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Math Help - Stimulation and Queuing

  1. #1
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    Dec 2011
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    Stimulation and Queuing

    A small shop is run by two people, John and Judy, the time between arrivals at this shop is shown in table 1. All customers form a single queue and are served on a first come first served basis. The distributions of service times are shown in tables 2 and 3. Assume that no one is being served or waiting to be served when the first customer arrives. Also assume that John serves the customer first if both of them are idle.

    Table 1-Inter-arrival distribution of customers

    Time between arrivals (minutes) 1 2 3 4
    Probability 0.15 0.35 0.30 0.20

    Table 2-Service distribution of John

    Service Time (minutes) 2 3 4 5
    Probability 0.20 0.35 0.30 0.15

    Table 3- Service distribution of Judy

    Service Time (minutes) 2 3 4 5 6
    Probability 0.15 0.25 0.30 0.20 0.10

    a) Show the mapping between random numbers and inter-arrival and service distributions. Use the following random numbers:

    For arrival
    62, 16, 70, 20, 31, 20, 56, 97, 55, 71, 05, 70, 65, 83, 16

    For service
    71, 92, 97, 16, 90, 30, 78, 13, 92, 80, 10, 15, 81, 53, 35


    b) Simulate the arrival of 15 customers and derive the number of customers who have to wait, the average waiting time and the percentage of the time Judy is busy.

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    I have done part a but not sure how to do part b) on excel
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  2. #2
    MHF Contributor
    Joined
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    Re: Stimulation and Queuing

    i cant see how to answer your question without doing the whole thing for you.

    you could try having each row of the spreadsheet representing 1 unit of time (so that nothing happens on most rows) and basing your calculations off that, but this isn't the only approach that would work.
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