1. North of 116th, as stops spread out, speeds can be quite high. Late in the evening, when the speed is the highest, it can go up to almost 7 blocks per minute. During the day in the off-peak, 6-6.5 is more common. I’m not sure about peak.

2. South of 116th, 5 blocks per minute is rare. At rush hour, speeds go down to about 4 blocks per minute. Off-peak, 4.5-5 is more common. The 1 is crowded and has high dwells well into the night – it’s often full at 11. Later, speeds go up to about 5.5 blocks per minute.

(If you want another example: Toronto more or less gets signal priority right on its streetcars, even at Manhattan block density. The problem with Toronto’s signal priority is that if there’s a station right before an intersection, the light will turn green as the train pulls into the station, which may make it red as the train pulls out.)

Signal priority is not absolute. The bus will still be stopping for red lights. I doubt it will average 15 mph.

And not many people ride a local like the 1 for long distances when an express is available. The 1 has easy transfers to the express and to plenty of intersecting lines. The M15, unfortunately, is too far east to intersect with any subway stations north of 14th Street – while I could see it included in the subway map, it’s really far better integrated with the bus system.

Also, bear in mind that scheduled running times on lots of subway lines (I don’t know about the 1 specifically) have been increased in the past few years. (Howard Roberts placed great emphasis on on-time performance.) Your 15 mph calculation may include a bunch of padding. You may want to recalculate based on a schedule from a few years ago.

Traffic signal priority is always based on communication between the bus and the signal system – the timed system in New York covers all vehicular traffic, and it happens to do a decent job on limited bus lines. But traffic signal priority usually doesn’t guarantee that the light will always be green for a bus (that would completely destroy cross traffic, including other buses, including pedestrians waiting to cross the street to reach the bus stop on the other side) – it merely gives the bus a bit of extra priority, perhaps extending a green light that was about to turn yellow, maybe turning a red light green a few seconds early.

But anyway, good signal priority is based on communication between the bus and the signal system, not on timed signals. A bus in Monaco automatically turns the light ahead of it green, even when it’s off-schedule (which happens a lot – Monaco isn’t Tokyo and buses aren’t trains).