queueing theory.

please show all work and explain, i need help understanding the problems

6. A parts center in a large factory has two servers each having an exponentially distributed service time with a mean of 1/4 hr. Workers arrive to get parts with exponentially dis- tributed interarrivale times at a mean arrival rate of 5 per hour. The plant manager has determined that because of lost time spent a the parts center getting parts, the factory loses $15 per hour per worker. Each server costs the factory $10 per hour. (a) Calculate the expected total cost per hour for this parts center. (b) Suppose the two servers can be replaced with a single "super server" who has an exponential service time distribution with a mean of 1/10 hr. How much per hour should management be willing to pay this super server? Hints for this problem. We did not cover a question like this in class. Here are a series of hints that should help you. Please note that in your write up, I would like you to explain each step. The Total Expected Cost ETC) is the sum of the Expected Wait Cost E{WC) and the Expected Service Cost E(SC). Notice that the following E(SC) = 10s = $20/hr and E(WC)=15mp. = 15L You will need to find L. For part b, notice that there is only one server, so L= - So, generate the new ETC), set the two Total Costs togther and solve for the unknown. 7. Extra for Experts - Consider a stedas-state queueing system with s servers each having exponentially distributed service times with mean 1/4. Suppose interarrival times are exponentially distributed with a mean arrival rate of 2. Derive the formula, P (1) where p=N/)