned with the help of Soviet experts and the concept originally unveiled in 1953. Chinese planners took particular interest in the use of the Moscow Metro during the Battle of Moscow during World War II, and so the Beijing Metro was designed from the very beginning to serve both civilian and military ends. The deterioration of relations between China and Soviet Union disrupted subway planning. Soviet experts began to leave in 1960, and were completely withdrawn by 1963. The government of China decided to press ahead.
• Cut and Cover Tunneling : At that time, it was sure the subway would be built deep underground for its military use. There was a debate on the method of constructing tunnels. Considering the geographical factors, such as soft stratum, cut and cover tunneling was used. But this method result in pavement destruction and traffic interference on the road surface in Beijing. So higher risk shield-tunneling was used when the line was extended after several years[2].
• Rail and Rolling Stocks : The subway trains run on 1,435mm standard gauge rail and draw power from the 750V DC third rail. The original metro stock was built by Changchun Railway Vehicle Company. It was classified with the Latin-alphabet letters DK (Diandong keche ), which stand for Electric multiple-unit (EMU). In 1967, two DK1-class cars were built, but there was no record whether they did in fact operate in Beijing. From 1967 to 1970, 80 DK2-class metro cars were built by Changchun Railway Vehicle Company and 76 went to Beijing[3]. The Beijing Subway Rolling Stock Equipment Co. Ltd., a wholly owned subsidiary of the Beijing Mass Transit Railway Operation Corp. Ltd., provides local assemblage, maintenance and repair services[3].

### Early Market

• Limitation of Auto: In the 1970s, there are only 100,000 automobiles in Beijing, and nearly all of these cars are owned by the local administrative departments, enterprise and institution[4]. At that time, cars were too expensive for people to buy and it wasn’t until 1990s when the economic developed rapidly and the quality of people’s life improved in Beijing, cars were popular as private use than they had been previously. In the 1970s, the price of transit is reasonable and can be accepted. So, transit was the only traffic tool for people, especially when long distance tips were needed.
• Limitation of Bus: The bus network was rapid growth at that time. There were 96 routes in 1975 but the number of buses for long distance trips is not very big[5]. Long distance trips may require several transfers. The low frequency and poor reliability cost a lot of waiting time. Some other limits include the slow speed and small capacity of the bus.
• Market and Advantages of Subway: After the emphasis of subway changes from the military to civilian, the initial 21 km line from the army barracks at Fushouling to the Beijing Railway Station stimulate the development of the west part of the city. It became the most important traffic tool for the west residents to go to work at that time, for example there were nearly 80,000 commuters in the Shijingshan district rely on the subway for commute. It was seen as a bridge which is built between the west and the central city. Even in the rapid growth period, the subway is so attractive for many reasons. The designing speed of subway 60km/ hour was much faster than the highest speed of the bus 40 km/hour. The 21kilometers line satisfied many people who want to have long trip and do not want to transfer. It is more reliable, which was one of the most important factor commuter cared about.

### Policies in the Beginning

When the subway was started open in 1971, it was ruled that only members of the public with credential letters from their work units were permitted entry into the subway. In 1973, the policy changed that any passenger can take the subway buying a ¥0.10 ticket. The flat fare was not a burden in the early years for the Beijing people at that time. In 1978, joint commutation ticket for subway and electric car was launched to push the transit system in Beijing[1].

On November 11, 1969, an electrical fire which killed three people, injured over 100 reminded the government to attach more importance to the safety of the subway. Premier Zhou Enlai placed the subway under the control of the People’s Liberation Army in 1970. “Safe, accurate, efficient and service” was the operation tenet at that time[1].

## Growth of the Beijing Subway

### Technical Improvement

All but two of the subway's 15 lines were built in the past decade as the system has undergone rapid expansion. The Olympic is a catalyst to expand the subway. The subway set a daily ridership record of 4.92 million on August 22, 2008, the day of the Games' closing ceremony. In 2008, total ridership rose by 75% to 1.2 billion. However, the Olympic is not the only contributor to the rapid development; technical improvement and policy support which would be discussed in the following part are also important factors of the success of the Beijing subway.

