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29 January, 12:24

A single-channel queuing system has an average service time of 10 minutes and an average time between customer arrivals of 15 minutes. Service times and inter-arrival times both have exponential distributions. Find: a. customer arrival rate b. average number of customers in queue c. average time customers spend in the system

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  1. 29 January, 14:50
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    Answer: (a) 4 per hour (b) 4.5 minutes (c) 3 minutes

    Explanation:

    Average time between customer arrival = 15 minutes

    Average service time = 10 minutes

    (a) To calculate the customer arrival rate

    Arrival rate = 1 / time between Arrival

    = 1 / 15

    = 0.066 * 60

    = 4 per hour

    (b) To calculate the average number of customers in queue

    (Arrival time) ^2 / service time (service time - Arrival time)

    = (15) ^2 / 10 (10 - 15)

    = 225 / 10 (-5)

    = 225 / 50

    = 4.5 minutes

    (c) To calculate the average time customers spend in the system

    Arrival time / service time - Arrival time

    = 15 / 10 - 15

    = 15 / - 5

    = 3 minutes
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