The meaning and role of value in scheduling flexible real-time systems

Quasi-Static Scheduling for Multiprocessor Real-Time Systems with Hard and Soft Tasks

“…We can define, for instance, a switching point Ω t 1 ; [2,6] −−−→ Ω for the example given in Figure 2, with Ω = {t 1 t 3 t 5 , t 2 t 4 t 6 t 7 } and Ω = {t 1 t 5 t 3 , t 2 t 4 t 6 t 7 }, such that the system starts executing according to the schedule Ω; when t 1 completes, if 2 ≤ τ 1 ≤ 6 the tasks not yet started execute in the order given by Ω , else the execution order continues according to Ω. While the solution {Ω, Ω } as explained above guarantees meeting the hard deadlines, it provides a total utility which is greater than the one by the static schedule Ω in 43% of the cases at a very low on-line overhead.…”

“…Another quasi-static solution, similar to the one discussed above, is {Ω, Ω } but with Ω t 1 ; [2,7] −−−→ Ω which actually gives better results (it outperforms the static schedule Ω in 56 % of the cases and yields an average total utility 1.1, yet guaranteeing no hard deadline miss). Thus the most important question in the quasi-static approach discussed in this report is how to compute at design-time the set of schedules and switching points such that they deliver the highest quality (utility).…”

“…In this case the initial schedule is Ω = {t 1 t 3 t 5 , t 2 t 4 t 6 t 7 }, that is, t 1 and t 2 start executing at time zero and their completion time intervals are [2,10] and [1,4] respectively. We initially consider two situations: t 1 completes before t 2 (2 ≤ τ 1 ≤ 4); t 2 completes before t 1 (1 ≤ τ 2 ≤ 4).…”

“…We initially consider two situations: t 1 completes before t 2 (2 ≤ τ 1 ≤ 4); t 2 completes before t 1 (1 ≤ τ 2 ≤ 4). For the first one, we computeÛ i (τ 1 ), 2 ≤ τ 1 ≤ 4, for each one of the Ω i that satisfy the precedence constraints, and we find that Ω = {t 1 t 5 t 3 , t 2 t 4 t 7 t 6 } is the schedule to follow after t 1 completes before t 2 at τ 1 ∈ [2,4]. For the second situation, in a similar manner, we find that when t 2 completes before t 1 in the interval [1,4], Ω = {t 1 t 3 t 5 , t 2 t 4 t 6 t 7 } is the schedule to follow.…”

“…Utility-based scheduling [2], [15] has been addressed before, for instance, in the frame of imprecise computation techniques [20], [9]. These assume tasks as composed of a mandatory and an optional part: the mandatory part must be completed by its deadline and the optional one can be left incomplete at the expense of the quality of results.…”