Optimizing QoS in energy-aware real-time systems

Abstract

We consider the problem of optimizing application quality of service subject to energy and real-time constraints. The system is composed of n sporadic and independent real-time tasks to be scheduled on a single CPU capable of operating at different frequency/voltage levels, which can be selected at run-time. Each task i may run at a selected frequency fi and mode of operation ki with each mode inducing a quality of service level. Due to schedulability and energy bounds, CPU frequencies and task modes should be selected by the system aiming at maximizing the overall system quality of service, an optimization problem formulated as:where QoS represents the considered objective function, and constraints (1b) and (1c) are related to bounds on CPU (ub) and energy (eb), respectively. The set F may contain either the CPU frequency values allowed or represents a continuous frequency interval, a usual frequency model assumed in literature [1]. The set Ki represents a discrete set of modes that task i may operate. Different classes of optimization problems, with distinct degrees of difficulty, can be obtained depending on how F and Ki are modeled. In any case, the objective function QoS must capture some aspects: (I) mode degradation with priority given to the high quality operational modes; (II) task value which is associated with every task being strongly related to the application semantics; (III) task weight specifying the processing resources required by each task, thus a task that requires 10% of CPU should be treated differently from one that requires only 1%, possibly by receiving a higher task weight. Function (2) takes these aspects into account:where Ki = {1, 2, . . .} has the indices of the task modes and wi ∈ [0, 1] is the task value. Mode ki has quality higher than mode k i whenever ki > k i . Notice that QoS will be a value between 0 and 1 since the CPU utilization ui(fi, ki) cannot exceed the unit. The reduction of CPU frequency results in an increase of task execution time which can further delay the completion of the tasks, specially those that need more resources than predicted, a common scenario for soft real-time systems. For this reason the task values should be adjusted depending on the CPU frequency, with higher values for tasks running at high frequency. Assuming that wi = f 2 i , F = {100%, 50%, 25%} and a task with 3 modes, where the utilization at fi = 100% are respectively 0.042, 0.34, 0.60, the QoS function (2) ensures that a configuration with high mode and frequency will always have greater value/system benefit, thereby avoiding unnecessary degradation of the system as shown in Table 1. Table 1: Task configuration benefits QoS(fi, ki) ki = 1 ki = 2 ki = 3 QoS(100%, ki) 0.014 0.448 0.866 QoS(50%, ki) 0.007 0.391 0.766 QoS(25%, ki) 0.003 0.362 0.716 Scheduling problems can be modeled as continuous or discrete as shown in [3]. Continuous and convex models can be efficiently solved by interior-point methods [2]. Discrete models can be solved with relaxation-based heuristics [3,4] or with speciali...

A Model Considering QoS for Real-Time Systems with Energy and Temperature Constraints

“…To control CPU temperature and save energy the CPU Dynamic Voltage and Frequency Scaling (DVFS) is a technique commonly used in real-time systems, such as the system discussed in [2], [3], [4], [5], [6] that offer guarantees on minimal energy savings and improve the system quality of service. For example, in [6], QoS increases as the probability of deadline task miss decreases.…”

“…In [4], [5] it is proposed an on-line mechanism that guarantees energy savings, ensures schedulability, and avoids QoS degradation. Nevertheless, this mechanism does not take into account the temperature effects.…”

“…muAccording to [4], the task profit must capture aspects as the task weight, the degradation of execution quality, and its importance for the system as the function below:…”