• Rolling Stocks: Considering some earlier batches having been subject to severe reliability and build quality problems, different classes of rolling stocks are introduced, including DK (“diandongkeche”-electrically operated passenger car), BD (“beijing ditie”-Beijing subway), DKZ(“diandongkeche zu”-a group of electrically-operated passenger car), SFX (updated DKZ5, train sets with full articulation and a radically redesigned front bulkhead)[6]. At the same time, train capacities have increased to more than 1,400, up 340 over previous formations. To cope with the increased demands, Automatic Train Control (ATC) systems were introduced. With the Automatic Train Control (ATC), stopping is accurate and journey times, headways and energy consumption are optimized. A signaling headway of 100 seconds was achieved. This has reduced service headway from 3 to 2 minutes and increased capacity by almost 50% per hour per direction[7].
• Control System:In 2005, in order to better schedule trains and accurately calculate operating costs Beijing subway started to introduce Electro Industries GaugeTech (EIG). Its integrated power quality and energy management system allows the Beijing subway to monitor the operating conditions of all subway lines simultaneously, in the subway’s control center[8].
• Operation:In the early days, the subway has only one operator, the wholly state-owned Beijing Mass Transit Railway Operation Corp., but now the Beijing MTR Corp., a public-private joint-venture with the Hong Kong MTR, manages two lines. MTR owns a 49% stake in the project, was required to provide 30% of the capital, and will receive a concession to run the line for 30 years[9].
• Passenger Friendly: The subway became more passenger friendly with several infrastructure improvements. Early interchange stations in the Beijing subway are notorious for their long transfers. The average transfer distance in an early interchange station is 128 meters[10]. To solve this problem, some old stations were rebuilt to reduce the transfer time. The newer stations were built with more efficient transfers in mind. The stations capable of cross-platform interchanges are the first choice for the planners. Even if the alignment of the lines prevents cross-platform interchange, new interchanges will have a transfer distance no more than 100 meters[11]. The average transfer distance of new interchange stations is 63 meters, which compared with the older transfers is halved. By August 2008 it was claimed that all 123 stations had at least one access point available to wheelchair users. By the summer of 2008, the use of paper tickets, hand checked by clerks for 38 years, was discontinued and replaced by “Yikatong” (electronic tickets) that are scanned by automatic fare collection machines upon entry and exit of the subway. Stations are outfitted with touch screen vending machines that sell single-ride tickets and multiple-ride Yikatong fare cards. By 2011, Mobile phones can be used throughout the system, except for in the tunnels between stations on Lines 1 and 2.

### Policy Support

A policy not to the subway but helped it by attracting more passengers is the traffic restriction policy in Beijing in 2008. This traffic regulations designed to limit the number of cars in use on weekdays based on car number plates. The drivers may shift to use the subway when they are restricted to use their cars. After a period of time, they may used to taking the subway and keep taking it even when their car are not restricted.

Child with height under 120 cm doesn't need to pay to travel by Beijing subway.

## Future of the Beijing Subway

### Near Future (2012-2015)

Beijing subway is planning to have 19 lines totaling 660km of track in operation by 2015, with an expected nine million passenger journeys a day. A “3,4,5,7” network, which means 3 circle lines, 4 horizontal lines, 5 vertical lines and 7 radial lines are planned to be built before the end of 2015. It is estimated the average walk distance will be less than 1 km within the Third Ring Road in Beijing. With the significant construction of urban rail systems, the government hopes that the public transit can have a mode capture of 50% in the central city in 2015[12].

To help improve the system, some new technologies are planned to be introduced into the system: advanced SCADA software systems will be used in the second phase of the Beijing subway Line 8 extension which can interlink various automation subsystems at station level; Train guard MT automatic train control system will be used in the Olympic Line 8 and Ring Line 10 of the network; Operations control center which can interlock components will be installed for 82 trains；Communication based train control (CBTC) system will be built on the Yizhuang and Changping lines of the Beijing subway network[13].

### Far Future

According to the 2011-2020 plan, there will be 30 lines, totaling 450 stations and 1050km of track in operation by 2020. It will form a “Chessboard network” for the center region and “Radial network” for the suburban region. There is not a detail official plan for the subway after 2020[14], but some experts speculate that the construction of the whole subway system will be finished before 2040, and we find that this the trend seems meets our S curve very well. The curve indicates that the subway will be mature around 2040. However, it dose not mean the ridership will not increase after then. As we have seen, from the beginning of the life cycle till now, the technology continue to improve, which make the system more passenger friendly, more reliable and safer. A better service level will definitely attract large numbers of passengers from other modes. Policy is another tool to increase the mode capture. Flat price policy and Motor vehicle limit policy worked well and other policies should be taken adapt to and even orient the urban development. Population growth will also contribute to the increase of ridership, which requires the planners to take it into consideration and make sure the system can meet the demand.

# References

1. Beijing Subway official website: <http://www.bjsubway.com/node/2607>.
2. (Chinese) Shao genda "The newest technique in Beijing Subway system." China Academy of Railway Sciences.1992.
3. a b
4. (Chinese)"The history of the development of China's automobile". http://www.hudong.com/wiki/%E4%B8%AD%E5%9B%BD%E6%B1%BD%E8%BD%A6%E5%8F%91%E5%B1%95%E5%8F%B2
5. "The history of the Beijing bus". http://www.beijingimpression.cn/beijing-guide/beijing-bus.shtml
6. "Rolling stock of Beijing Subway". http://www.nycsubway.org/wiki/Beijing,_China