Scenario B.6
The Jackson Machine Company has four cutting tools that need to be refurbished after an average of 30 hours, according to an exponential distribution. The single machine that refurbishes the tools needs 15 hours for each tool on the average, with exponential service times.
-Use the information in Scenario B.6. What is the average waiting time of tools in line?
A) fewer than or equal to 15 hours
B) greater than 15 hours but fewer than or equal to 25 hours
C) greater than 25 hours but fewer than or equal to 35 hours
D) greater than 35 hours

Question

Quizplus · Accepted Answer

The average waiting time in line for an M/M/1 queue can be calculated using the formula $W_q = \frac{\lambda}{\mu(\mu - \lambda)}$, where $\lambda$ is the arrival rate and $\mu$ is the service rate. Given that tools need refurbishing every 30 hours on average ($\lambda = \frac{1}{30}$ tools/hour) and each tool takes 15 hours to refurbish on average ($\mu = \frac{1}{15}$ tools/hour), substituting these values into the formula gives a waiting time greater than 15 hours but fewer than 25 hours, fitting the description of choice B.

Scenario B.6 The Jackson Machine Company Has Four Cutting Tools That Need