For simplicity, let's assume that no requests occur simultaneously across floors. The elevator does not accept requests while in motion. This means you don't need to store requests in a queue. There is no down button on the first floor, and no up button on the third floor.

$$Based on the conditions provided in the question, the user's perspective is from outside the elevator. The elevator only moves to the caller's location and displays the floor number and direction of movement. There is no need to proceed further with moving to any specific floor.

When the elevator moves from the $1$st floor to the $3$rd floor, it will stop at the $2$nd floor before reaching the $3$rd floor $($the $7-$segment LED will display the number $2).$