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24 October, 00:24

Consider a single-server queuing system. If the arrival rate is 82 units per hour, and each customer takes 36 seconds on average to be served, what is the average # of customers in the line? Round to whole person.

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  1. 24 October, 00:27
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    The average # of customers in the line is 4.

    Explanation:

    arrival rate, x = 82/3600

    = 0.023

    service rate, y = 1/36

    = 0.028

    utilisation, p = x/y

    = 0.023/0.028

    = 0.821

    average number of costomers = p^2/[1 - p]

    = (0.821) ^2/[1 - 0.821]

    = 3.75

    Therefore, The average # of customers in the line is 4.
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