Consider the following preemptive priority-scheduling algorithm based on dynamically changing priorities. Larger numbers imply higher priority. Tasks are preempted whenever there is a higher priority task. When a task is waiting for CPU (in the ready queue, but not running), its priority changes at a rate of a:

P(t) = P₀ + a (t - t₀)

where t₀ is the time at which the task joins the ready queue and P₀ is its initial priority, assigned when the task enters the ready queue or is preempted. Similarly, when it is running, the tasks priority changes at a rate b. The parameters a, b and P₀ can be used to obtain many different scheduling algorithms.

a. What is the algorithm that results from P₀ = 0 and b > a > 0?

b. What is the algorithm that results from P₀ = 0 and a < b < 0?

c. Suppose tasks are assigned a priority 0 when they arrive, but they retain their priority when they are preempted. What happens if two tasks arrive at nearly the same time and a > 0 > b?

d. How should we adjust the algorithm to eliminate this pathology?