Consider a queueing system with five single-server stations in series, each with its own F...

Consider a queueing system with five single-server stations in series, each with its own FIFO queue. Suppose that interarrival times to the system (at station 1) are exponential with a mean of 10 minutes. Suppose further that all service times are exponentially distributed, with the mean service times at stations 1 through 5 being 8, 6, 9, 7, and 5 minutes, respectively. The system is initially empty and idle, and it runs for exactly 100,000 minutes.

(a) At what station should a second server be added to reduce the average time in system by the greatest amount? Perform a  fractional factorial design with n = 10 replications at each of the 16 design points; the different system configurations should be simulated using CRN. Construct 90 percent confidence intervals for the expected main and two-factor interaction effects. Which effects are statistically significant?

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(b) For the original system with one server at each station, compute the utilization factor for each station (see App. 1B). Do these five values shed any light on your results from part (a)?

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(c) How could we answer the question in part (a) by simulating only a “small” number of design points?