# Transportation Deployment Casebook/2018/Chinese High-Speed Railway

## Introduction

### Maturity Phase (2018 - future)

China has never had a market economy. Public service facilities including high speed railways have always been monopolised by the government. Thus, there is no significant industry competition within the sector of HSR, and consequently, the market is stable. New types of trains are being inventing simultaneously so that the CRH group can keep pace with other countries.

In 2018, the CRH returned back to speeds of 350 km/hr. Although high-speed rail has only existed in China for 10 years, its expansion rate is faster than any other countries in the same time frame. In 2020, the CRH network will cover 80% of the cities in China, and the mileage will reach 30 thousand kilometres. By 2025, the CRH mileage will be 38 thousand kilometres and by 2030, 45 thousand kilometres. It already has the largest high-speed rail network in the world, but obviously China has greater ambitions.[20]

## Quantitative

The raw data and the predicted market size for each corresponding year is shown as follow. As the HSR in China has only been existed for just 10 years since 2008. So the time scope of the data is relatively short.

 Year Market size Mileage (kilometer) Predicted market size Mileage (kilometer) 2008 120 10188 2009 1189 10935 2010 7531 11703 2011 8849 12488 2012 9356 13286 2013 11028 14091 2014 16318 14899 2015 19000 15705 2016 22000 16504 2017 25000 17291 2018 28500 18062

Table 1: The collected raw data and the market size

### Define Equation:

The above data in table 1 is used to estimate a three-parameter logistic function, which is shown as follow. It is used to predict the tendency of the data.

${\displaystyle S(t)=\left({\frac {K}{1+exp(-b(t-t0))}}\right)}$  (1)

Where:

·     S(t) is the status measure (mileage for each year)

·     t is time in year

·     t0 is the inflection time (year in which ½ k is achieved)

·     K is the saturation status level

·     b is a coefficient

K and b are to be estimated through the regression analysis

In addition, the equation 1 is derived into a linear form to estimate the value K, b and t0. The equations are shown are follow.

y = bX + c (2)

${\displaystyle y=LN\left({\frac {Passenger}{K-Passengers}}\right)}$

### Finding the value of K and b

At the beginning, the values of K were randomly assigned. But K must be ensured to be bigger than the largest value in the raw data. In this case, 28500 kilometre is the largest data, hence the initial K was set to be 28600.  A total of 20 k values were listed in order to induce the k value with the biggest R square.

Figure 1:Calculation for regression - dependent variable

Through using the RSQ function , it was found k equalled 29200 would result in the largest R square. (figure 2) Furthermore, the value of b and t0 was found though the regression analysis, where t0 = intercept/(-b). A summary of the obtained value for each variable is shown in table 2.

Figure 2:Calculation for regression - dependent variable
 Variable Value K 29200 b 0.6925 R squared 0.8842 t0 2013.5

Table 2: The values of corresponding variables

### S - curve

Graph 1: Mileage Vs years

The R squared value of 0.88 suggests a mediocre fit to the curve. However, from the generated S curve, the predicted CHR mileage does not match with the actual mileage tendency in a very decent manner. There are many reasons that may cause this particular result:

1)   Lack of sufficient data. The CHR has only been operated for 10 years, so the time scope is too small to reflect a proper trend of the mileage.  In addition, the sample size is too small, any outliers will have a significant impact on the final result. For example, the 120km mileage in 2008. It is too small compares to data from other years, which imposed a large impact of the data tendency

2)   Inaccurate data. All the raw data are collected from authoritative media, but they are not official data. Especially in the case of a small sized group of data, the inaccuracy is magnified. As a result, it results mismatch between the actual mileage and the predated mileage.

3)   At the practical level, the CHS growth rate is very unusual. It increases in an exponential manner. For example, in 2009 and 2010, the mileage increased 890% and 533% respectively, compared to the previous year. Until 2011, the mileage growth rate became relatively stable. This unusual pattern differs the predicted trend from the actual trend.

In addition, a regression analysis was performed when the mileage data from 2008 and 2009 are excluded (Graph 2). The value of R was found to be 0.933 and the predict-mileage graph matched with the actual-mileage graph at a nice manner.

Graph 2: Mileage Vs years(2010-2018)

The birth region is defined as the first 15% percentile of the graph and the mature region is the 85% percentile. Therefore, the birth state is defined from 2008 to 2010 and the mature state is after 2017.

 Phase Year Birth 2010 mature 2017

Table 3: Birth and Mature year

## Reference

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