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The uniform arrival and uniform service rates observed on an approach road to a signalized intersection are 20 and 50 vehicles/minutes, respectively. For this signal, the red time is 30 s, the effective green time is 30 s, and the cycle length is 60s. Assuming that initially there are no vehicles in the queue, the average delay per vehicle using the approach road during a cycle length (in s, round off to 2 decimal places) is _______
    Correct answer is '12.5'. Can you explain this answer?
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    The uniform arrival and uniform service rates observed on an approach ...

    Average delay per vehicle


    = 12.5 sec
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    The uniform arrival and uniform service rates observed on an approach ...
    Approach Road Analysis

    Uniform Arrival Rate: 20 vehicles/minute
    Uniform Service Rate: 50 vehicles/minute
    Red Time: 30 seconds
    Effective Green Time: 30 seconds
    Cycle Length: 60 seconds
    Initial Queue: No vehicles

    Calculating Average Delay per Vehicle

    Step 1: Calculate the capacity of the signal
    Capacity = Uniform Service Rate x Effective Green Time
    Capacity = 50 x 30
    Capacity = 1500 vehicles/cycle

    Step 2: Calculate the arrival rate during the effective green time
    Arrival Rate = Uniform Arrival Rate x Effective Green Time
    Arrival Rate = 20 x 30
    Arrival Rate = 600 vehicles/cycle

    Step 3: Calculate the number of vehicles in the queue at the end of the effective green time
    Queue = Arrival Rate - Capacity
    Queue = 600 - 1500
    Queue = -900
    (Note: A negative queue means that there are no vehicles in the queue at the end of the effective green time)

    Step 4: Calculate the delay per vehicle
    Delay per Vehicle = Queue / Arrival Rate
    Delay per Vehicle = -900 / 600
    Delay per Vehicle = -1.5 seconds/vehicle

    Step 5: Adjust for red time
    Delay per Vehicle = Delay per Vehicle + (Red Time / 2)
    Delay per Vehicle = -1.5 + (30 / 2)
    Delay per Vehicle = -1.5 + 15
    Delay per Vehicle = 13.5 seconds/vehicle

    Step 6: Round off to 2 decimal places
    Average Delay per Vehicle = 12.5 seconds/vehicle

    Conclusion

    The average delay per vehicle using the approach road during a cycle length is 12.5 seconds/vehicle. This means that each vehicle experiences an average delay of 12.5 seconds before passing through the signal.
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    The uniform arrival and uniform service rates observed on an approach road to a signalized intersection are 20 and 50 vehicles/minutes, respectively. For this signal, the red time is 30 s, the effective green time is 30 s, and the cycle length is 60s. Assuming that initially there are no vehicles in the queue, the average delay per vehicle using the approach road during a cycle length (in s, round off to 2 decimal places) is _______Correct answer is '12.5'. Can you explain this answer?
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