Comparison of hybrid minimum laxity/first-in-first-out scheduling policies for real-time multiprocessors

The behavior of two policies for scheduling customers with deadlines until the beginning of service onto multiprocessors is studied. Both policies attempt to approximate the performance of the minimum laxity (ML) scheduling policy without incurring its complete overhead by dividing the queue in two: one, of maximum size n>0, managed using the minimum laxity policy, and another, of unbounded size, managed in a first-in-first-out manner. One policy, F/ML(n), places the ML queue at the front, i.e. customers finding n or more in the system enter the first-in-first-out (FIFO) queue which in turn feeds the ML queue. The other policy, ML(n)/F, places the ML queue at the back, i.e. arriving customers enter the ML queue and if the total number in the system exceeds n, forces one customer from the ML queue to the FIFO queue. It is shown that these seemingly dissimilar policies exhibit exactly the same behavior for a fixed value of n both when customers are allowed to be discarded when they miss their deadlines before entering service and when they are not allowed to be discarded. Monotonicity properties are established for both policies