Consider an infinite-buffer single-server manufacturing workstation where arrivals occur according to a Poisson process with rate = 10 hr1 . Each arrival has a size of 1 to 5 parts, with uniform distribution. Part processing times have mean = 1.5 min and st. deviation = 1.0 min.

i. (10 pts) Model this workstation as a G/G/1 queue, treating each arrival as a single job, What are the mean processing time and the coefficient of variation of the processing times for the jobs processed in this G/G/1 model?

ii. (5 pts) Show that the considered G/G/1 queue is stable.

iii. (5 pts) Compute the throughput of this workstation in terms of number of parts per hour .

iv. (5 pts) What is the expected number of parts in the waiting queue of this workstation? v. (5 pts) Assuming that each arriving batch also leaves as a single batch, what is the expected sojourn time of a batch in this station?