TECS1501-14 ACM-TRANSACTION January 2, 2016 10:1
14:6 J. Sun et al.
Fig. 3. An example CRT task τ .
Fig. 4. An example FJRT task that cannot be ex-
pressed by a CRT model.
model into a regular substructure of the hypergraph, which can subsequently be used205
to construct an equivalent FJRT model for the original CRT model. Finally, we present206
the counterexample of t he parallel task that can be expressed by the FJRT model but207
cannot be expressed by the CRT model.208
Definition 2.5 (Concurrent Real-Time Task System [Ejsing-Duun et al. 2013]). A209
Concurrent Real-Time Task System (CRT) S isatupleS = (τ, J, e, d), where210
—J is a finite set of jobs,211
—e: J → N is a mapping from jobs to worst-case execution times,212
—d: J → N is a mapping from jobs to relative deadlines, and213
—τ is a configuration defined by the following grammar.214
—Configuration: τ ::= T | T τ215
—Task: T ::= j | T
1
xT
2
| S
1
S
2
| T
1
+ T
2
| T
ω
216
—Subtask: S ::= j | S
1
xS
2
| S
1
S
2
| S
1
+ S
2
217
Here, j ∈ J is a job and x ∈ N, T
1
xT
2
is the sequential composition of tasks T
1
and218
T
2
, with interrelease time x, T
1
+ T
2
is the choice between tasks T
1
and T
2
, S
1
S
2
is219
the parallel composition of subtasks S
1
and S
2
,andT
ω
is one or more iterations of T .220
In contrast to the definition of our FJRT model, the CRT model is inductively defined221
by some regular grammar. The grammar of the configuration defines the task system,222
which can be viewed as a composition of arbitrarily many independent tasks running in223
parallel (intertask parallelism). Moreover, a nondeterministic choice between different224
execution paths or subtasks running in parallel can be expressed by the grammar of225
tasks and subtasks. Note that the subtasks defined in the CRT are restricted to not226
include any cycles. This article considers only acyclic parallel subtasks in the FJRT227
model.228
Example 2.6. Figure 3 represents the CRT task τ = ( j
1
30(( j
2
40 j
3
)( j
4
+ j
5
)))
ω
,229
where e( j
1
) = 1, d( j
1
) = 20; e( j
2
) = 4, d( j
2
) = 25; e( j
3
) = 6, d( j
3
) = 25; e( j
4
) =230
2, d( j
4
) = 25; and e( j
5
) = 4, d( j
5
) = 25. As shown in Figure 3, the vertices in the231
graph represent jobs, each labeled with an execution time and a deadline. The arcs in232
the graph represent dependencies between jobs and are labeled with their minimum233
interrelease time.234
The combination of Theorem 2.7 and Example 2.8 proves that our digraph-based235
FJRT model is more expressive than the CRT models.236
THEOREM 2.7. The FJRT model is at least as expressive as the CRT model.237
PROOF. We prove by induction that each grammar rule listed in Definition 2.5 can238
be fully expressed by a substructure of the hypergraph. We do this by first introducing239
the prefix and suffix operations for tasks, as follows.240
ACM Transactions on Embedded Computing Systems, Vol. 15, No. 1, Article 14, Publication date: December 2015.
剩余28页未读，继续阅读
weixin_38747126
- 粉丝: 5
- 资源: 921
我的内容管理
展开
最新资源
- AirKiss技术详解：无线传递信息与智能家居连接
- Hibernate主键生成策略详解
- 操作系统实验：位示图法管理磁盘空闲空间
- JSON详解：数据交换的主流格式
- Win7安装Ubuntu双系统详细指南
- FPGA内部结构与工作原理探索
- 信用评分模型解析：WOE、IV与ROC
- 使用LVS+Keepalived构建高可用负载均衡集群
- 微信小程序驱动餐饮与服装业创新转型：便捷管理与低成本优势
- 机器学习入门指南：从基础到进阶
- 解决Win7 IIS配置错误500.22与0x80070032
- SQL-DFS：优化HDFS小文件存储的解决方案
- Hadoop、Hbase、Spark环境部署与主机配置详解
- Kisso：加密会话Cookie实现的单点登录SSO
- OpenCV读取与拼接多幅图像教程
- QT实战：轻松生成与解析JSON数据
资源上传下载、课程学习等过程中有任何疑问或建议，欢迎提出宝贵意见哦~我们会及时处理！
点击此处反馈
