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Trains Directions

Trains Directions
QUESTION: Dear Prof Randy

We always see Trains - Up and Down moving either in North - South
OR East - West Direction.

Example : Four Tracks

1. Train 1 moving Towards North On Track 1
2. Train 2 moving Towards South On Track 2
3. Train 3 moving Towards North On Track 3
4. Train 4 moving Towards South on Track 4

Will this type of Trains Direction Movements also applicable i.e. Railways running in real scenarios in specific countries?

i.e. Some Trains Moving in North-South, South-North Direction but at the Same time, Some Trains are also moving in East - West, West-East Direction.

Cases
------

1. Train 1 Moving from North to South , Train 2 Moving from East to West.

2. Train 1 Moving from South to North , Train 2 Moving from East to West.

3. Train 1 Moving from North to South, Train 2 Moving from West to East.

4. Train 1 Moving from South to North, Train 2 Moving from West to East.

5. Train 1 Moving from East to West, Train 2 Moving from North to South.

6. Train 1 Moving from East to West, Train 2 Moving from South to North.

7. Train 1 Moving from West to East, Train 2 moving from North to South.

8. Train 1 Moving from West to East, Train 2 moving from South to North.

Either Train 1 or Train 2 has to halt in all cases so that the other Train moves in the specific direction to avoid collision.

Can complexity arise in building this rail model ?

As a Example :

Four Tracks - Four Trains running towards North-South Direction.
Train 1, Train 3 Running towards North
Train 2, Train 4 Running towards South
Four Tracks - Four Trains running in East-West Direction.
Train 5, Train 7 Running towards East
Train 6, Train 8 Running towards West

Awaiting your reply,

Thanks & Regards,
Prashant S Akerkar

ANSWER: Is your example of the configuration of the trains and tracks feasible? I suspect that theory and algorithms exist that can address this, but it is not in my area of expertise. You should try one of the other experts.

At any rate, you might want to clarify your definition of feasible. It should take into account cost (building bridges, tunnels, etc.), efficiency (running trains in only one direction at a time) and generality (is the solution amenable to broader, established theory or would you settle for a one-off solution).

Goodluck,

Randy

---------- FOLLOW-UP ----------

QUESTION: Dear Prof Randy

Thank you.

I was exploring whether this type of railway networks are running in real scenarios in different countries.

To Summarize,

Trains running simultaneously in North-South,South-North Direction as well as Trains running in East-West, West-East Direction similar to Road Junction in attached image.

i.e. will there be also Rail Road Junctions in Rail Networks similar to Road Junctions ?

Awaiting your reply,

Thanks & Regards,
Prashant S Akerkar

Answer
Rail networks like you describe do exist, of course. The subway systems of Boston and Washington DC are shown in the links below. I've been on both. The junctions for these types of networks are invariably multi-level. I'm not sure if I've ever heard of train tracks crossing at the same level, as in a roadway junction. The closest I can think of where trains need to be regulated by signals is when 2 trains share the same track, usually going in opposite directions. One train has to wait for the other to cross past a segment of side track. Disasters have occurred recently here in LA when one train didn't heed the signal.

Though the railroad equivalent of automobile roadway junctions may not exist (to my knowledge), managing traffic in a network, including switching at crossings, has, as I have said, a full theory associated with it but with which I am not familiar.

Anecdote: In the town of Carlsbad here along the Southern California coast, they run a 5k foot race that crosses passenger train tracks twice. The trains go by at about 1/2 hour intervals and the organizers have to be very careful about when they start the race so that people don't get run over!

http://www.mbta.com/schedules_and_maps/subway/

http://www.wmata.com/rail/maps/map.cfm

Randy
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Dear Prof Randy Thank you. Thanks & Regards, Prashant S Akerkar

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randy patton

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college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

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26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

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J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

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