# Transportation Deployment Casebook/2024/Sydney's Bus Network

The lifecycle of the Sydney bus network is about analysing the birthing, the growth, the maturity and potential decline of its service through data analytics and computer modelling. A time based approach is used to plot scale of its yearly patronage or track length over the network's entire lifetime. An S-curve model using the Logistics equation with three parameters forms the theoretical basis for this approach.

## Background

The bus network in Sydney, Australia forms the second largest public mode of travel by patronage in the state of New South Wales, behind the train line service. According to Transport NSW, in 2023, 48.9% of single trips completed using the train/metro whereas 38.1% of trips were completed by the bus. As of 2015, it covers over 25,000 km of route length. It services the CBD and the suburban areas of the Greater Sydney region and operates under Opal Card scheme introduced in 2013 to 2014.
The lifecycle of the bus network in Sydney spans over a 100 years and has changed based on the technology, and policy needs of the city. This lineage includes the early adoptions of the horse carriage omni buses to the modern engine powered articulated and double decked buses. It is estimated that the city has grown from 8.4 million yearly passengers in 1900 to over 308.8 million in 2014 as of latest figures by Bureau of Infrastructure, Transportation and Research Economics (BITRE), before the introduction of Opal.
The bus network is considered quite a mature mode of transport as it has saturated the region for 30 years without increasing its ridership significantly. Due to recent events such as Covid-19, the ridership has still been in recovery as it has only surpassed 200 million yearly passengers again in 2023 still below its pre-Covid numbers of 308.5 million in 2019.

## History

The historical context of the bus network in Sydney puts the numbers into a more human perspective. The trends in the bus network tend to reflect saturation without much room for growth only maintenance.

### Birthing

In the early 20th century, the tram network dominated the city followed by the ferry and heavy rail network. Since the modern car had not been motorised to take over the market just yet, the bus network was simply made of horse carriage omnibuses, that could hold not hold more than around 10-15 people before it was put under severe stress. This is in contrast to the early trams that were, at the time, just recently electrified, and could serve well over twice the capacity of a regular bus while having more connections and integration for faster travel time.
Following the end of the Great War, the buses too became motorised and received traction for their versatility and low maintenance and running costs. This was happening at the same as the modern personal car became a staple as production costs decreased, paved roads became more common and the urban landscape increased. This sparked large amount of privately owned bus companies to run as the transport had not been formally systematised by the state government. In 1927, over 500 buses that ran on a motor engine served the city while being unregulated. In contrast, the trams were widely adopted by the city and plans to control major modes of public transport was an important opportunity to seize.
In 1930, the New South Wales government intervened the bus network operations by limiting its freedoms to open new routes and more services through taxation and legislation. The Transport Act of 1931 passed to stifle the competition as its private owners could pay the high costs that the government enforced. A condensed timeline from BITRE shows that the bus service was still in its infancy but it was gaining popularity as the technology continued to accelerate especially post Second World War.

### Growth

The comparison and competition with the tram system continued through the 40s and 50s as the popularity of one mode sacrificed the patronage of the other. The exception occurred in the middle of World War Two where integration of the two services was used to save running costs for buses and trams, which proved important as this became a bigger problem later on and was experienced across the globe. After the war, the buses were upgraded and received further funding as the idea of a wide spread bus urban public transport (UPT) mode became more popular. Similarly to the trends overseas, like in the U.S.A., car adoption with decrease in fuel price, stronger and lighter metals meant that the government could look into cheaper options that could gain capital. BITRE shows one perspective how attractive it would have been for petrol or diesel owned vehicles as their real price compared to 2011-12.
From the beginning of WW II until the end 1939 - 1945), it saw an increase in yearly ridership by nearly 100 million people from 65.8 to 159.8 million. This can be thought of as the inflexion point of highest rise in the mode's lifecycle. From 1946 all the way to end of the 70s, the bus saw a steadier rise in popularity as the tram network was virtually phased out in favour of the light capacity UPT that could now reach greater distances and was more versatile and flexible in times of need. In 1969, bus patronage reached a maximum yearly patronage of over 328.1 million, which is the first true peak of the mode and the sign of maturity and saturation over the upcoming decade.

### Maturity

Despite the evolution of the bus taking over the tram system and becoming dominant the dominant UPT in the 70s and 80s, the numbers show a stagnation in the service as it was saturated and had reached most of the regions in the Greater Sydney region. Again, it followed similar paths to Australian cities such as Melbourne as it stagnated its development due to filling most of its areas with bus links. However, Melbourne had a resurgence that is up to dispute based on boundary conditions of city limits as pointed by the BITRE analysis. As such, the data is not 100% conclusive as even the bureau agrees with through its inclusion of different accuracy classifications for its 'UPT Bus' figures in Sydney.

