Results 1 to 2 of 2

Math Help - Need Help in working with this question :(

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    7

    Need Help in working with this question :(

    At my local post office there is a central queue served by three assistants. From past experience, I know that the service times of the assistants are exponentially distributed with means 12 minutes, 2 minutes and 3 minutes.
    One day a customer enters the post office to discover that all three assistants are busy, but nobody else is waiting to be served.
    (i) Find the distribution of the time she has to wait before she can move forward for service, and hence show that her expected waiting time is 40 seconds.
    Calculate the probability that she has to wait more than three minutes for an
    assistant to be free to serve her.

    I know that the combination of three exponential processes with rates r1,
    r2, r3 is a single exponential process with a rate r1 + r2 + r3.

    How can I do that?


    (ii) Three minutes after entering the post office she is still waiting. Another
    customer enters the post office and stands behind her in the queue. (So now
    there are the same three people being served as there were at the start, and
    two people standing in the queue.) State the distribution of this latest> arrival?s waiting time before his service commences, and hence find the mean
    and standard deviation of his waiting time.

    I think I will have to condition on the relative probabilities of
    the first person in line being served by each server. Is that right??? HOW???
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by wallace View Post
    At my local post office there is a central queue served by three assistants. From past experience, I know that the service times of the assistants are exponentially distributed with means 12 minutes, 2 minutes and 3 minutes.
    One day a customer enters the post office to discover that all three assistants are busy, but nobody else is waiting to be served.
    (i) Find the distribution of the time she has to wait before she can move forward for service, and hence show that her expected waiting time is 40 seconds.
    Calculate the probability that she has to wait more than three minutes for an
    assistant to be free to serve her.

    I know that the combination of three exponential processes with rates r1,
    r2, r3 is a single exponential process with a rate r1 + r2 + r3.

    How can I do that?


    (ii) Three minutes after entering the post office she is still waiting. Another
    customer enters the post office and stands behind her in the queue. (So now
    there are the same three people being served as there were at the start, and
    two people standing in the queue.) State the distribution of this latest> arrival?s waiting time before his service commences, and hence find the mean
    and standard deviation of his waiting time.

    I think I will have to condition on the relative probabilities of
    the first person in line being served by each server. Is that right??? HOW???
    These questions form part of a graded assessment. Thread closed.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: May 28th 2011, 02:30 PM
  2. Replies: 3
    Last Post: March 21st 2010, 04:40 AM
  3. [SOLVED] Quick question on working with cdfs to find pdfs
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 14th 2010, 06:09 PM
  4. Replies: 1
    Last Post: November 17th 2008, 06:01 PM
  5. Replies: 1
    Last Post: August 7th 2007, 12:52 PM

Search Tags


/mathhelpforum @mathhelpforum