On the Eecient Scheduling of Non-periodic Tasks in Hard Real-time Systems

This paper proposes eecient scheduling algorithms for the joint scheduling of hard aperiodic, sporadic and periodic real time tasks, in systems based on preemptive, xed-priority dispatching. Our scheme guarantees or rejects hard aperiodic real time tasks without any prior knowledge of their attributes, by managing the idle processor capacity dynamically. The method assigns xed priorities to periodic tasks based on the Deadline Monotonic (DM) scheme and analyzes their schedule oo-line. We derive closed form solutions for the idle processor capacity process Z(t) within a schedule. In the absence of pending dynamic tasks, periodic tasks execute in their earliest possible schedule S F , called the Fixed-Priority First (FPF). Upon the arrival of a non-periodic task Ja, the scheduler directly determines its admissibility, based on closed form equation of the available processor time in the current schedule, until the deadline of Ja. If Ja cannot be guaranteed under FPF, the scheduler evaluates the idle processor capacity of an alternative schedule S L , where periodic tasks are delayed to execute at their latest possible times, called the Latest Deadline Last (LDL). If LDL ooers suucient idle capacity, the scheduler switches all periodic tasks from FPF to LDL, assigns Ja the lowest priority and admits it into the system. Otherwise, it immediately rejects Ja. We develop the theoretical framework and derive eecient algorithms to compute the idle processors capacity Z(a; b) within a time interval a; b], and maintain it when the schedule is adjusted. The algorithms can also reclaim unused capacity from guaranteed tasks. Our admission control procedure has computational complexity (n) when the non-periodic task queue is serviced in FIFO order, with n periodic tasks. Previously proposed methods have pseudopolynomial time and space complexity. Experimental results show that with n = 160 periodic tasks, the actual computation time for the admission control procedure is less than 90-secs on a SUN Ultra-Sparc I, 143MHz machine and less than 30-secs on a SGI Origin 2000, 250MHz workstation. Experiments on well known task sets show overheads which are below 10-secs even for the slowest machine. The proposed methodology easily extends to algorithms that minimize total task tardiness and number of tardy tasks.