thank for your help in advance. I'm dealing with the following problem:
Attempt to the solution of the problem:
a) If my understanding is right, we have two servers, the first server's throughput rate is $\frac{1}{3} min^{-1}$ and the second server's throughput rate is $\frac{1}{4}min^{-1}$. Now, I assume it wouldn't be sensible to state that the overall throughput would actually be $\frac{1}{3 + 4}min^{-1}$, as they are not dependent? How would I be able to state throughput as a whole? Should I average the two fractions?
b) I assumed the capacity was just 1 customer served at a time, but I read online that we should also include the customers present in the queue. If 7 minutes total are required for a customer to be served, the other customer would arrive 1 minute before the first one leaves, meaning the maximum number of customers at a time is 2, and this would be our capacity?\
c) Here I would find the $L_q$ value for each server. $L_q(Pop) = \dfrac{\lambda_1}{\mu_1} =\dfrac{10~per~hour}{20~per~hour} = 0.5 (from~the~tables)$, then $L_q(Mom) = \dfrac{\lambda_2}{\mu_2} = \dfrac{10~per~hour}{15~per~hour} = 1.207 (from~the~tables)$. Then the total waiting time would be $W_1 + W_2 = \dfrac{L_1}{\lambda_1} + \dfrac{L_2}{\lambda_2} = \dfrac{0.5}{10} + \dfrac{1.207}{10} = 0.17 hours$. Would that be correct? Thank you so much!