Question

In: Operations Management

A computer lab has a dozen machines, but at any given time some of them may...

A computer lab has a dozen machines, but at any given time some of them may be out of commission. Usually the problem is something as simple as the operating system locking up, which requires that a staff person reboot the machine and make sure that all the standard settings are correct. Sometimes the problem may be more serious, taking more time to correct. Overall, the repair time for any individual computer is negative exponentially distributed with a mean of thirty minutes. Once a computer is operating, the time until failure is negative exponentially distributed with a mean of ten hours.

a. If there is only one staff person to do the repairs, what is the average number of operating computers in the lab over the long run?

b. If there were two staff people to do the repairs, how much would that same average be?

Expert Solution

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(a)

Let the state be the number of operating computers. We generate the following transition diagram:

Based on the formula for steady state probability for birth-and-death process

we have the steady state probability as follows

The mean number of operating computers is P12 i=1(ºi £i) = 10.96

(b)

Similarly, when 2 staff people are doing the repairs, we generate the following transition diagram and get the mean number of operating computers being 11.39.

Thus we conclude that a new added staff will increase the mean number of operating computers. However, the improvement is not significant.

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keosha answered 1 month ago

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