How should Newton time its traffic signals to promote pedestrian safety and convenience?
According to WalkBoston and Streetsblog/Streetfilms, give the folks on foot a little headstart. The headstart has a technical name: Leading Pedestrian Interval. Instead of the crosswalk going green at the same time as same-direction motorists (concurrent) or pedestrians getting an exclusive walk signal, pedestrians get a few seconds of green before the same-direction motorists. This gives the pedestrians a chance to get into the crosswalk where they are more visible to right-turning traffic and less likely to be hit.
WalkBoston breaks it down (PDF):
Re-time lights for longer WALK time: Time traffic
signals so that pedestrians cross with, and for as long
as, the motorists’ green light in the same direction
[concurrent WALK light]. This gives pedestrians more
time to cross. Concurrent WALK also gives a shorter
wait between WALK phases.
Ask for short light cycles: 60-90 second cycles are
ideal. Walkers will wait about 30 seconds for a WALK
light; longer waits lead to jaywalking and danger.
Request countdown signals and advance WALK:
Countdown lights show how much crossing time
remains. When installed at a high-accident intersection,
pedestrian crashes drop by 50%. A WALK shown
4 seconds before the green light gives walkers a
head start before cars begin to turn. Thus, walkers
will be more visible to drivers.
Here's three minutes of Streetfilm that animates and explains it all:

