# Transportation Deployment Casebook/2019/Sydney Trains
## Overview

This Wikibook page provides a Qualitative and Quantitative assessment of Sydney Trains. It also incorporates the life-cycle analysis of Sydney Trains during its birthing, growth and development, maturity and the regeneration of growth phases. Eventually, a three-parameter logistic function and the S-Curve model provides a prediction based on the annual number of passenger journeys made on the Sydney Trains network.

## Qualitative
### Characteristics

Sydney Trains is a suburban passenger rail network that covers over 815 km of rail track and 178 stations serving the city of Sydney, Australia since 1855. It operates over 22,200 services a week carrying approximately 1.3 million customers and has till date served more than 23 billion passengers over its lifetime. Currently, Sydney Trains is controlled and operated by Transport for NSW.

### Advantages

* Economic benefits - Currently, Sydney Trains provides a major economic contribution of about $26 billion per year which represents about 1.6% of the Australian economy. It is also one of the most energy efficient mode of transport given that a train line can move 50,000 people per hour in comparison to a freeway lane which can only move 2500 people per hour. In fact, greenhouse emissions per passenger kilometre are up to five times less than that of automobiles. There is also a direct correlation between refined access to Sydney Trains network and increase in property values. This in turn helps the government to collect more duties when properties are bought or sold in turn increasing their tax revenue.
* Social benefits - Sydney Trains plays a significant role in social inclusion. By improving the access to its network it enables individuals who are low-income earners, elderly and the unemployed who are at the risk of social isolation to interact socially. This in turn contributes to the overall fabric of the society. Another social benefit it provides is equality of access to employment and services.

### Main Markets

The main market of Sydney Trains consists of the people around the metropolitan Sydney area. Currently, Sydney has a population of about 5.5 million, but in the coming years it is projected to reach 6 million by 2027 and 7 million by 2037 which is the current population in London. Sydney Trains plans to accommodate for this population growth while at the same time providing reliable and efficient train services.

### Alternative Modes

* Water transport - Between 1788 and 1888, people covered more distance on sea than on land. This coupled with the growing demand of moving food and people towards Port Jackson lead to the creation of the local water transport industry. By late 1789, the first sailing vessel (Rose Hill Packet) was built to carry passengers and stores along the parramatta river between Sydney Cove and the Rose Hill (currently Parramatta). Almost immediately, this vessel was joined by new boats that provided regular row and sail ferry services on the Parramatta river between 1789 and 1833. In the early 1790s, the colonists envisioned the incentive to build larger vessels as they discovered the opportunity of capturing bay whales near the islands of Bass Strait for trading purposes. This whole new industry of bay whales attracted foreign fleets to Hobart Town which became a crucial port for the foreigners who captured the whales in the southern oceans. Consequently, the foreigners brought along an expertise in boat making which provided the local shipwrights with the skills to create larger vessels. It is reported that between 1812 and 1825 there were 445 vessels built near the Tasmanian yards that transported good to New South Wales. Gradually, the size of the vessel developed such that it was able to reach various islands as further as New Zealand. With the introduction of new technology between 1821 and 1837 - steamships including Sophia Jane, William the Fourth and James Watt were introduced in the Australian waters. By 1890s, steamships began venturing the international waters for goods trade. The limitations of the water transport was such that there was abundant number of small crafts and vessels in the waters which forced the colonists to think about diverting the traffic of goods transportation to other modes of transport.
* Land Transport - Unlike water transport, land transport was inferior and entirely new. However, the difficulties of terrain were mastered by colonists and development was rapid regarding the methods of road construction. The roads of the colonies were mostly used by convicts who were used as draught animals to carry goods and haul carts for their employers. It took a long time for colonists to import more resources from overseas as they were content with the convicts driven haul carts. However, the introduction of bullock wagons in 1800 and box wagons in 1860 provided an alternative to using convicts for goods transportation. This had its limitations though, such as the difficulty to manage these wagons on rough roads as they lacked brakes. Donkeys and camels were also extensively used in wagons in the 19th century. The introduction of rail in 1855 then began to become the main mode of transportation of goods and people.

