M$/$M$/1$ Queueing System: Problem

Customers arrive at a fast$-$food restaurant as a

Poisson process with an arrival rate of $5$ per min

Customers wait at a cash register to receive

their order for an average of $5$ minutes

Service times to customers are independent and

exponentially distributed

What is the average service rate at the cash

register? $($Answer: $5\mathrm{.}2)$

If the cash register serves $10\%$ faster, what is

the average waiting time of customers?

$($Answer: $1\mathrm{.}39$min $)$