April 06, 2014

Horse 1648 - All Stations To Everywhere Via Everywhere Else

I was wondering what to do on Easter Monday that might be different to simply going to the mountains or the beach or something and wandering around. Since doing this Ten Suburbs project, I've again thought of Sydney's Trains Network and how vast it is.

There are 176 stations in the Sydney Trains Network and what I was wondering is, is it possible to visit all 176 stations in a day and if so, how quickly could you do it? The criteria would be that the train would have to stop at the station; maybe get out and take a photo of the station sign to prove you'd been there.
After playing with physical timetables and the sydneytrains.info website, the answer is that it is possible to visit all 176 stations but not something that you'd want to attempt unless you were going for a record.

The problem is that Sydney has lots of spurs in the network. The whole of the Richmond line or the Cronulla spur off of the Illawarra line must be either traveled along up and back unless you'd chosen one of them as your starting point. Then there's the annoying split on the Bankstown line where there is a teardrop at one end but two loose ends at the other.
One thing I found much improved was the Carlingford line. It has been vastly improved now that it mainly operates as a shuttle service. There used to be only a few services during the morning and afternoon peak periods; which meant that if you wanted to travel at lunchtime or late, you were stuck.

Actually this whole thing is really a topological exercise which is in the realm of combinatorial graph theory. The Sydney Trains Network is non-Euleran and so there will be double-backs and cross overs. This is sort of reminiscent of the Chinese Postman Problem or the Travelling Salesman Problem. It is overlaid with issues such as timetabling and connection problems and even then, I couldn't get around the real world problems of a replacement bus service and a short walk in one instance.
I tried to make the changes between trains tolerable; taking into account things like the time it would take to walk between them and to allow for late running. The longest wait anywhere is at Macarthur of 22 minutes.
Euler himself laid the foundations of this branch of mathematics with his Seven Bridges of K√∂nigsberg problem, which he eventually proved was impossible in 1735.

If anyone does really want to press me and do this hideous task (which I think is probably as arduous as cleaning the Augean stables), then I might consider it... might. If not, then have a glance at this map and have a go at solving this problem yourself:

Dep 06:17 - Richmond
Arr 07:22 - Lidcombe

Dep 07:32 - Lidcombe
Arr 08:26 - Town Hall

Dep 08:34 - Town Hall
Arr 09:20 - Sutherland

Replacement Bus - Route T41 Sutherland; All Stations to Waterfall, then return (allow 40 mins)
Dep UNK - Sutherland
Arr 10:00 - Sutherland

Dep 10:10 - Sutherland
Arr 10:26 - Cronulla

Dep 10:32 - Cronulla
Arr 11:36 - Bondi Junction

Dep 11:38 - Bondi Junction
Arr 11:49 - Town Hall

Dep 11:54 - Town Hall
Arr 12:40 - Riverwood

Dep 12:50 - Riverwood
Arr 13:28 - Macarthur

Dep 13:50 - Macarthur
Arr 14:09 - Glenfield

Dep 14:18 - Glenfield
Arr 15:04 - Strathfield

Dep 15:11 - Strathfield
Arr 15:13 - Homebush

Dep 15:21 - Homebush
Arr 15:48 - Central

Dep 15:58 - Central
Arr 17:07 - Berowra

Dep 17:16 - Berowra
Arr 17:30 - Hornsby

Dep 17:40 - Hornsby
Arr 18:11 - Chatswood

Dep 18:28 - Chatswood
Arr 19:28 - Epping

Dep 19:44 - Epping
Arr 19:57 - Strathfield

Dep 20:05 - Strathfield
Arr 20:11 - Lidcombe

Dep 20:20 - Lidcombe
Arr 20:25 - Olympic Park

Dep 20:28 - Olympic Park
Arr 20:34 - Lidcombe

Dep 20:41 - Lidcombe
Arr 20:47 - Clyde

Dep 20:52 - Clyde
Arr 21:06 - Carlingford

Dep 21:12 - Carlingford
Arr 21:26 - Clyde

Walk to Granville station < 15 Mins.

Dep 21:49 - Granville
Arr 21:55 - Lidcombe

Dep 22:02 - Lidcombe
Arr 22:12 - Birrong

Dep 22:20 - Birrong
Arr 22:41 - Liverpool

Dep 22:56 - Liverpool
Arr 23:19 - Granville

Dep 23:20 - Granville
Arr 00:01 - Penrith

Dep 00:13 - Penrith
Arr 00:16 - Emu Plains

Total Time: 18hrs 1min.

What I find disappointing about this is that the record for the Tube Challenge in London is 16 hours, 20 minutes and the Underground has 270 stations, or the New York City Subway Challenge which is 22 hours, 52 minutes and has 468 stations.

Now you can see why I don't really want to undertake such a project. As much as I like traveling on trains, 18hrs is roughly the same as travelling to Paris; riding the Metro just seems more appealing to me anyway.

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