Queuing Theory

mydata <- c(90, 53, 94, 303, 138, 116, 179, 82, 78, 64) #data in seconds
mean(mydata)/60 #sample mean in minutes

## [1] 1.995

1/(mean(mydata)/60) #MLE for rate

## [1] 0.5012531

pexp(3, rate=1/2, lower.tail=TRUE) - pexp(1, rate=1/2, lower.tail=TRUE) #bounded CI

## [1] 0.3834005

7*qexp(.1, rate=1/2, lower.tail=TRUE) ; 7*qexp(.9, rate=1/2, lower.tail=TRUE) #80% CI

## [1] 1.475047

## [1] 32.23619

7*qexp(.025, rate=1/2, lower.tail=TRUE) ; 7*qexp(.975, rate=1/2, lower.tail=TRUE) #95% CI

## [1] 0.3544493

## [1] 51.64431