### Regeneration of Growth Cycle
## Quantitative

The tabulated data below shows the annual patronage of passenger's travelling in the Sydney trains network over its 162-year lifespan (i.e.from 1855 to 2017). It is to be noted that until 1959-1960 the data is based on 5 yearly intervals with the intermediate years interpolated. All data from the year 1960 on wards is reported yearly and the data points are official figures.
RAW DATA :
| Year | Annual Passenger Journeys (Millions) | Predicted Annual Passenger Journeys (Millions) |
| 1855 | 0 | 4.2 |
| 1856 | 0 | 4.3 |
| 1857 | 0 | 4.5 |
| 1858 | 0 | 4.7 |
| 1859 | 0 | 4.9 |
| 1860 | 0 | 5.1 |
| 1861 | 0 | 5.3 |
| 1862 | 0 | 5.5 |
| 1863 | 0 | 5.7 |
| 1864 | 0 | 5.9 |
| 1865 | 0 | 6.1 |
| 1866 | 0 | 6.4 |
| 1867 | 0 | 6.6 |
| 1868 | 0 | 6.9 |
| 1869 | 0 | 7.2 |
| 1870 | 0 | 7.5 |
| 1871 | 1 | 7.8 |
| 1872 | 1 | 8.1 |
| 1873 | 2 | 8.4 |
| 1874 | 2 | 8.7 |
| 1875 | 3 | 9.1 |
| 1876 | 3.3 | 9.4 |
| 1877 | 3.7 | 9.8 |
| 1878 | 4.1 | 10.2 |
| 1879 | 4.5 | 10.6 |
| 1880 | 5 | 11.0 |
| 1881 | 5.3 | 11.5 |
| 1882 | 5.7 | 11.9 |
| 1883 | 6.1 | 12.4 |
| 1884 | 6.5 | 12.9 |
| 1885 | 7 | 13.4 |
| 1886 | 7.4 | 13.9 |
| 1887 | 7.7 | 14.4 |
| 1888 | 8.1 | 15.0 |
| 1889 | 8.6 | 15.6 |
| 1890 | 9 | 16.2 |
| 1891 | 9.5 | 16.8 |
| 1892 | 10.1 | 17.5 |
| 1893 | 10.7 | 18.2 |
| 1894 | 11.3 | 18.9 |
| 1895 | 12 | 19.6 |
| 1896 | 13 | 20.3 |
| 1897 | 14.1 | 21.1 |
| 1898 | 15.3 | 21.9 |
| 1899 | 16.6 | 22.8 |
| 1900 | 18 | 23.7 |
| 1901 | 19.9 | 24.6 |
| 1902 | 22.1 | 25.5 |
| 1903 | 24.5 | 26.5 |
| 1904 | 27.1 | 27.5 |
| 1905 | 30 | 28.5 |
| 1906 | 32.2 | 29.6 |
| 1907 | 34.6 | 30.7 |
| 1908 | 37.2 | 31.9 |
| 1909 | 40 | 33.1 |
| 1910 | 43 | 34.3 |
| 1911 | 48.3 | 35.6 |
| 1912 | 54.3 | 36.9 |
| 1913 | 61 | 38.3 |
| 1914 | 68.3 | 39.7 |
| 1915 | 77 | 41.1 |
| 1916 | 81.6 | 42.6 |
| 1917 | 86.5 | 44.2 |
| 1918 | 91.7 | 45.8 |
| 1919 | 97.2 | 47.5 |
| 1920 | 103 | 49.2 |
| 1921 | 105.8 | 50.9 |
| 1922 | 108.8 | 52.8 |
| 1923 | 111.8 | 54.6 |
| 1924 | 114.8 | 56.6 |
| 1925 | 118 | 58.6 |
| 1926 | 121.4 | 60.6 |
| 1927 | 124.9 | 62.7 |
| 1928 | 128.5 | 64.9 |
| 1929 | 132.2 | 67.1 |
| 1930 | 136 | 69.4 |
| 1931 | 138.7 | 71.8 |
| 1932 | 141.4 | 74.2 |
| 1933 | 144.2 | 76.7 |
| 1934 | 147.1 | 79.2 |
| 1935 | 150 | 81.9 |
| 1936 | 153.8 | 84.6 |
| 1937 | 157.7 | 87.3 |
| 1938 | 161.7 | 90.1 |
| 1939 | 165.8 | 93.0 |
| 1940 | 170 | 96.0 |
| 1941 | 180.4 | 99.0 |
| 1942 | 191.5 | 102.1 |
| 1943 | 203.3 | 105.3 |
| 1944 | 215.8 | 108.5 |
| 1945 | 229 | 111.8 |
| 1946 | 232.1 | 115.2 |
| 1947 | 235.3 | 118.6 |
| 1948 | 238.5 | 122.1 |
| 1949 | 241.7 | 125.7 |
| 1950 | 245 | 129.3 |
| 1951 | 249.1 | 133.0 |
| 1952 | 253.2 | 136.7 |
| 1953 | 257.4 | 140.5 |
| 1954 | 261.7 | 144.4 |
| 1955 | 266 | 148.3 |
| 1956 | 263.5 | 152.3 |
| 1957 | 260.9 | 156.3 |
| 1958 | 258.4 | 160.4 |
| 1959 | 256 | 164.5 |
| 1960 | 252.5 | 168.6 |
| 1961 | 252.7 | 172.8 |
| 1962 | 257.8 | 177.1 |
| 1963 | 263.8 | 181.4 |
| 1964 | 261.7 | 185.7 |
| 1965 | 257.6 | 190.0 |
| 1966 | 255.3 | 194.4 |
| 1967 | 253.3 | 198.8 |
| 1968 | 248.5 | 203.2 |
| 1969 | 252.6 | 207.6 |
| 1970 | 254.8 | 212.0 |
| 1971 | 230.7 | 216.5 |
| 1972 | 201.2 | 221.0 |
| 1973 | 198.5 | 225.4 |
| 1974 | 190.9 | 229.9 |
| 1975 | 179.5 | 234.3 |
| 1976 | 181.1 | 238.8 |
| 1977 | 180 | 243.2 |
| 1978 | 179 | 247.6 |
| 1979 | 204.9 | 252.1 |
| 1980 | 207.8 | 256.4 |
| 1981 | 216 | 260.8 |
| 1982 | 202.9 | 265.1 |
| 1983 | 198.9 | 269.4 |
| 1984 | 197 | 273.7 |
| 1985 | 214.9 | 277.9 |
| 1986 | 220.6 | 282.1 |
| 1987 | 242.6 | 286.3 |
| 1988 | 246.1 | 290.4 |
| 1989 | 248.4 | 294.5 |
| 1990 | 251.6 | 298.5 |
| 1991 | 243.8 | 302.4 |
| 1992 | 229.8 | 306.3 |
| 1993 | 234.8 | 310.2 |
| 1994 | 249.6 | 314.0 |
| 1995 | 256.4 | 317.7 |
| 1996 | 264.7 | 321.4 |
| 1997 | 266.5 | 325.0 |
| 1998 | 270.5 | 328.5 |
| 1999 | 278.7 | 332.0 |
| 2000 | 293.1 | 335.4 |
| 2001 | 267.1 | 338.8 |
| 2002 | 263.7 | 342.1 |
| 2003 | 263.6 | 345.3 |
| 2004 | 259.9 | 348.5 |
| 2005 | 261.9 | 351.5 |
| 2006 | 269 | 354.6 |
| 2007 | 283.3 | 357.5 |
| 2008 | 292.2 | 360.4 |
| 2009 | 289.1 | 363.2 |
| 2010 | 294.5 | 365.9 |
| 2011 | 303.5 | 368.6 |
| 2012 | 306.2 | 371.2 |
| 2013 | 315.1 | 373.8 |
| 2014 | 326.5 | 376.3 |
| 2015 | 361.1 | 378.7 |
| 2016 | 385.9 | 381.0 |
| 2017 | 405.9 | 383.3 |

