juanra

Hi guys, this is the problem I don't get to solve (Maybe is very easy
for you):


At a bank there is a central queue served by four assistants. The
service times of three of the four assistants are exponentially
distributed with a mean 3 minutes, and the service time of the fourth
assistant is exponetially distributed with mean 4 minutes.


A customer enters the bank to find all four assistants busy, but nobody

waiting.


My question is:
Which is the distribution of the time the new customer has to wait
before moving forward for service? and how can I calculate the expected

time?


I know the exponential probability distribution function (pdf) for:
mean=3 minutes is f(x)=λexp(-λt) ; λ=1/3
mean=4 minutes is f(x)=λexp(-λt) ; λ=1/4
and their expected time (mean) are 3 and 4 minutes respectively.


But what about the new pdf taking into account both distributions? Do I

need to add both values of λ ? or take into account the probabilities
of both types of assistants? (I know that the answer is 40 seconds for
the expected time)


(I guess that if I'm able to find the new pdf, I just need to integrate

between 0 and infinity this new f(x) * x and I have the expected time.)

Please help !
Thank you very much in advance :-))


PS/ Does it have any thing to do with a hyperexponential distribution ?