Customers arrive at a single self$-$serve coffee machine in a busy mall at the rate of $20$ per hour, following Poisson distribution. Each customer takes exactly $90$ seconds to get his or her coffee. What is the expected number of customers in queue at this coffee machine?

$0\mathrm{.}5$

$3\mathrm{.}0$

$1\mathrm{.}0$

$2\mathrm{.}0$

$1\mathrm{.}5$