6 Consider a queuing system consisting of three stations in series. Each station consists of a single server, who can process an average of 20 jobs per hour (processing times at each station are exponential). An average of 10 jobs per hour arrive (interarrival times are exponential) at station 1.

When a job completes service at station 2, there is a .1 chance that it will return to station 1 and a .9 chance that it will move on to station 3. When a job completes service at station 3, there is a .2 chance that it will return to station 2 and a .8 chance that it will leave the system. All jobs completing service at station 1 immediately move on to station 2.

a Determine the fraction of time each server is busy.

b Determine the expected number of jobs in the system.

c Determine the average time a job spends in the system.