party_pants said:
OK – here’s a little mathematical problem.
Let’s say I have laid out a city light rail system in the shape of an equilateral triangle with sides 10 km each. Let’s call the points Commercial District, Harbour and Airport.
The heaviest residential districts are between Commercial and Harbour. Therefore most of the demand will be between Harbour and Commercial District, with less traffic out to the Airport. I want to run trains every 5 minutes between Harbour and Commercial District, but only every 10 minutes to the Airport – in each direction.
I’m looking for the most effective/efficient layout. My idea is to run a triangle loop serving all three with trains running every 10 minutes, in both directions. Then to have a loop at both of Harbour and Commercial and run additional trains just between those two which slot in between the airport services.
Assume that there are other stations in between and the average speed taking into account all the stops is 30 km/h between Harbour and Commercial, and 40 km/h (fewer stops) out to the Airport.
How many trains would I need?
Is this the most efficient layout? Can you think of a better layout.
is there any free software I can model this and play around?
> My idea is to run a triangle loop serving all three with trains running every 10 minutes, in both directions. Then to have a loop at both of Harbour and Commercial and run additional trains just between those two which slot in between the airport services.
That’s definitely the best layout for that timing. I can’t prove it, but it requires fewest reversals of direction and at every reversal of direction you lose all passengers at the reversal point.
By the way, I’ve noted that melbourne-sydney and new york have completely different operating strategies. Melbourne-Sydney minimises the number of reversals of direction. New York maximises the number of reversals of direction, there are no loop trains.
The one big advantage of the new york system is that minimum effort on the part of passengers to plan their route, and it means that a new subway has zero effect on the pre-existing train times. I suppose that the the other big advantage is that during track work there’s a minimum amount of disruption. Suppose for instance that between Harbour and Commercial there’s track work. Then in the maximum passenger system all train times are disrupted, even out to Airport, but in the New York system there can still be trains every 10 minutes between Harbour and Commercial.
> average speed taking into account all the stops is 30 km/h between Harbour and Commercial, and 40 km/h (fewer stops) out to the Airport. How many trains would I need?
10 km at 30 km/hr = 20 mins. 10 km at 40 km/hr = 15 mins. Time to complete loop = 50 mins. At every 10 minutes both ways around the loop is 5 trains each way. At 10 minutes apart on the Harbour-Commercial shuttle that’s 2 trains each way. 2 * (5 + 2) = 14 trains.
Plus an extra train to take the place of any train that fails or for some other reason is undergoing maintenance. 15 in all.
> is there any free software I can model this and play around?
Have a look at “traffic simulation software” on Google.
For road traffic, mr Google recommends PTV VISSIM and TRANSYT 7F and TransModeler. But those are nor really suitable here.
For trains, I don’t know if this is any good. https://www.anylogic.com/rail-logistics/ . It advertises “Rail route optimization system. Rail yards can be better utilized by integrating their services and balancing their loads. Optimal train scheduling can be determined in relation to station throughput, which itself can be optimized with informed track and platform placement. Through understanding a system from the basic components up to the network scale, demands can be met, and opportunities realized.”
Wikipedia suggests: Strategy simulation
Railroad-themed strategy simulation video games are focused mostly on the economic part of the railroad industry rather than on technical detail. The A-Train series (1985 to present) is an early example. Chris Sawyer’s Transport Tycoon (1994) was an influential game in this genre, spawning remakes such as Simutrans (1999 to present), OpenTTD (2004 to present) and Sawyer’s own Locomotion (2004). Sid Meier designed two railroad simulations: Railroad Tycoon (1990) and Railroads! (2006). The Railroad Tycoon series itself inspired other rail games such as Rails Across America (2001).
There’s also https://en.wikipedia.org/wiki/Train_simulator_(disambiguation)