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Route A

library(Rlab)

## Rlab 2.15.1 attached.

## 
## Attaching package: 'Rlab'

## The following objects are masked from 'package:stats':
## 
##     dexp, dgamma, dweibull, pexp, pgamma, pweibull, qexp, qgamma,
##     qweibull, rexp, rgamma, rweibull

## The following object is masked from 'package:datasets':
## 
##     precip

sim <- data.frame(matrix(, nrow=1000000, ncol=0))
sim$traffic <- round(rnorm(1000000, 1,5))
sim$trafficadjusted<- ifelse(sim$traffic>30,30,ifelse(sim$traffic<0,0,sim$traffic))
sim$emergency <- nrow(sim)
sim$construction <- rbern(n = sim$emergency, prob = 0.03)*5
sim$redlight1 <- nrow(sim)
sim$redlight1<- rbern(n = sim$redlight1, prob= 0.5)*3
sim$redlight2 <- nrow(sim)
sim$redlight2<- rbern(n = sim$redlight1, prob= 0.5)*3
sim$redlight3 <- nrow(sim)
sim$redlight3<- rbern(n = sim$redlight1, prob= 0.5)*3
sim$redlight4 <- nrow(sim)
sim$redlight4<- rbern(n = sim$redlight1, prob= 0.5)*3
sim$redlight5 <- nrow(sim)
sim$redlight5<- rbern(n = sim$redlight1, prob= 0.5)*3
sim$rain<- round(rnorm(1000000, 5,10))
sim$rainadjusted<- ifelse(sim$rain<0,0,sim$rain)
simoveralltime<- sim$trafficadjusted+sim$construction + sim$redlight1+ sim$redlight2+sim$redlight3+sim$redlight4+sim$redlight5+sim$rainadjusted   

summary(simoveralltime)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    0.00   10.00   16.00   17.15   23.00   70.00

plot(simoveralltime)

Route B

library(Rlab)
sim2 <- data.frame(matrix(, nrow=1000000, ncol=0))
sim2$traffic <- round(rnorm(1000000, 5,1))
sim2$trafficadjusted<- ifelse(sim2$traffic>30,30,ifelse(sim2$traffic<0,0,sim2$traffic))
sim2$emergency <- nrow(sim)
sim2$construction <- rbern(n = sim$emergency, prob = 0.01)*5
sim2$redlight1 <- nrow(sim)
sim2$redlight1<- rbern(n = sim$redlight1, prob= 0.33)*2
sim2$redlight2 <- nrow(sim)
sim2$redlight2<- rbern(n = sim$redlight1, prob= 0.33)*2
sim2$redlight3 <- nrow(sim)
sim2$redlight3<- rbern(n = sim$redlight1, prob= 0.33)*2
sim2$redlight4 <- nrow(sim)
sim2$redlight4<- rbern(n = sim$redlight1, prob= 0.33)*2
sim2$redlight5 <- nrow(sim)
sim2$redlight5<- rbern(n = sim$redlight1, prob= 0.33)*2
sim2$redlight6 <- nrow(sim)
sim2$redlight6<- rbern(n = sim$redlight1, prob= 0.33)*2
sim2$redlight7 <- nrow(sim)
sim2$redlight7<- rbern(n = sim$redlight1, prob= 0.33)*2
sim2$redlight8 <- nrow(sim)
sim2$redlight8<- rbern(n = sim$redlight1, prob= 0.33)*2
sim2$redlight9 <- nrow(sim)
sim2$redlight9<- rbern(n = sim$redlight1, prob= 0.33)*2
sim2$redlight10 <- nrow(sim)
sim2$redlight10<- rbern(n = sim$redlight1, prob= 0.33)*2
sim2$rain<- round(rnorm(1000000, 5,10))
sim2$rainadjusted <- ifelse(sim2$rain<0,0, sim2$rain)

sim2overalltime <- sim2$trafficadjusted+sim2$construction+sim2$redlight1+sim2$redlight2+sim2$redlight3+sim2$redlight4+sim2$redlight5+sim2$redlight6+sim2$redlight7+sim2$redlight8+sim2$redlight9+sim2$redlight9+sim2$redlight10+sim2$rainadjusted

summary(sim2overalltime)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##     1.0    13.0    18.0    19.3    24.0    69.0

plot(sim2overalltime)

From the two simulations, Route A takes on average 17 min while route B takes on average 19 min. 75% of time route A will take less than 23 min while route B will take less than 24 min. However max time in route A can reach 69, while Route B it reaches 68. I would say, to save time it will be better to opt for route A.