Continuing Problem 50, you might expect that the system will be only as good as the station with the smallest value of s_iµ_i (called the bottleneck station). This problem asks you to experiment with the simulation to gain some insights into bottlenecks. For each of the following parts, assume a Poisson arrival rate of λ = 1 per minute, and assume that processing times are exponentially distributed. Each station has s_i = 1 and there are five stations. Each station, except for the bottleneck station, has a processing time mean of 1/µ_i = 0.6 minute. The bottleneck station has mean 0.9minute. Each part should be answered independently. For each, you should discuss the most important outputs from your simulation.

a. Suppose there are 100 (essentially unlimited) buffers in front of all stations after station 1. Run the simulation when station 1 is the bottleneck. Repeat when it is station 2; station 3; station 4; station 5.

b. Repeat part a when there are only two buffers in front of each station after station 1.

c. Suppose station 3 is the bottleneck station and you have 4 buffers to allocate to the whole system. Experiment to see where they should be placed

Problem 50

Referring to the multi station serial system in the Series Simulation.xlsm file, let s_i and 1/µ_i be the number of machines and the mean processing time at station i. Then the mean processing rate at station i is siµi. You might expect the system to operate well only if each siµi is greater than λ, the arrival rate to station 1. This problem asks you to experiment with the simulation to gain some insights into congestion. For each of the following parts, assume a Poisson arrival rate of λ = 1 per minute, and assume that processing times are exponentially distributed. Each part should be answered independently. For each, you should discuss the most important outputs from your simulation.

a. Each station has s_i = 1 and the µi s are constant from station to station. There are 100 (essentially unlimited) buffers in front of all stations after station 1. Each processing time has mean 1/µi = 0.6 minute and there are three stations.

b. Same as part a, except that there are 10 stations.

c. Same as part a, except that each processing time has mean 0.9 minute.

d. Same as part c, except that there are 10 stations.

e. Repeat parts a to d but now assume there are only two buffers in front of each station.