On average, 40 jobs arrive per day at a factory. The time between arrivals of jobs is exponentially distrib-uted. The factory can process an average of 42 jobs per day, and the time to process a job is exponentiallydistributed.a. On average, how long does it take before a job iscompleted (measured from the time the job arrivesat the factory)?b. What fraction of the time is the factory idle?c. What is the probability that work on a job willbegin within two days of its arrival at the factory?
On average, 40 jobs arrive per day at a factory. The time between arrivals of jobs is exponentially distrib-uted. The factory can process an average of 42 jobs per day, and the time to process a job is exponentiallydistributed.a. On average, how long does it take before a job iscompleted (measured from the time the job arrivesat the factory)?b. What fraction of the time is the factory idle?c. What is the probability that work on a job willbegin within two days of its arrival at the factory?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section12.5: Analytic Steady-state Queueing Models
Problem 9P
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Question
On average, 40 jobs arrive per day at a factory. The
time between arrivals of jobs is exponentially distrib-
uted. The factory can process an average of 42 jobs
per day, and the time to process a job is exponentially
distributed.
a. On average, how long does it take before a job is
completed (measured from the time the job arrives
at the factory)?
b. What fraction of the time is the factory idle?
c. What is the probability that work on a job will
begin within two days of its arrival at the factory?
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