[PPT] - Semi-Federated Scheduling of Mixed-Criticality System for Sporadic PowerPoint Presentation

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2019/5/16

Semi-Federated Scheduling of Mixed-Criticality System for Sporadic DAG Tasks

NEU & Polyu 1

Tao Yang1, Yue Tang2, Xu Jiang2, Qingxu Deng1, Nan Guan2

1Northeastern University, China, 2The Hong Kong Polytechnic University, Hong Kong

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⚫Background & Contributions ⚫Preliminaries ⚫Semi-Federated Mixed-Criticality Algorithm ⚫Evaluation

Outline

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⚫Background & Contributions ⚫Preliminaries ⚫Semi-Federated Mixed-Criticality Algorithm ⚫Evaluation

Outline

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Mixed-Criticality Systems

Sub-systems with different criticality levels (e.g. avionics):

⚫ Monitoring and control sub-system ⚫ Anti-collision sub-system ⚫ Navigation sub-system ⚫ … ⚫ Infotainment sub-system

high low

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Mixed-Criticality Systems

Characteristics :

More complex functions of system
No reduction in system security requirements

Challenges:

Multicore: no enough analytical techniques
Task parallelization: dependencies and competitions among tasks

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Facing the problem

How to assign computation resources to parallel tasks on a multicore platform while guaranteeing security ?

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Our work Propose a semi-federated mixed-criticality scheduling algorithm

Propose a mapping algorithm: from mixed-criticality tasks to a

middleware layer (mixed-criticality container tasks)

Prove the schedulablity of our proposed algorithm

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⚫Background & Contributions ⚫Preliminaries ⚫Semi-Federated Mixed-Criticality Algorithm ⚫Evaluation

Outline

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Implicit-deadline sporadic parallel
Each task is denoted by a directed acyclic graph

✓ Vertices: sequential subtasks ✓ Edges: dependencies

Two types: low-criticality and high-criticality

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Mixed-Criticality Task Model

v0 v1 v2 v3 v4 v5

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Mixed-Criticality Task Model

WCET of a vertex (subtask): 𝑑𝑂 and 𝑑𝑃
WCET of a task: 𝐷𝑂 and 𝐷𝑃
The longest chain of a task: 𝑀𝑂 𝑏𝑜𝑒 𝑀𝑃
Deadline of a task: 𝐸
Virtual deadline of a task: 𝐸′
Task utilization: 𝑣𝑂 = 𝐷𝑂

𝐸′ 𝑣𝑃 = 𝐷𝑃 𝐸 − 𝐸′

v0 v1 v2 v3 v4 v5

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Existing work: Federated Mixed-Criticality Scheduling

In the worst case, half of the resources are wasted

…

𝟐 + 𝝑 𝟐 + 𝝑 𝟐 + 𝝑

Task types: LH, HVH, HMH
System states: normal state and critical state
Assigning strategy: independently usable cores to each task

in the normal and critical states.

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⚫Background & Contributions ⚫Preliminaries ⚫Semi-Federated Mixed-Criticality Algorithm ⚫Evaluation

Outline

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Architecture of Our Algorithm

Dispatcher: Mapping algorithm

Semi-Federated Mixed-Criticality Algorithm:

Two-level hierarchical scheduling

framework

Top Bottom

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Architecture of Our Algorithm

Dispatcher: Mapping algorithm

Semi-Federated Mixed-Criticality Algorithm:

Two-level hierarchical scheduling

framework

Top-level calculates the mapping from

mixed-criticality tasks to mixed-criticality container-tasks.

Top

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Dispatcher: Mapping algorithm

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Architecture of Our Algorithm Semi-Federated Mixed-Criticality Algorithm:

Two-level hierarchical scheduling

framework

Top-level calculates the mapping from

mixed-criticality tasks to mixed- criticality container-tasks.

Bottom-level schedules mixed-

criticality container-tasks on physical processors.

