vbriot_hw5

Problem 2, Chapter 4

In this problem we will compare a M/M/1 queue with arrival rate, \(\lambda\)=120/hour and service rate, \(\mu\)=190/hour. We are interested in the following steady stae measures: time entities spent in system and expected number of entities processed in 100 hours.

W denotes the steady-state average time in the system and \(W=\frac { 1 }{ \mu -\lambda }\)

We will determine the number of expected entities processed by dividing the 100 hours by W and truncating to a round number.

Calculation will be done in R.

l <- 120
m <- 190

W <- 1/(m-l)

Entities <- floor(100*l)

W

## [1] 0.01428571

Entities

## [1] 12000

We will compare with result of simulation ran for 100 hours.
Result of simulation we have Average time in system = 0.0145 and number of entities processed = 11935 in 100 hours of simulations.

m/m/1 100 hours simulation run

Please note that when we ran model and capature statistic, we did not account for warm-up period.

Problem 3, chapter 4

Using the model previously set-up, we ran experiment of 100 repetitions. We set-up warm-up time to be 50 hours.

m/m/1 SMORE example

Problem 9, chapter 4

We will now build a simio model m/m/1 using processes instead of objects from standard library.

m/m/1 Model built using processes

Running the simulation for 50 repetitions of 100 hours.

m/m/1 Model built using processes Results

The results are similar than the one obtained by building the model using standar library objects.

Problem 12, chapter 4

m/m/1 Model Animation