A summary of some research done on pedestrian safety and waiting times:

Regarding waiting times at signalised crossings - studies done by the UK Road Transport Laboratory show 30 seconds was the longest pedestrians would wait at signalised crossings before attempting to cross against the red man. Focus group studies with adults & children report that 30 seconds is the maximum amount of time they are willing to wait at a signalised crossing before they become impatient. Impatience peaks at 40 to 45 seconds. The recommendation from the Road Transport Laboratory is that traffic collisions can be reduced by developing a control system that does not cause pedestrians to wait an unduly long time.

We are dealing with human behaviour - very complex !