The checkout area of a supermarket has one express cashier who can serve customers

with $12$ items or less, and a regular cashier who can serve any customer regardless of

the number of items bought. Both cashiers have the same service efficiency and enough

space $($i$.$e$.,$ a queue$)$ to accommodate all waiting customers. When a regular customer

$($has more than $12$ items$)$ arrives to the checkout area, the customer joins the regular

cashier$$s queue. However, when an express customer $($has $12$ items or less$)$ arrives to

the checkout area, the customer joins the express cashier$$s queue only if the express

cashier$$s queue length is less than $1\mathrm{.}5$ times the regular cashier$$s queue length. Express

customers represent $60\%$ of the customers, while $40\%$ of the customers are regular

customers. The time between customers$$ arrivals to the checkout area $($Table $1)$ and

service$-$time distributions of express customers $($Table $2)$ and regular customers $($Table

$3)$ are given below.