Chapter 13 ICE Name Problem 131 page 450 A generalpurpose au

Chapter 13 ICE Name: Problem 13.1, page 450 A general-purpose auto-repair garage has one mechanic who specializes in muffler in installations Customers seeking service at an average rate of 2 per hour, with a Poisson distribution. T average time to install a muffler is 20 minutes, with negative exponential distribution. a. On arrival at the garage, how many customers should one expect to find in the system? Problem 13.2, page 450 A business school is considering replacing its copy machine with a faster model. Past records show that the average student arrival rate is 24 per hour, Poisson distributed, and that the service times are distributed exponentially. The selection committee has been instructed to consider only machines that will yield an average turnaround time (i.e., expected time in the system) of 5 minutes or less. What is the smallest processing rate per hour that can be considered?

Solution

Arrival rate (A) = 2 per hour

Service rate (S) = 20 minutes or 6/20 = 3 per hour

Average number of customers waiting in system = Lq + r

Lq = A^2/(S*(S-A)) = 2^2/(3*(3-2)) = 4/3

r = A/S = 2/3

Average number customers = 4/3+2/3 = 2