### Methodology

The data shown in the table above is then used to estimate the three-parameter logistic function that is given as:
$S(t)={\operatorname {K} \! \over \operatorname {1+\exp[-b(t-t{0})]} \!}$
Where:
* S(t) = Predicted annual passenger journeys (millions)
* K = Saturation level (millions)
* b = coefficient
* t = time (year)
* t$_0$ = Inflection time (year)
To estimate parameters K, b and t$_0$, a linear regression model with the following equations are used as shown:
* $Y=bX+C$
* $Y=LN{Annualpassengerjourneys \over K-Annualpassengerjourneys}$
Using excel, the parameters were estimated and are summarized below:
Summary of parameter values :
| Variables | Values |
| K | 450 |
| b | 0.0397 |
| R$^2$ | 0.8273 |
| t$_0$ | 1972.91 |

### S Curve

The S curve predicts that the number of passenger journeys will reach 450 million by the year 2100. The S curve also helps affix the dates of the various phases encountered in the life span of Sydney trains. These are summarised in the table below. Sydney trains has the second most expensive ticketing system after London and this coupled with the introduction of future projects such as the Sydney Metro Northwest, Sydney Metro CBD & Southwest and the planning of Parramatta link suggests that these will ease the congestion of passenger journeys on Sydney trains and effectively reduce it. While the S curve provides a good fit of the current trend there is a possibility that the introduction of a new technology coupled with future changes in regulations (keeping in mind that elections are around the corner) would significantly impact the number of passenger journeys over the years. While the S curve provides a good prediction of the annual number of passenger journeys in the short term, it does not account for policy changes and technological innovations in its future prediction and hence it does not provide a good approximation for the future predictions.
Life-cycle of Sydney trains using S curve :
| Phase | Year |
| Birthing | 1855 |
| Growth | 1945 |
| Maturity | 1972 |
| Regeneration of growth | 1987+ |

## References

* 1 2 3 https://www.transport.nsw.gov.au/sites/default/files/media/documents/2017/Train%20Statistics%202014.pdf
* ↑ https://www.transport.nsw.gov.au/projects/environment-and-safety/sydney-trains-environment-and-sustainability/why-rail-travel-a
* 1 2 3 4 5 https://www.ttf.org.au/wp-content/uploads/2016/06/TTF-The-Benefits-Of-Public-Transport-2010.pdf
* ↑ https://www.abs.gov.au/AUSSTATS/abs@.nsf/mf/3222.0
* ↑ http://www.population.net.au/sydney-population/
* 1 2 3 4 5 6 7 http://www.austehc.unimelb.edu.au/tia/446.html
* ↑ https://www.transport.nsw.gov.au/data-and-research/passenger-travel/all-modes-patronage-historical/all-modes-historical-patronage