FIGURE 9–13 Relative flow times: SPT versus FCFS 0.9 Source: Adapted from tabled results in Conway, Maxwell, and Miller (1967), p. 184. 0.8 0.7 0.6 0.5 0.4 F 0.3 0.2 0.1 0.2 0.4 0.6 0.8 Relative flow
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A critical resource in a manufacturing operation experiences a very high traffic intensity during the shop’s busiest periods. During these periods the arrival rate is approximately 57 jobs per hour. Job processing times are approximately exponentially distributed with mean 1 minute.
a. Compute the expected flow time in the system assuming an FCFS processing discipline, and the expected flow time under SPT using Figure 9–13.
b. Compute the probability that a job waits more than 30 minutes for processing under FCFS.
c. Using a normal approximation, estimate the probability that a job waits more than 30 minutes for processing under LCFS.
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