Consider a queuing system consisting of three stationsin series. Each station consists of a single server, who canprocess an average of 20 jobs per hour (processing times ateach station are exponential). An average of 10 jobs perhour arrive (interarrival times are exponential) at station 1.When a job completes service at station 2, there is a .1chance that it will return to station 1 and a .9 chance that itwill move on to station 3. When a job completes service atstation 3, there is a .2 chance that it will return to station 2and a .8 chance that it will leave the system. All jobscompleting service at station 1 immediately move on tostation 2.a Determine the fraction of time each server is busy.b Determine the expected number of jobs in thesystem.c Determine the average time a job spends in thesystem.
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.
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