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n1<br />
L'<br />
2a<br />
= ,[/, -, )* '(,<br />
1,. yt \y -rY rl *2(w+1)<br />
a<br />
if the response time is greater than<br />
the yellow light time. (In this unrealistic<br />
case the yellow light time<br />
does not a1low any decision making.)<br />
This also occurs when the term<br />
containing the acceleration is small<br />
in comparison to the difference in<br />
the yellow light and reaction times.<br />
If the radical is positive, we will<br />
always get two positive values forvn.<br />
Calling the smaller root yr and the<br />
larger rootv, we see that there will<br />
always be a dilemmazofle if vo> v,<br />
or vo < v, and an overlap zonetf.v, <<br />
vo < vz. Physically it's easy to understand<br />
why a high speed can produce<br />
a dilemma zone. Why can a low<br />
speed produce a dilemmazone?<br />
Another way of<br />
viewing the problem<br />
is to realize that<br />
people will usually<br />
betraveling atatypical<br />
speed for this<br />
type of road and we<br />
wish to set the yellow<br />
light time to<br />
make it a safe intersection.<br />
In this case/ we should solve<br />
the equation for the yellow light<br />
time fr. The dilemmazofieexists for<br />
the following values of tr:<br />
(w+1) vo<br />
Ytvo2a<br />
t..
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