Bottom

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Mixed-Criticality Container Task

Dispatcher: Mapping algorithm

Processor resources interface

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Mixed-Criticality Container Task

Dispatcher: Mapping algorithm

Processor resources interface
Calculate number of mixed-

criticality container tasks in both normal states and critical states

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Mixed-Criticality Container Task

Dispatcher: Mapping algorithm

Processor resources interface
Semi-federated:

Mixed-criticality container tasks provide virtual resources, so the number of mixed-criticality task can be decimal, avoiding resource waste

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Mixed-Criticality Container Task

Dispatcher: Mapping algorithm

Processor resources interface
If the WCET of a task equals c

when it executes on a unit speed processor, then its WCET on a container-task with speed σ is:

𝒖 = 𝒅 𝝉

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Mapping Algorithm A mixed-criticality task

𝑑𝑤0

𝑂 = 1 𝑑𝑤0 𝑃 = 2,

𝑑𝑤1

𝑂 = 1 𝑑𝑤1 𝑃 = 3

𝑑𝑤2

𝑂 = 1 𝑑𝑤2 𝑃 = 3,

𝑑𝑤3

𝑂 = 1 𝑑𝑤3 𝑃 = 3

𝑑𝑤4

𝑂 = 1 𝑑𝑤4 𝑃 = 3,

𝑑𝑤5

𝑂 = 1 𝑑𝑤5 𝑃 = 2

𝐸 = 13, 𝐸′ = 5

v0 v1 v2 v3 v4 v5

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Mapping Algorithm A mixed-criticality task

v0 v1 v2 v3 v4 v5

𝐷𝑂 = 6, 𝐷𝑃= 16, 𝑀𝑂= 3, 𝑀𝑃= 7 𝑑𝑤0

𝑂 = 1 𝑑𝑤0 𝑃 = 2,

𝑑𝑤1

𝑂 = 1 𝑑𝑤1 𝑃 = 3

𝑑𝑤2

𝑂 = 1 𝑑𝑤2 𝑃 = 3,

𝑑𝑤3

𝑂 = 1 𝑑𝑤3 𝑃 = 3

𝑑𝑤4

𝑂 = 1 𝑑𝑤4 𝑃 = 3,

𝑑𝑤5

𝑂 = 1 𝑑𝑤5 𝑃 = 2

𝐸 = 13, 𝐸′ = 5

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Mapping Algorithm A mixed-criticality task

v0 v1 v2 v3 v4 v5

𝑣𝑂 = 𝐷𝑂 𝐸′ = 6 5 > 1 𝐷𝑂 = 6, 𝐷𝑃= 16, 𝑀𝑂= 3, 𝑀𝑃= 7 𝑑𝑤0

𝑂 = 1 𝑑𝑤0 𝑃 = 2,

𝑑𝑤1

𝑂 = 1 𝑑𝑤1 𝑃 = 3

𝑑𝑤2

𝑂 = 1 𝑑𝑤2 𝑃 = 3,

𝑑𝑤3

𝑂 = 1 𝑑𝑤3 𝑃 = 3

𝑑𝑤4

𝑂 = 1 𝑑𝑤4 𝑃 = 3,

𝑑𝑤5

𝑂 = 1 𝑑𝑤5 𝑃 = 2

𝐸 = 13, 𝐸′ = 5

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A mixed-criticality task

Calculating the mapping

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Mapping Algorithm

v0 v1 v2 v3 v4 v5

𝐷𝑂 = 6, 𝐷𝑃= 16, 𝑀𝑂= 3, 𝑀𝑃 = 7, 𝐸 = 13, 𝐸′= 5 Using our mapping equation:

