Sweet-Dreams Inc.manufactures custom pillows.Five jobs are waiting to be processed using the SPT priority rule.Their processing times are shown in the following table.What is the average number of jobs in the system?

Question

Quizplus · Accepted Answer

To calculate the average number of jobs in the system, we need to use Little's Law. Little's Law states that L = λW, where L is the average number of jobs in the system, λ is the arrival rate of jobs, and W is the average time a job spends in the system.

We are given the processing times of the five jobs, but we don't know their arrival rate. However, the SPT priority rule tells us that we should process the shortest job first, which means that the jobs are arriving randomly and independently of each other. Therefore, we can assume that the arrival rate is constant and equal to 1/processing time.

Using this assumption, we can calculate W as the sum of the processing times divided by the number of jobs:
W = (4 + 8 + 10 + 12 + 14)/5 = 9.6

Then, we can calculate L as the arrival rate (λ) times W:
L = 1/4 + 1/8 + 1/10 + 1/12 + 1/14 * 9.6 = 3.38

Therefore, the best choice is E, with an average number of jobs in the system of 3.38.