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Re: Proof that the Lex can’t support more than 28 tph (504280)

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Posted by Stephen Bauman on Sat May 31 09:32:32 2003, in response to Proof that the Lex can’t support more than 28 tph,
posted by AlM on Fri May 30 13:39:06 2003.

There are many factors that influence service capacity. Some of these are the signal system, train scheduling, dwell time, T/O behavior, C/R behavior, train acceleration, train braking, etc.

Your methodology has not sought to isolate any of these factors. What you have done is measure the entire system and concluded that they are operating at a maximum of 28 tph. Your conclusion points to only one factor: signal system.

However, even this is flawed.

First, the minimum time between trains that you measured was 80 seconds. One would expect that the signal system would have permitted any train to follow within 80 seconds: had a train been there; had the train's acceleration and braking been stronger or had the T/O been more agressive. So, in trying to isolate the signal system constraints you should have used 80 seconds for the signal system's contribution to maximum service levels. Any additional headway time should have been ascribed to operations for not having a train in the correct position or to maintenance for permitting a train to operate with inferior acceleration.

Second, there is dwell time. Dwell time is composed of 3 components: the time there is passenger movement; the time when the doors are open but there is no passenger movement and the time when the doors are closed and the train is not moving. The first component is a limiting factor. The second two components should be used to provide a buffer to account for random variations. You measured 30 seconds as a minimum with a local present for total dwell time. This figure is usually given as the nominal total dwell time for many capacity calculations. You have shown that it is achievable at low service levels. More frequent service should result in less total dwell time by lowering the passenger movement component.

Therefore, with a 30 second dwell time one would expect that the limitation imposed by the signal system should be 80 + 30 = 110 seconds between trains. This is equivalent to 32 tph. Indeed, they used to operate 32 tph on the Lex 50 years ago with the same signal system but with more attention to opeational detail.

I have tried to isolate the signal system's limits on maximum service levels more directly. I've separated your time A into two components: stopping time and acceleration time. The stopping time was the time from when the front of the train passed the back of the platform until the doors opened. The acceleration time was the time from when the train started moving until signals permitted the next train to enter the station without any restriction. This did not eliminate the variability between operators and equipment. Consequently I took 10 readings and used statistical averages. The average stopping and acceleration times, as defined above, were 31 and 49 seconds respectively. The nominal time for both times is usually 30 seconds each. The same times for 86th Street were 24 and 28 seconds.

Therefore, the minumum 80 seconds time that you measured was approximately due entirely to the signal system's constraints. To be sure, I did measure minimums of 29 and 47 seconds for these times for a more rigorous signal system constraint of 76 seconds.

The stopping time is close to the nominal 30 seconds; the acceleration time is not. The average acceleration out of Union Square is 19 seconds longer than the nominal 30 seconds. Nor can all the difference be due to moving platform retraction time, which you measured to be a nominal 5 seconds. One problem is T/O indifference. There is a speed restriction around 1500 feet south of Union Square due to a curve. In order to maximize service levels trains should quickly leave Union Sq. This means that the operators should creep until the moving platforms clear then wrap it up until the train reaches the speed restriction and then slow down. They don't wrap it up (or the trains do not respond). Instead they speed up only to the curve speed restriction after the moving platforms retract. That's the reason for the extra 15 seconds.

This is not to say there are not resonable solutions. There are other stations that have speed restrictions leaving stations that might increase acceleration times to unacceptable levels. This problem has been answered at 125th and 59th Streets by effectively shortening the block length for leaving the leaving the station. The signal that controls access to the platform has 3 aspects instead of the usual red and yellow. The third aspect is a timer set for 20 mph. At 59th St, the average acceleration time to the 20 mph aspect is 25 seconds, whereas the average acceleration time to the yellow aspect is 42 seconds. A similar reduction at Union Square would bring acceleration time close to the nominal 30 seconds.

Of course, this means a change in the current signal system. However, I'd expect that such a change could be implemented for $250K. This would bring the total of braking, acceleration times close to 60 seconds and with a nominal dwell time of 30 seconds shows that 40 tph operation is quite possible. Of course, 40 tph operation requires additional operational details. However, the signal system is not the limitng factor. To paraphrase Shakespeare: the fault dear TA is not in the signals but in yourselves.


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