𝑻𝒋

𝑶 = ൞

𝑣𝑗

𝑂

when 𝑣𝑗

𝑂 < 1

𝐷𝑗

𝑂 − 𝑀𝑗 𝑂

𝐸𝑗

′ − 𝑀𝑗 𝑂

when 𝑣𝑗

𝑂 ≥ 1

𝑻𝒋

𝑷 = ൞

𝑗𝑔 𝑢𝑏𝑡𝑙 𝑗𝑡 𝑀𝑃 𝐷𝑗

𝑃 − 𝑇𝑗 𝑂𝐸𝑗 ′ − 𝑀𝑗 𝑃

𝐸𝑗 − 𝐸𝑗

′ − 𝑀𝑗 𝑃

𝑗𝑔 𝑢𝑏𝑡𝑙 𝑗𝑡 𝐼𝐽

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A mixed-criticality task

Calculating the mapping

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Mapping Algorithm

𝑇𝑂 = 𝐷𝑂 − 𝑀𝑂 𝐸′ − 𝑀𝑂 = 6 − 3 5 − 3 = 𝟐. 𝟔 𝑇𝑃 = 𝐷𝑃 − 𝑇𝑂𝐸′ − 𝑀𝑃 𝐸 − 𝐸′ − 𝑀𝑃 = 16 − 1.5 ∗ 5 − 7 13 − 5 − 7 = 𝟐. 𝟔

v0 v1 v2 v3 v4 v5

𝐷𝑂 = 6, 𝐷𝑃= 16, 𝑀𝑂= 3, 𝑀𝑃 = 7, 𝐸 = 13, 𝐸′= 5

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A mixed-criticality task

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Mapping Algorithm

Normal State 𝜏 = 1 𝜏 = 0.5 𝜏 = 1 𝜏 = 0.5 Critical State

Mapping

v0 v1 v2 v3 v4 v5

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Mixed-Criticality tasks are encapsulated into mixed-criticality

container-tasks

Scheduling these mixed-criticality container-tasks to physical

processors with a partitioned or global algorithm Runtime of a Mixed-Criticality Task

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v0 v1 v2 v3 v4 v5

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Runtime of a Mixed-Criticality Task

Mixed-Criticality tasks are encapsulated into mixed-criticality

container-tasks

➢ Encapsulating the vertex v0

𝜏 =1 𝜏 = 0.5 Normal State 𝑑𝑤0

𝑂 = 1 𝑑𝑤0 𝑃 = 2,

𝑑𝑤1

𝑂 = 1 𝑑𝑤1 𝑃 = 3

𝑑𝑤2

𝑂 = 1 𝑑𝑤2 𝑃 = 3,

𝑑𝑤3

𝑂 = 1 𝑑𝑤3 𝑃 = 3

𝑑𝑤4

𝑂 = 1 𝑑𝑤4 𝑃 = 3,

𝑑𝑤5

𝑂 = 1 𝑑𝑤5 𝑃 = 2

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v0 v1 v2 v3 v4 v5

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Mixed-Criticality tasks are encapsulated into mixed-criticality

container-tasks

➢ Setting the deadline of the mixed-criticality container-task

𝜏 =1 𝜏 = 0.5 Normal State deadline=1

Runtime of a Mixed-Criticality Task

𝑑𝑤0

𝑂 = 1 𝑑𝑤0 𝑃 = 2,

𝑑𝑤1

𝑂 = 1 𝑑𝑤1 𝑃 = 3

𝑑𝑤2

𝑂 = 1 𝑑𝑤2 𝑃 = 3,

𝑑𝑤3

𝑂 = 1 𝑑𝑤3 𝑃 = 3

𝑑𝑤4

𝑂 = 1 𝑑𝑤4 𝑃 = 3,

𝑑𝑤5

𝑂 = 1 𝑑𝑤5 𝑃 = 2

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v0 v1 v2 v3 v4 v5

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Mixed-Criticality tasks are encapsulated into mixed-criticality

