Hi Members,

Problem is as follows.

C arrives at a two-server post office to find A being served by server 1 and B by server 2. C will enter service as soon as either A or B departs. If the service time of server i are exponential random variables with rates $\mu_i=1,2 $, find

a)The probability that A is the first one to depart.

b)The probability that A is the last one to depart.

c)The expected time until C departs.

Solutions:

I don't know what are the correct solutions, but I solved them as follows.

a)$\frac{\mu_1}{\mu_1+\mu_2}$

b)$\frac{(\mu_2)^2}{(\mu_1+\mu_2)^2}$

c)$\frac{1}{\mu_1}\left( \frac{(\mu_1)^2}{(\mu_1+\mu_2)^2}\right) +\frac{1}{\mu_2}\left( \frac{(\mu_2)^2}{(\mu_1+\mu_2)^2}\right)$

Please reply me, if my solutions are wrong.Your comments about the correctness of answers are always welcome