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30 October, 21:38

in a waiting line system, there is only one server. Customer arrivals follow Poisson distribution with mean inter-arrival time 5 minutes. Service time follow exponential distribution and a server can serve 15 customers per hour on average. What is the average waiting time? a. 2 minb. none of the answerc. 20 mind. 30 mine. 16 min

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  1. 31 October, 00:39
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    The problem can be represented by single queue model.

    Inter-arrival time = 5 min

    Arrival rate = 60 min / 5 min

    Arrival rate = 12 customers per hour

    Service rate = µ = 15 customers per hour

    Utilization of server

    P = λ/µ

    P = 12 / 15

    P = 0.80

    Number of customers in queue

    L = (12^2) / 15 (15 - 12)

    L = 3.2 customers per hour

    Waiting time in queue

    W = 3.2 / 12

    W = 0.266 hour

    Convert hours into minutes as follows:

    Waiting time in queue = 0.2667 x 60

    Waiting time in queue = 16 minutes

    Waiting time in system

    Ws = 02667 + 1/15

    Ws = 0.333 hour

    Waiting time in system = 0.333 x 60

    Waiting time in system = 20 mins

    Average waiting time in queue = 16 mins

    Average waiting time in system = 20 mins

    Therefore, average waiting time in the system is 20mins.
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