Many real-time systems include tasks that need to suspend their execution in order to externalize some of their operations or to wait for data, events or shared resources. Although commonly encountered in real-world systems, study of their timing analysis is still limited due to the problem complexity. In this paper, we invalidate a claim made in one of the earlier works [1], that led to the common belief that the timing analysis of one self-suspending task interacting with non-self-suspending sporadic tasks is much easier than in the periodic case. This work highlights the complexity of the problem and presents a method to compute the exact worst-case response time (WCRT) of a self-suspending task with one suspension region. However, as the complexity of the analysis might rapidly grow with the number of tasks, we also define an optimization formulationto compute an upper-bound on the WCRT for tasks with multiple suspendion regions. In the experiments, our optimization framework outperforms all previous analysis techniques and oftenfinds the exact WCRT. Abstract-Many real-time systems include tasks that need to suspend their execution in order to externalize some of their operations or to wait for data, events or shared resources. Although commonly encountered in real-world systems, study of their timing analysis is still limited due to the problem complexity. In this paper, we invalidate a claim made in one of the earlier works [1], that led to the common belief that the timing analysis of one self-suspending task interacting with non-self-suspending sporadic tasks is much easier than in the periodic case. This work highlights the complexity of the problem and presents a method to compute the exact worst-case response time (WCRT) of a self-suspending task with one suspension region. However, as the complexity of the analysis might rapidly grow with the number of tasks, we also define an optimization formulation to compute an upper-bound on the WCRT for tasks with multiple suspendion regions. In the experiments, our optimization framework outperforms all previous analysis techniques and often finds the exact WCRT.

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Owing to the current trends for higher performance and the ever growing availability of multiprocessors in the embedded computing (EC) domain, there is nowadays a strong push towards the parallelization of modern embedded applications. Several real-time task models have recently been proposed to capture different forms of parallelism. However, they do not deal explicitly with control flow information as they assume that all the threads of a parallel task must execute every time the task is activated. In contrast, in this paper, we present a multi-DAG model where each task is characterized by a set of execution flows, each of which represents a different execution path throughout the task code and is modeled as a DAG of sub-tasks. We propose a two-step solution that computes a single synchronous DAG of servers for a task modeled by a multi-DAG and show that these servers are able to supply every execution flow of that task with the required cpu-budget so that the task can execute entirely, irrespective of the execution flow taken at run-time, while satisfying its precedence constraints. As a result, each task can be modeled by its single DAG of servers, which facilitates in leveraging the existing single-DAG schedulability analyses techniques for analyzing the schedulability of parallel tasks with multiple execution flows. ABSTRACTOwing to the current trends for higher performance and the ever growing availability of multiprocessors in the embedded computing (EC) domain, there is nowadays a strong push towards the parallelization of modern embedded applications. Several real-time task models have recently been proposed to capture different forms of parallelism. However, they do not deal explicitly with control flow information as they assume that all the threads of a parallel task must execute every time the task is activated. In contrast, in this paper, we present a multi-DAG model where each task is characterized by a set of execution flows, each of which represents a different execution path throughout the task code and is modeled as a DAG of sub-tasks. We propose a two-step solution that computes a single synchronous DAG of servers for a task modeled by a multi-DAG and show that these servers are able to supply every execution flow of that task with the required cpu-budget so that the task can execute entirely, irrespective of the execution flow taken at run-time, while satisfying its precedence constraints. As a result, each task can be modeled by its single DAG of servers, which facilitates in leveraging the existing single-DAG schedulability analyses techniques for analyzing the schedulability of parallel tasks with multiple execution flows.