This is morally the last post in my series on improving the MBTA: see here, here, and here for the three previous posts. However, it’s a more general principle concerning interlined regional rail services.
Good practice for running transit service that isn’t at show-up-and-go frequency – say, anything that comes every 10 minutes or more, certainly anything that comes every 15 minutes or more – is to have regular clockface intervals. This is memorable for passengers, and works as a baseline with which to work on providing extra connections. In addition, if there is interlining, then it makes it easy to schedule trains to come at a uniform frequency on the share segment. If service is uniform throughout the day, then this is very easy. The problems start when it is not.
Normally, if extra peak service is required, then rigid clockface systems, such as those found in the German-speaking world, will usually interpolate in the middle of the period. In other words, if a station gets inbound trains at :00 and :30 every hour, then in the peak it will also get them at :15 and :45. This is what’s done in Stuttgart on two of the S-Bahn lines, interpreting peak very liberally, and less rigidly on the TER in Nice. Many systems instead use similar peak and midday service, dropping service only in the evening, such as the Berlin S-Bahn, and BART.
To see where problems could occur, let us look at Berlin again. There are three services on the Stadtbahn: the S5, the S7, and the S75. At the peak, all three run every ten minutes, with westbound trains departing Ostkreuz at :02, :00, and :05 respectively. Off-peak, the S75 drops to 20-minute frequencies, introducing 8-minute gaps into a schedule whose average headway is 4 minutes.
For a cleaner, contrived example, let’s say we interline two services, each with a 15/30 frequency; a factor-of-2 difference in frequency is more or less the norm on commuter lines in Tokyo and Paris, which do not have rigid clockface schedules – more local lines have a slightly smaller gradient than more long-distance lines. There is an inherent tradeoff between uniform frequency at the peak and uniform frequency off-peak. It’d be much easier to do if both services were bound to have the same frequency but the frequency varied continuously, as it does on most subways; however, what works on a dedicated line when passengers show up and go fails when passengers consult schedules and when timed connections or overtakes are involved.
More concretely, if Line 1 leaves a station at :00 and Line 2 leaves at :08, providing uniform peak frequency of 7-8 minutes, then off-peak we will have a 22-minute gap when we reduce to half-hourly frequency on each line; and if Line 2 instead leaves nearly at :15 to provide uniform off-peak frequency, then there will be a gap of nearly 15 minutes at the peak. The sum of the largest peak and off-peak gaps is necessarily 30 minutes, whereas the ideal would be for the sum to be 22.5 minutes.
Extra constraints can force one choice of gaps. For example, the Providence and Stoughton Lines are (or should be) constrained by the need to fit faster intercity trains on the line, at least in the future; for details of those constraints, see my posts on MBTA-HSR compatibility. In short, if we choose the symmetry axis to be :00, then Providence Line trains are compelled to leave South Station at :02 to meet up with trains to Woonsocket, and high-speed trains leave South Station at :10-11 and begin to overtake Providence trains at Readville at :15. Stoughton trains should then leave immediately after the high-speed trains so that they can leave the line toward Stoughton just before they’d get overtaken (at Sharon, if they continued), which means at :12-13. Thus we obtain about a 10-minute gap at the peak and a 20-minute gap off-peak, which is an acceptable compromise.
In contrast, one thing that clockface scheduling does not limit is short-turns. Indeed the Berlin S-Bahn often short-turns every other train, without trouble. Moreover, it is not difficult to drop to half the peak frequency with short-turns. If a train that leaves at :00 runs all the way to the end and a train that leaves at :08 short-turns (both repeating every 15 minutes), then it is not difficult to change things so that in the off-peak, a train that leaves at :00 or :30 runs to the end and a train that leaves at :15 and :45 short-turns. People beyond the short-turn point would still only need to memorize at what minute between :00 and :29 the trains serve their stations, and it would be regular all day; people before the short-turn point would again only need to memorize one number, from :00 to :14. In the case of the MBTA, this means that the Fairmount Line (which should get a train that turns at Readville for every train that continues toward the Franklin Line) can get a perfectly regular timetable.