Waiting Line $($Queuing$)$ Systems$-$Homework

A small town post office employs a single postal worker. Customers arrive at the postal branch at a rate of $30$ customers per hour. The average service time at the post office is $1\mathrm{.}5$ minutes per customer. Calculate the following performance measures for this $\frac{M}{M}\frac{?}{1}$ system.

$=$

$=$

$=\frac{}{}=$

$L=\frac{}{-}=$

$L_Q=L=$

$W=\frac{1}{-}=$

$W_Q=W=$

$P_{10}=(1-){}^{10}=$

$P_{15+}={}^{16}=$

What are your conclusions about the performance of the post office's waiting system?

$2.$ A fast food restaurant has a single drive$-$thru lane. A single customer service window is used to place orders, make the cash transaction, and deliver the food. Customers arrive at the window at an average of $40$ customers per hour. The fast food worker has an average service time of $1$ minute for each customer. Calculate the following performance measures for this $\frac{M}{M}\frac{?}{1}$ system.