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## Suppose you are hired by the STAR Lab to analyze vehicle arrivals at the right lane of the Evergreen Point Bridge on Westbound SR-520 for th

Question

Suppose you are hired by the STAR Lab to analyze vehicle arrivals at the right lane of the Evergreen Point Bridge on Westbound SR-520 for the period from 12:00am to 4:00am in a weekday. It is known that vehicle arrivals follow a Poisson process at this location and time period. There is a single-loop detector embedded on this lane at the east end of the bridge. Since you do not want to go to the bridge to count vehicles at this time period, you decided to use the loop detector data for the analysis. Of the 720 20-second intervals (the loop detection system stores data every 20 seconds), 508 intervals were identified to have at least one vehicle detected. Assume the loop detector is free of error. Please estimate the vehicle arrival rate (vehicles per second) for this lane. With the estimated arrival rate, please calculate the probability of having three or more vehicles detected in a 20-second interval and the probability of having a headway shorter than 10 seconds. [15 points]

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Mathematics
6 months
2021-07-23T09:27:09+00:00
2021-07-23T09:27:09+00:00 1 Answers
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## Answers ( )

Answer:

0.126

Step-by-step explanation:

Given :

Total time interval = 720

Number of interval in which one vehicle is detected =508

Proportion of atleast one detected vehicle :

508 / 720 = 0.7056

The mean arrival rate per second :

P(x ≥ 3) = 1 – P(x ≤ 3)

P(x ≥ 3) =1 – [p(x =0) + p(x = 1) + p(x =2) + p(x = 3)]

P(x ≥ 3) = 1 – 0.8745

P(x ≥ 3) = 0.1255

P(x ≥ 3) = 0.126