Results 1 to 3 of 3

Math Help - simple queue problem

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    6

    simple queue problem

    Hi everyone, I hope you can help me:

    There is a shop with one seller and when I enter to it, there are already 3 customers waiting in the queue. The service of one customer is an exponential distribution with an average of 5 minutes, what is the distribution of my waiting time?

    I thought it was a gamma distribution because I have a sum of 4 exponential distributions (3 in the queue and 1 being served) but the results I get are not very reliable (for example I got a too low average time waiting).

    Thank you very much
    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 mosquetero View Post
    Hi everyone, I hope you can help me:

    There is a shop with one seller and when I enter to it, there are already 3 customers waiting in the queue. The service of one customer is an exponential distribution with an average of 5 minutes, what is the distribution of my waiting time?

    I thought it was a gamma distribution because I have a sum of 4 exponential distributions (3 in the queue and 1 being served) but the results I get are not very reliable (for example I got a too low average time waiting).

    Thank you very much
    Won't the mean be 20 minutes since the mean of the gamma distribution is (4)(5) = 20 minutes ..... (see http://en.wikipedia.org/wiki/Gamma_distribution).


    Thread of related interest: http://www.mathhelpforum.com/math-he...variables.html
    Last edited by mr fantastic; November 1st 2008 at 04:00 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2008
    Posts
    6

    Red face Thanks

    Yes it has more sense. I read somewhere that the sum of exponentials was a gamma and I thought that this was the case but obviously it is not. Thank you very much
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Queuing Theory problem, M/M/1/K queue with twist
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: July 12th 2011, 11:05 PM
  2. Simple queue
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: March 24th 2010, 10:41 AM
  3. Queue markov ? sos help
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: January 28th 2010, 09:34 AM
  4. queue
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: July 15th 2008, 07:52 PM
  5. Probability of a good queue
    Posted in the Statistics Forum
    Replies: 1
    Last Post: January 2nd 2007, 07:22 AM

Search Tags


/mathhelpforum @mathhelpforum