GATE EE 2017 Set 2 — Question 17
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Engineering Mathematics → Probability → Expectation & Variance
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Question
Assume that in a traffic junction, the cycle of the traffic signal lights is 2 minutes of green (vehicle does not stop) and 3 minutes of red (vehicle stops). Consider that the arrival time of vehicles at the junction is uniformly distributed over 5 minute cycle. The expected waiting time (in minutes) for the vehicle at the junction is _______
Correct answer
0.9 to 0.9
Solution
Let the total cycle time be minutes.
Assume the cycle starts with green for and red for .
If a vehicle arrives at time , the waiting time .
If a vehicle arrives at time , the waiting time (the time remaining until the next green light).
The expected waiting time is given by:
Assume the cycle starts with green for and red for .
If a vehicle arrives at time , the waiting time .
If a vehicle arrives at time , the waiting time (the time remaining until the next green light).
The expected waiting time is given by:
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