14. a. M/M/1 queue with arrival rate \(\lambda\) = 1 per minute and service rate \(\mu\) = 1/.9 per minute.

library(tidyverse)
library(queueing)
mmc_1 <- NewInput.MMC(lambda = 1, mu = 1/.9, c = 1, n = 0, method = 0) %>% QueueingModel()
list(L = L(mmc_1), W = W(mmc_1), Wq = Wq(mmc_1), Lq = Lq(mmc_1), Pn = Pn(mmc_1))

## $L
## [1] 9
## 
## $W
## [1] 9
## 
## $Wq
## [1] 8.1
## 
## $Lq
## [1] 8.1
## 
## $Pn
## [1] 0.1

Model

Simulation Results

25 Hours - Warm up and 25 replication with a confidence interval of [8.793, 9.5906]. I think there are opportunities to try other combinations of warm up and replication but the results look sufficient.