 
Summary: ISyE 4803 Ayhan
Summer 2010
Homework 1
1. Consider a production system consisting of three singleserver stations in series. Customer
orders arrive at the system according to a Poisson process with rate 1 per hour. Each customer
order immediate triggers a job that is released to the production system to be processed at
station 1 first, and then at station 2. After being processed at station 2, a job has p1 = 10%
probability going back to station 1 for rework and 1  p1 probability continuing onto station
3. After being processed at station 3, a job has p2 = 5% probability going back to station
1, p3 = 10% probability going back to station 2, and 1  p2  p3 probability leaving the
production system as a finished product. Assume that the processing times of jobs at each
station are iid, having exponential distribution, regardless of the history of the jobs. The
average processing times at stations 1, 2 and 3 are m1 = 0.8, m2 = 0.70 and m3 = 0.8 hours,
respectively.
(a) Find the longrun fraction of time that there are 2 jobs at station 1, 1 job at station 2
and 4 jobs at station 3.
(b) Find the longrun average (system) size at station 3.
(c) Find the longrun average time in system for each job.
(d) Reduce p1 to 5%. Answer (1c) again. What story can you tell?
2. Consider the production system in Problem 1 with following modification: p1 = 10%, p2 =