container-tasks

➢ Encapsulating the vertex v1

Normal State 𝜏 =1 𝜏 = 0.5 deadline=2

Runtime of a Mixed-Criticality Task

𝑑𝑤0

𝑂 = 1 𝑑𝑤0 𝑃 = 2,

𝑑𝑤1

𝑂 = 1 𝑑𝑤1 𝑃 = 3

𝑑𝑤2

𝑂 = 1 𝑑𝑤2 𝑃 = 3,

𝑑𝑤3

𝑂 = 1 𝑑𝑤3 𝑃 = 3

𝑑𝑤4

𝑂 = 1 𝑑𝑤4 𝑃 = 3,

𝑑𝑤5

𝑂 = 1 𝑑𝑤5 𝑃 = 2

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v0 v1 v2 v3 v4 v5

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Mixed-Criticality tasks are encapsulated into mixed-criticality

container-tasks

➢ Encapsulating the vertex v5

Normal State 𝜏 =1 𝜏 = 0.5 deadline=5

Runtime of a Mixed-Criticality Task

𝑑𝑤0

𝑂 = 1 𝑑𝑤0 𝑃 = 2,

𝑑𝑤1

𝑂 = 1 𝑑𝑤1 𝑃 = 3

𝑑𝑤2

𝑂 = 1 𝑑𝑤2 𝑃 = 3,

𝑑𝑤3

𝑂 = 1 𝑑𝑤3 𝑃 = 3

𝑑𝑤4

𝑂 = 1 𝑑𝑤4 𝑃 = 3,

𝑑𝑤5

𝑂 = 1 𝑑𝑤5 𝑃 = 2

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Mixed-Criticality tasks are encapsulated into mixed-criticality

container-tasks

➢ State transition: normal -> critical

Runtime of a Mixed-Criticality Task

𝜏 =1 𝜏 = 0.5 Additional overload Normal State 𝑑𝑤0

𝑂 = 1 𝑑𝑤0 𝑃 = 2,

𝑑𝑤1

𝑂 = 1 𝑑𝑤1 𝑃 = 3

𝑑𝑤2

𝑂 = 1 𝑑𝑤2 𝑃 = 3,

𝑑𝑤3

𝑂 = 1 𝑑𝑤3 𝑃 = 3

𝑑𝑤4

𝑂 = 1 𝑑𝑤4 𝑃 = 3,

𝑑𝑤5

𝑂 = 1 𝑑𝑤5 𝑃 = 2

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Runtime of a Mixed-Criticality Task

Normal State 𝜏 =1 𝜏 = 0.5 Critical State 𝜏 =1 𝜏 = 0.5

5 5

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Mixed-Criticality tasks are encapsulated into mixed-criticality

container-task

➢ In critical states

Critical State 𝜏 =1 𝜏 = 0.5

v0 v1 v2 v3 v4 v5

Runtime of a Mixed-Criticality Task

deadline

5 5

𝑑𝑤0

𝑂 = 1 𝑑𝑤0 𝑃 = 2,

𝑑𝑤1

𝑂 = 1 𝑑𝑤1 𝑃 = 3

𝑑𝑤2

𝑂 = 1 𝑑𝑤2 𝑃 = 3,

𝑑𝑤3

𝑂 = 1 𝑑𝑤3 𝑃 = 3

𝑑𝑤4

𝑂 = 1 𝑑𝑤4 𝑃 = 3,

𝑑𝑤5

𝑂 = 1 𝑑𝑤5 𝑃 = 2

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Mixed-Criticality tasks are encapsulated into mixed-criticality

container-tasks

Scheduling these mixed-criticality container-task to physical

processor with a partitioned or global algorithm

➢ First, system is in normal state and only normal mixed-criticality container-tasks are scheduled ➢ When the system experiences state transition, all normal mixed-criticality container-tasks are banned from scheduling and only critical mixed-criticality container-tasks can run

Runtime of a Mixed-Criticality Task

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⚫Background & Contributions ⚫Preliminaries ⚫Semi-Federated Mixed-Criticality Algorithm ⚫Evaluation

Outline

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Evaluation

Our task sets are generated based on OpenMP benchmarks

and ompTG tool.

Evaluate the acceptance ratio of task sets with different

normalized utilizations.

We compare our results with those in existing work for

federated mixed-criticality scheduling.

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Evaluation

Semi-federated mixed-criticality algorithm has better schedulability performance

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