### Decline

Excluding Covid due to its external impacts on the wide transport network across the globe, Sydney bus system has stayed relatively consistent in terms of patronage numbers despite rising city population and possible demand for greater amount of bus services.
As of 2020, the network is 5 times the size that of 1925 and with more suburban and outer Sydney buses that travel longer distances. However, with rise of suburban sprawl, cars have become dominant mode of transport for most residents and trains have gained more patronage becoming leading mode transport in 2023.
Thus, bus network has reached an equilibrium in terms of its usage, or it is not utilised as has been argued in recent media and government pieces that debate efficacy of the system.

## S-Curve Projection
### Methodology

For the projection to occur, the logistic S-curve is a sensible approach to assess the state of the bus network or any mode of transport or moving of goods. The unique aspect of being able to project a peak instead of an infinite rise like in an exponential rise give it more realistic use scenarios. However, it has to be noted that this logistic curve does not account for lag as is more evident in this mode of transport as it has not significantly decreased in its use but has also not found a resurgence or a second rise. The following equation sets the foundation for the predicted projection of the network vs the actual figures.
$S(t)=S_{m}/\left(1+e^{-b(t-t_{i})}\right)$
* S(t) = given yearly passenger value at a given year
* Sm = maximum predicted level
* b = a coefficient representing the slope from predicted saturation and actual value at given time.
* t = time in years
* ti = inflection time
The b coefficient is represents a lot of challenge as the slope represents the natural log of the different cases where the actual value is compared against the difference between the actual and predicted saturation value.
$x(t)=\ln \left({\cfrac {S(t)}{(K-S(t))}}\right)$
* x(t) = a point in time
* K = chosen predicted saturation max passenger value.
For this data set, 114 years or points are chosen and the b is the slope in between them. The intercept is also calculated. This forms a straight line with an intercept which can be compared against real data. The R squared value (RSQ) is modelled in Excel to evaluate its effectiveness in realising the logistic S-curve. It is not only an approximation in terms of the method as it does not account for deviations or sudden falls or rises.

