On-line scheduling of real-time distributed computers with complex communication constraints

Abstract

We consider the scheduling of periodic tasks running on distributed computers. Every execution of a task must meet its deadline. Response time analysis of the tasks is used to prove the schedulabilty of hard real-time distributed systems according the on-line priority rules that schedule the processors and the network. Its main advantage is to take into account the precedence dependencies of the schedules of the tasks on the processors and the messages sent on the network(s). Past works have addressed the issue of tasks related by asynchronous communication constraints with the senders and the receivers working at the same rate. In this paper we study more general relations among tasks when the rates of dependent tasks are not equal. We call such relations generalized communication constraints. Usually distributed systems are scheduled using a synchronization protocol and an on-line scheduling algorithm by processor. We present in this paper a graph theoretical approach to this schedulability analysis. Our algorithm transforms complex communication relations into classical ones, so that the classical scheduling analysis can be fully applied. That transformation is independent of the architecture of the distributed systems and no assumption is made on the synchronization protocol considered.

Modeling Multi-Periodic Simulink Systems by Synchronous Dataflow Graphs

“…Concerning the formalism, Richard et al [22] have developed the principle of generalized dependence to describe a synchronous multi-periodic system. Their equations are similar to those of SDFG.…”

Monoprocessor Real-Time Scheduling of Data Dependent Tasks with Exact Preemption Cost for Embedded Systems

“…In the systems considered, since the tasks can have different execution periods, a consumer task can consume the first data, the last, all the data, or any other combinations of data from a producer task. In [8], when the consumer task has a period greater than or equal to that of the producer task, then the data consumed is the last data produced during the execution of the consumer. The authors transform the extended precedences constraint into a simple precedence constraint by replacing a task τ i by n i = Hn Ti duplicated tasks of period H n (H n is the least common multiple of the periods of the tasks and T i is the period of τ i ).…”

“…each execution of τ j is preceded by an execution of τ i and extended precedence constraints [8], [7], i.e. the tasks do not have the same periods and are executed at different rate.…”

Dynamic priority scheduling of periodic tasks with extended precedences

“…When communicating tasks do not share the same rate, several precedence models have been studied in the literature, which enable to represent different subclasses of extended precedence constraints: problem is, given a task precedence graph (which can contain cycles), given a WCET for each task and assuming that each job is executed on its own processor, to find the task rates in the steady state of the system, such that the jobs are executed as often as possible (the objective is thus quite different from ours). The precedences of the task graph are characterized by 4 natural numbers q, k, q ′ , k ′ such that: ∀n ∈ N, τ i.qn+k → τ j.q ′ n+k ′ • Generalized Precedence Constraints (GPC) presented in [7] are a particular case of Linear Precedence Constraints. The objective is different, the authors focus on the scheduling of periodic tasks, related by generalized precedence constraints given in an acyclic graph.…”

“…For instance, in Figure 4(c), we have a pattern that consists of three successive instances of τ i and one of τ j , where the first instance of τ i (in the pattern) is related to the only instance of τ j in the pattern, and this pattern is repeated indefinitely (patterns are depicted by dotted lines in Figure 4). Generalized precedence constraints [7] can represent constraints like those in Figure 4(d) and 4(c) but not the others. A generalized precedence constraint can be represented using a counting semaphore and we propose a simple extension consisting in allowing semaphore counts to be initialized to a value different from 0.…”