POISSON (Random) EVENTS 3
Poisson arrivals produce headways that are negative exponential distributed.
u= 0.167
Headway P(H=t)
0 0.167
1 0.141
2 0.119
3 0.101
4 0.086
5 0.072
6 0.061
7 0.052
8 0.044
IV. P(H = t) = ue-ut
u = lambda Notice that short headways are more likely than long headways
What is the probability of observing a headway that is 2.5 seconds long if the mean arrival rate is 600 vph?
u = (600 veh/hour)(1 hour/3600 sec) = 0.167 veh/hr
P(H = 2.5)=(0.167 veh/sec)e-(0.167 veh/sec)(2.5 sec) = 0.110
V. P(H < t) = 1-e-ut
What is the probability of observing a headway that is less than 2.5 seconds if u = 600 vph?
P(H < 2.5)= 1 - e-(0.167 veh/sec)(2.5 sec) = 0.341
VI. P(H >= t) = e-ut
What is the probability of observing a headway that is greater than or equal to 2.5 sec if u = 600 vph?
P(H >= 2.5)= e-(0.167 veh/sec)(2.5 sec) = 0.659