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