The Optimality of PFPasap Algorithm for Fixed-Priority Energy-Harvesting Real-Time Systems

Abstract

The paper addresses the real-time fixed-priority scheduling problem for battery-powered embedded systems whose energy storage unit is replenished by an environmental energy source. In this context, a task may meet its deadline only if its cost of energy can be satisfied early enough. Hence, a scheduling policy for such a system should account for properties of the source of energy, capacity of the energy storage unit and tasks cost of energy. Classical fixed-priority schedulers are no more suitable for this model. Based on these motivations, we propose P F PASAP an optimal scheduling algorithm that handles both energy and timing constraints. Furthermore, we state the worst case scenario for non concrete tasksets 1 scheduled with this algorithm and build a necessary and sufficient feasibility condition for non concrete tasksets. Moreover, a minimal bound of the storage unit capacity that keeps a taskset schedulable with P F PASAP is also proposed. Finally, we validate the proposed theory with large scale simulations and compare our algorithm with other existing ones.

Periodic charging scheme for fixed-priority real-time systems with renewable energy

“…The total power P σ0 consumed by the system in the active state is the sum of processor power and total power consumption of the specific subsets of peripherals in use by the running task; thus, at any time, P CP U ≤ P σ0 ≤ P CP U + P dev . As in [7], [8], we do not assume DVFS capability in the system; i.e., task execution takes place at a constant frequency level.…”

“…In systems with renewable energy, the concept of feasibility is extended to consider also battery (or, energy) failures ( [7], [8]). Specifically, in addition to guaranteeing task completions no later than their respective deadlines, in order to ensure feasibility, the algorithm must also guarantee that the battery level never drops below a certain threshold E low : ∀t, E(t) > E low .…”

“…• P F P asap : the computation-greedy algorithm whose optimality for fixed-priority systems with renewable energy, but only under negligible state transition overheads assumption, was formally proven in [8]; • P F P st (also called EDeg, from [7]): the energy-greedy algorithm whose feasibility performance was shown to lag slightly behind P F P asap in [8]; • P CS * that evaluates only the sufficient condition given by Eq. (2) at design time, to guarantee the feasibility;…”

“…For fixed-priority real-time embedded systems which are more common in practice, the two well-known algorithms are P F P st (also called EDeg) [7] and P F P asap [8], that represent energy-greedy and computation-greedy algorithms, respectively. In particular, P F P asap is shown to be optimal in [8]: any task set that can be feasibly scheduled by any other fixed-priority energy-harvesting scheduling algorithm can be also scheduled by P F P asap .…”

“…In particular, P F P asap is shown to be optimal in [8]: any task set that can be feasibly scheduled by any other fixed-priority energy-harvesting scheduling algorithm can be also scheduled by P F P asap . On the other hand, the same paper shows that in terms of the preemption numbers and other run-time overhead metrics, P F P st has a clear advantage, while its average feasibility performance lags behind P F P asap by a small margin.…”