There are... one of them is given in the article—which calls the current system "one-shot"—there exists k-shot variants which allow for at least k opportunities/warnings before automagically braking. The (apparent) reasoning behind the MTA not putting these (for some number k>1) was "safety," but the article states that, in general, the timing circuits are much more complicated therefore resulting in a higher cost.[0]
Additionally, a simple case would be to have circuits which do, after a certain point in time, force slow (but safe) braking into the required velocity---I could see problems with robustness here due to the specific application, but at least in theory this should be possible (we all know the difference between theory and practice, though).
On the general case, this all seems a little weird to me since it seems like such a trivial problem (increase error bands, etc), but may have some deeper reasons that aren't explained in the article(?). It's quite difficult to tell since the primary sources are not provided at any point in time.
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[0] I'm reluctant to accept this claim since most of these things aren't done in an analog way, anymore. Timing is a matter of figuring out empirical constants and programming them in directly, which, while not totally trivial, seems to have roughly the same difficulty (amortized over all of the lights that need to be put in) as doing the timing for a 'one-shot' light.
Indeed, this is my understanding of how most non-US high-speed-rail controllers work - the driver sets a target speed, the physical location on the track has a maximum speed, and the traffic system looks at the cars ahead and sets its own maximum speed (e.g. zero when another train is right in front of you). Instead of stopping the train when the driver exceeds the speed limit, it just uses the minimum of all the target speeds.
TVM is the system I'm most familiar with when it comes to HSR (used on the LGV in France and HS1 in the UK); it has a variable overspeed allowance (5 to 15 km/h depending on current maximum speed). If you exceed that, an emergency brake application occurs.
Japanese ATC and ATS-P, used on all Shinkansen lines and most busy metro/commuter lines, just apply service break until the train is under back speed limit. AFAIK no overspeed allowance.
I think the reason that it's a single shot instead of multi shot and full emergency braking instead of moderate is that the stops are all track based not train based, at least for the 'train in circuit' stops. The original signals basically put up a metal arm that trips the emergency brakes on the train itself so if they piggy backed off this existing system by just adding a speed sensor there's no way to do a slow deceleration because the signals are designed to work without any real cooperation from the train beyond the emergency brake functioning.
Additionally, a simple case would be to have circuits which do, after a certain point in time, force slow (but safe) braking into the required velocity---I could see problems with robustness here due to the specific application, but at least in theory this should be possible (we all know the difference between theory and practice, though).
On the general case, this all seems a little weird to me since it seems like such a trivial problem (increase error bands, etc), but may have some deeper reasons that aren't explained in the article(?). It's quite difficult to tell since the primary sources are not provided at any point in time.
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[0] I'm reluctant to accept this claim since most of these things aren't done in an analog way, anymore. Timing is a matter of figuring out empirical constants and programming them in directly, which, while not totally trivial, seems to have roughly the same difficulty (amortized over all of the lights that need to be put in) as doing the timing for a 'one-shot' light.