Your objective is to test the accuracy of the G/G/1 network model approximation. Consider a line with 4 single machine workstations in series with infinite buffer spaces between the stations. The process parameters for each station are as follows:
Station 1:
Process time distribution: GAMMA
Process parameters:
Alpha = 0.5
Beta = 10
Station 2:
Process time distribution: GAMMA
Process parameters:
Alpha = .4
Beta = 16
Station 3:
Process time distribution: GAMMA
Process parameters:
Alpha = .45
Beta = 13
Station 4:
Process time distribution: GAMMA
Process parameters:
Alpha = .33
Beta = 18
Note that the mean for a gamma distribution = Alpha * Beta
Variance for a gamma distribution = Alpha * Beta*Beta
C2 = Variance/Mean^2 = 1/Alpha
Negative exponential (M) is special case of Gamma distribution with alpha=1
Simulation Steps:
1. Take the single station simulation model (HW 8) and extend it to 4 station model
2. Validate the model by comparing it to 4 station M/M/1 queuing network as follows:
a. calculate the average process time for each station
b. Run the simulation model for 500 parts with 5 replications with arrival rate varying from 0.05 parts//min to 0.15 parts/min with Markovian arrivals
c. compare the cycle time for the simulation model vs. the M/M/1 network model.
3. Now change the processing time distribution for each work station to gamma distribution using the parameters listed above and run the simulation model for three input rates of 0.05, 0.10, and 0.13 parts min.
4. Compare the results of the G/G/1 approximation against the simulation model and validate the approximation.