# simple queue problem

• Nov 1st 2008, 02:12 PM
mosquetero
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
• Nov 1st 2008, 02:27 PM
mr fantastic
Quote:

Originally Posted by mosquetero
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
• Nov 1st 2008, 02:35 PM
mosquetero
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