### Results

For this example, total 18 guesses were made for possible peak ranging from K = 330 - 500 million yearly patrons with a positive increment of 10 million.
The biggest RSQ was chosen out of the 18 calculations. The range between smallest and biggest number was 0.033967. This suggests that it is not conclusive what the maximum number could be and that it could range anywhere from 330 - 500 million without much difference. However, the maximum number was 360 million patrons.
| RSQ | 0.769418 |
| b | 0.060491 |
| Sm | 360,000,000 |
The graph visualises the logistic S-curve and how it generally follows the trend of the rise and peak of the Sydney buses. The extrapolation is not shown to reach 360 million passengers which is predicted to happen in 2027. It also shows the inability to account for the stagnation in the numbers its sharp climb happening during 40-70s not accounted. This might be because of the WW II dip that slowed down progress and the war efforts being the main capital investment for the government, with the addition of restrictions and rations.
The table of results is listed below:
| Year | Actual Passengers (millions) | Predicted Passengers (millions) |
| 1900 | 8.4 | 7 |
| 1901 | 8.0 | 8 |
| 1902 | 7.6 | 8 |
| 1903 | 7.2 | 9 |
| 1904 | 6.8 | 9 |
| 1905 | 6.5 | 10 |
| 1906 | 6.2 | 11 |
| 1907 | 6.0 | 11 |
| 1908 | 5.7 | 12 |
| 1909 | 5.4 | 13 |
| 1910 | 4.9 | 13 |
| 1911 | 4.5 | 14 |
| 1912 | 4.1 | 15 |
| 1913 | 3.7 | 16 |
| 1914 | 3.1 | 17 |
| 1915 | 2.5 | 18 |
| 1916 | 2.2 | 19 |
| 1917 | 2.3 | 20 |
| 1918 | 3.0 | 21 |
| 1919 | 4.4 | 23 |
| 1920 | 6.4 | 24 |
| 1921 | 9.2 | 25 |
| 1922 | 12.7 | 27 |
| 1923 | 16.4 | 28 |
| 1924 | 20.4 | 30 |
| 1925 | 24.5 | 32 |
| 1926 | 29.3 | 33 |
| 1927 | 34.6 | 35 |
| 1928 | 39.8 | 37 |
| 1929 | 45.9 | 39 |
| 1930 | 50.5 | 42 |
| 1931 | 51.0 | 44 |
| 1932 | 51.5 | 46 |
| 1933 | 52.0 | 49 |
| 1934 | 54.4 | 51 |
| 1935 | 56.9 | 54 |
| 1936 | 59.8 | 57 |
| 1937 | 60.4 | 60 |
| 1938 | 62.9 | 63 |
| 1939 | 65.8 | 66 |
| 1940 | 71.0 | 69 |
| 1941 | 92.6 | 73 |
| 1942 | 129.3 | 76 |
| 1943 | 143.1 | 80 |
| 1944 | 150.4 | 84 |
| 1945 | 159.8 | 88 |
| 1946 | 167.9 | 92 |
| 1947 | 179.0 | 96 |
| 1948 | 193.6 | 101 |
| 1949 | 231.1 | 105 |
| 1950 | 262.0 | 110 |
| 1951 | 268.0 | 114 |
| 1952 | 264.3 | 119 |
| 1953 | 257.3 | 124 |
| 1954 | 262.8 | 129 |
| 1955 | 269.2 | 134 |
| 1956 | 275.6 | 139 |
| 1957 | 235.9 | 144 |
| 1958 | 251.1 | 149 |
| 1959 | 275.9 | 155 |
| 1960 | 290.4 | 160 |
| 1961 | 311.6 | 166 |
| 1962 | 307.7 | 171 |
| 1963 | 295.4 | 176 |
| 1964 | 297.8 | 182 |
| 1965 | 301.8 | 187 |
| 1966 | 326.7 | 193 |
| 1967 | 323.3 | 198 |
| 1968 | 323.1 | 203 |
| 1969 | 328.1 | 209 |
| 1970 | 324.3 | 214 |
| 1971 | 319.8 | 219 |
| 1972 | 286.8 | 224 |
| 1973 | 300.5 | 230 |
| 1974 | 298.8 | 234 |
| 1975 | 289.5 | 239 |
| 1976 | 270.0 | 244 |
| 1977 | 266.6 | 249 |
| 1978 | 268.4 | 253 |
| 1979 | 260.9 | 258 |
| 1980 | 264.4 | 262 |
| 1981 | 269.6 | 267 |
| 1982 | 263.4 | 271 |
| 1983 | 265.3 | 275 |
| 1984 | 263.4 | 279 |
| 1985 | 268.5 | 282 |
| 1986 | 269.5 | 286 |
| 1987 | 275.5 | 289 |
| 1988 | 281.5 | 293 |
| 1989 | 280.7 | 296 |
| 1990 | 273.6 | 299 |
| 1991 | 282.7 | 302 |
| 1992 | 281.7 | 305 |
| 1993 | 270.1 | 308 |
| 1994 | 271.7 | 310 |
| 1995 | 274.7 | 313 |
| 1996 | 282.8 | 315 |
| 1997 | 288.9 | 318 |
| 1998 | 293.2 | 320 |
| 1999 | 295.8 | 322 |
| 2000 | 291.6 | 324 |
| 2001 | 286.6 | 326 |
| 2002 | 274.5 | 328 |
| 2003 | 275.1 | 329 |
| 2004 | 273.1 | 331 |
| 2005 | 278.6 | 333 |
| 2006 | 279.0 | 334 |
| 2007 | 283.7 | 336 |
| 2008 | 291.7 | 337 |
| 2009 | 297.8 | 338 |
| 2010 | 292.5 | 339 |
| 2011 | 299.0 | 341 |
| 2012 | 304.3 | 342 |
| 2013 | 306.7 | 343 |
| 2014 | 308.3 | 344 |

## References

* 1 2 3 NSW, Transport for (2023-06-22). "Public Transport Trips - All Modes". www.transport.nsw.gov.au. Retrieved 2024-03-03.
* 1 2 3 Rayaprolu, Hema (2021). "Evolution of Sydney's Bus Network: 1925 to 2020". ATRF. Retrieved 2024-03-03.
* ↑ "'The end of ticket queues': Minister announces Opal trial". The Sydney Morning Herald. 2013-06-02. Retrieved 2024-03-03.
* 1 2 3 4 5 "Long-term trends in urban public transport". BITRE. Retrieved 2024-03-03.
* 1 2 Solomons, Vic (1983). "50 Years of Government Bus Service" (PDF). Sydney Tramway Museum. Retrieved 2024-03-03.
* ↑ "ROUTE NUMBERING HISTORY – Sydney Bus Routes". Retrieved 2024-03-03.
* ↑ Munoz, Juan-Carlos (2016). Restructuring public transport through Bus Rapid Transit - An international and interdisciplinary perspective. Bristol: Policy Press. pp. 31–33. ISBN 9781447326168.
* ↑ "Petrol Prices and Diesel Prices in Australia" (PDF). BITRE. 2016. Retrieved 2024-03-03.
* ↑ "Privatisation of bus serivces" (PDF). Parliament NSW. 2022. Retrieved 2024-03-03.
* ↑ Smith, Alexandra (2023-04-30). "Bus privatisation under the spotlight as delays and driver shortages worsen". The Sydney Morning Herald. Retrieved 2024-03-03.