Both the LIRR and MNR number each and every one of their trains- from your regular morning commuter train to their work, equipment, and deadhead moves. Instead of just numbering each one down the line as the day goes through starting with one, they both follow a system segregating each trains number by what line/stops it's serves.
Almost all train numbers for both Long Island Railroad consist of 1, 2, 3, or even 4 digits. They all follow a naming system with the first digit or two serving as the "series" for the branch. Each branch is assigned a number "block" and every train on that branch must start with those numbers. Here's the table showing all the LIRR's train numbers:
To form weekend train numbers, you add 6000 to weekday train numbers (i.e train #5 would be #6005). To find non-revenue/deadhead moves, just add 3000. It's also very important to note that westbound trains are odd, meanwhile, eastbound trains are even. That rule is always followed, period.
At lunchtime (noon), train numbers generally skip-forward to the midpoint (i.e 350, 750, 850). This is mainly done on all branches except The Montauk Branch, where trains are numbered by terminal instead.
For the LIRR, train numbers are generally numbered sequentially, however, more then enough exceptions. As the LIRR has been tweaking train terminals for trains since East Side Access, gaps in the train numbers have formed. In addition, gaps were already present as they left gaps were they may add trains in the future (think the gap left between Montauk branch trains #17 and #21). If they can't add a train in the middle, then, they'll typically add the train in at the end of the series (#799, #6095, #2099), this is done to avoid changing already established train numbers. Numbers for special trains, extra trains, seasonal trains, etc are also added towards the end of the series.
Metro-North is a bit more complicated, however, as they do number their trains based on the branch, but, they do it in a way that is slightly less easy to understand.
As you can see, Metro-North does it in a more complicated way. You'll notice that like the LIRR, each terminal has it's own number, and diesel territory train numbers are separate from electric territory. The difference is, multiple of the terminals for MNR have a couple of different numbers. On The Harlem Line, for example, Metro-North has two train numbers for North White Plains, #300-399 and #500-599. For #300-399, all of the Crestwood trains are numbered through that, in addition to some of the locals, #500-599 is generally for the express trains from North White Plains, yet some of the locals are #500-599 too. There's no real consistency.
Metro-North's weekend train numbers are found by adding 9000. Unlike the LIRR, inbound trains to Grand Central are numbered even, meanwhile, outbound trains are numbered odd. Once Penn Station access is finished, the train numbers are expected to change for MNR once they roll out the brand new schedule. It'll be interesting to see how the schedule turns out.
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