A computer system queues up batch jobs and processes them on an FCFS basis.Between 2 and 5 P.M., jobs arrive at an average rate of 30 per hour and require anaverage of 1.2 minutes of computer time. Assume the arrival process is Poissonand the processing times are exponentially distributed. b. Using a normal approximation of the flow time distribution for the LCFS andrandom cases, estimate the probability that the flow time in the system exceeds10 minutes in each case.
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 computer system queues up batch jobs and processes them on an FCFS basis.
Between 2 and 5 P.M., jobs arrive at an average rate of 30 per hour and require an
average of 1.2 minutes of computer time. Assume the arrival process is Poisson
and the processing times are exponentially distributed.
b. Using a normal approximation of the flow time distribution for the LCFS and
random cases, estimate the probability that the flow time in the system exceeds
10 minutes in each case.
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