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Math Help - Queuing simulation.

  1. #1
    Newbie
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    Jan 2012
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    Unhappy Queuing simulation.

    CAN someone please help i been trying to work it out i been reading literally everything.

    if your not bothered to solve it please atleast tell me how i should lay it out or just tell me someone lol

    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 0.3 0.2
    --------------------------------------------------------------------------------------------------
    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.

    c) What can you conclude from the result in (b)? Justify your answer. Explain how, in practice,
    you would use simulation to solve this problem and how would you justify your results?


    this is the questionn
    Last edited by mr fantastic; January 7th 2012 at 04:52 PM. Reason: Re-titled.
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  2. #2
    Grand Panjandrum
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    Re: Queuing simulation.

    Quote Originally Posted by flowermaths View Post
    CAN someone please help i been trying to work it out i been reading literally everything.

    if your not bothered to solve it please atleast tell me how i should lay it out or just tell me someone lol

    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 0.3 0.2
    -------------------------------------------------------------------------------
    [snip]

    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

    [snip]
    1. You do not give sufficient context to allow us to help without guessing at things not included in the text you post.

    I will assume that the random numbers are supposedly samples from a uniform distribution on [1,2, .., 100]

    2. The inter-arrival time for the next customer is 1 minute if the random number is between 1 and 15, 2 minutes if it is between 16 and 50, 3 minutes if it is between 51 and 80, and 4 otherwise.

    CB
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