Least Slack Process Next (LSPN) is a real-time scheduler for periodic tasks. Slack is the amount of time between when a task would complete if it started now and its next deadline. Thus it can be expressed as:

Slack = D t C

(1) where D is the deadline time, t is the current time and C is the processor time needed. LSPN selects the task with the minimum slack time to execute next. If two tasks have the same slack, they are serviced based on FCFS. Answer the following questions:

(a) What does it mean for a task to have a slack of 0? [2 pts]

(b) What does it mean for a task to have a negative slack? [2 pts]

(c) How long may the scheduler delay starting a task (and still meet its deadline), if that task has a slack s? [2 pts]

(d) Consider 3 period tasks: A, B and C. Task A has a period 6 and execution time 2, task B has a period of 8 and execution time of 2 and task C has a period of 12 and execution time of 3. Illustrate (by drawing the executions of A, B and C over time) how LSPN would schedule these tasks in comparison to Earliest Deadline First and Rate Monotonic Scheduling. Assume that preemption *may* occur at 4-ms intervals for LSPN.