Chapter 4 Problem # 2

Develop a queueing model for the Simio model from Problem 1 and compute the exact values for the steady state time entities spend in the system and the expected number of entities processed in 100 hours.

lambda <- 120   # arrival rate; entities per hour
mu <- 190       # service rate; entities per hour

## calculate the M/M/1 metrics 

rho <- round(lambda / mu, 4)
L <- round(rho/(1-rho), 4)
W <- round(L/lambda, 4)
Wq <- round(W-(1/mu), 4)
Lq <- round(lambda*Wq, 4)

columns <- c('', 'Utilization', 'Number in System', 'Number in Queue', 'Time in System', 'Time in Queue')
theoretical <- c('Steady State', rho, L, Lq, W, Wq)
simulated <- c('Simulation', 0.6399, 1.8002, 1.1603, 0.0145, 0.0097)

result <- data.frame(rbind(theoretical, simulated)) 
colnames(result) <- columns
rownames(result) <- c()
Utilization Number in System Number in Queue Time in System Time in Queue
Steady State 0.6316 1.7144 1.08 0.0143 0.009
Simulation 0.6399 1.8002 1.1603 0.0145 0.0097

Simio Output

Source: Interarrival Time = Random.Exponential(1/120)
Server: Processing Time = Random.Exponential(1/190)

Units: Hours

Chapter 4 Problem # 3

Using the model from Problem 1, create an experiment that includes 100 rerplications. Run the experiment and observe the SMORE plot for the time entities spend in the system. Experiment with the various SMORE plot setting – viewing the histogram, rotating the plot, change the upper and lower percentile values.

SMORE Plots

Chapter 4 Problem # 9

Replicate the model from Problem 1 using Simio processes. Compare the run times to the model and the model from Problem 1 for 50 replications of length 100 hours.

The simulation using Simio processes ran significantly faster than the run times using the Standary library. Running the Simio process model for 50 replications of 100 hours each saw an average actual run time of approximately 0.8 seconds per replication. Replications using the Standard library took approximately 4.5 seconds per replication.

Chapter 4 Problem # 12

Animate your model from Problem 1 assuming that you are modeling a cashier at a fast food restaurant – the entities represent customers and the server represents the cashier at the cash register. Use Simio’s standard symbols for your animation.

Simio Models for the problems above

All Simio models available here: https://github.com/kfolsom98/DATA604/tree/master/Week5