Data 604 - Discussion #2

Attempt to complete 2.6 problem 1 from Kelton here (page 35). Discuss your calculations and approaches. See if you can simulate this problem in Simio. Share your work and discuss.

p

p is the steady state utilization of the server (in this case there is only one server)

\[ \begin{equation} p = \frac{\lambda}{\mu} \end{equation} \]

lam <- 1/1.25
mu <- 1

p <- lam/mu
p

## [1] 0.8

# p is less than 1 so we have a stable queue

Lq

Lq is the steady state average number of entities in the queue

\[ \begin{equation} Lq = \frac{p^2}{1-p} \end{equation} \]

Lq <- p^2 / (1-p)
paste(Lq, "minutes")

## [1] "3.2 minutes"

L

L is the steady state average number of entities in the system (rather than the number in queue)

\[ \begin{equation} L = \frac{p}{1-p} \end{equation} \]

L <- p / (1-p)
paste(L, "minutes")

## [1] "4 minutes"

W

W is the steady state average time in the system

\[ \begin{equation} W = \frac{1}{\mu(1-p)} \end{equation} \]

W <- 1 / (mu*(1-p))
paste(W, "minutes")

## [1] "5 minutes"

W

W is the steady state average time in the queue

\[ \begin{equation} W = \frac{p}{\mu(1-p)} \end{equation} \]

Wq <- p / (mu*(1-p))
paste(Wq, "minutes")

## [1] "4 minutes"

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I did something wrong here. Hopefully, we will go over it in the next meetup.

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