An average of 10 jobs per hour arrives at a job shop. Interarrival times of jobs are exponentially distributed. It takes an average of 10/3 minutes to complete a job. Unfortunately, 1/3 of all completed jobs need to be reworked. Thus, with probability 1/3, a completed job must wait in line to be reworked. In steady state, how many jobs would one expect to find in the shop? What would the answer be if it took an average of 5 minutes to finish a job?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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An average of 10 jobs per hour arrives at a job shop.
Interarrival times of jobs are exponentially distributed. It takes
an average of 10/3 minutes to complete a job. Unfortunately,
1/3 of all completed jobs need to be reworked. Thus, with
probability 1/3, a completed job must wait in line to be
reworked. In steady state, how many jobs would one expect to
find in the shop? What would the answer be if it took an
average of 5 minutes to finish a job?

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