There is a computer system that intends to service multiple users. All tasks from the users have different lengths $($i$.$e$.$ CPU time$),$ usage of the system resources, and urgency. The tasks may arrive in the system at different time. During the execution, all tasks do not require user interventions.

There are two requirements for the system.

Each process should be executed within the first $10$ milliseconds after it arrives in the system.

If some processes cannot complete within $10$ milliseconds, then a shorter process can have a higher priority for execution $($i$.$e$.,$ shortest job first$).$

$1)$ What CPU scheduling algorithm would you use? Your algorithm should satisfy the above two requirements. Explain your idea $(4$ pts$).$

$2)$ How would you avoid the starvation problem in the system? $(2$ pts$)$