3rd International Real-Time Scheduling Open Problems Seminar
Undoing the Task:
Moving Timing Analysis back to Functional Models
Marco Di Natale, Haibo Zeng
Scuola Superiore S. Anna – Pisa, Italy
McGill University – Montreal, Canada
Model-based Design
• Popular in many application domains
of real-time systems
– Automotive
– Avionics
• To deal with complexity
– Model everything for design (engineering)
and analysis (science)
– It is necessary to select a modeling language
in the most natural and easy way
• The four tenets on the right are
fundamental to model-based design
• No program by hand
• Starting point is functional model
• Automatic generation of
implementation is key
• Synthesis of tasks, priorities,
allocation, communication
mechanisms …
by Ali Behboodian, DSP
Magazine
Undoing the Task: Moving Timing Analysis back to Functional Models
M. Di Natale, H. Zeng
Undoing the Task
• Real-time research has been looking at ways to look inside the task and
find smaller granularity entities and/or models for conditional execution.
• Examples:
– Task graphs (see left)
– Identify a task
segment to be
managed without
preemption (see [1])
– Identify a task
segment to be
executed at a different
priority level (see [2])
–…
[1] M. Bertogna, G. Buttazzo, and G. Yao, “Improving feasibility of fixed priority tasks using non-preemptive
regions”, RTSS 2011
[2] R. Davis and A. Wellings, “Dual Priority Scheduling” RTSS, 1995.
Undoing the Task: Moving Timing Analysis back to Functional Models
M. Di Natale, H. Zeng
Synchronous Models: Simulink/Stateflow
• Synchronous FSMs are used in the most popular model-based
design tools
– SCADE
– Simulink/Stateflow
e1=2ms
e2=5ms
i1
e1/{action1();o1}
S1
o1
0.25
i2 e2/{action2();o2}
o2
e1/{action3();o1} 2
0.3
in
S2
0.1
1
S3
om
0.15 e2/{action4();o2}
The system is a network of
“dataflow” blocks and
Stateflow (EFSM) blocks
Where are the tasks?
Timing constraints?
Undoing the Task: Moving Timing Analysis back to Functional Models
M. Di Natale, H. Zeng
Problem Statement: Input
• System is a network of blocks bj of two types
– Regular (Dataflow):
• period Tj (an integer multiple of a system-wide base periodTb)
• inputs ij,p.
• at each kTj output and state are updated, with a WCET gj.
– State machine (Stateflow):
• can have multiple activation events ej,p.
• at any multiple of the event periods kTj,p, different transitions may be taken.
• each update function has a WCET labeled as gj,q
• Order of execution
– For two communicating blocks
bi
– If bj has a feedthrough semantics, then bi → bj
– This partial order of execution of functions can be enforced by
static code scheduling inside the task or by the scheduler
– This precedence constraint can be avoided by adding a delay
bj
Undoing the Task: Moving Timing Analysis back to Functional Models
M. Di Natale, H. Zeng
Problem Statement: Input
4 3 2
A
Behavior in Simulation
zero logical execution time
zero logical communication time
T=1
C
T=4
B
D
T=1
4
T=2
2 1 0
4
2
2
A B
D
fc(4,2)
C
tv=0: A,B,D,C
4 2
A B
3 1 2 0
A B A B
D
tv=1:A,B tv=2: A,B,D
3 1
A B
2 0
A B
D
4
tr=0
Order in simulation: A->B->D->C
C
tr=1
1
fc(4,1)?
C
tr=2
Behavior in Implementation
 The requirement of preserving
the behavior in functional model
can impose additional constraints
• Either tighter deadline for block C
• Or other mechanisms (but possibly
with memory overhead)
Undoing the Task: Moving Timing Analysis back to Functional Models
M. Di Natale, H. Zeng
Problem Statement
• Unlike traditional manual programming, in MBD
– the task (or threads) model becomes an intermediate artifact
– the timing analysis becomes part of a synthesis problem (to
facilitate automatic code generation)
• Analysis problem
– deadline may depends on the function-to-task mapping
– additional requirements from the correct implementation of
function models
• Synthesis problem:
–
–
–
–
mapping functions into tasks
assigning the execution order of functions inside tasks,
assigning the task parameters (priority, deadline, offset)
assigning scheduling attributes to functions (including
preemptability and preemption threshold)
– designing communication
Undoing the Task: Moving Timing Analysis back to Functional Models
M. Di Natale, H. Zeng
Example Open Problem
• Given
– functional model (composed of multiple communicating state
machine blocks and dataflow blocks)
– a multicore platform as the implementation architecture
• Find
– mapping of state machine actions and block reactions onto tasks
– placement of tasks onto the cores
– assignment of task activation offsets and priorities
• Such that
– functional model semantics are preserved
– each block finish in time for the follower blocks
Undoing the Task: Moving Timing Analysis back to Functional Models
M. Di Natale, H. Zeng
Example Open Problem II
• Given
– functional model (composed of multiple communicating state
machine blocks and dataflow blocks)
– a multicore platform as the implementation architecture
• Find
–
–
–
–
mapping of state machine actions and block reactions onto tasks
placement of tasks onto the cores
assignment of task activation offsets and priorities
assignment of preemption thresholds to actions inside the tasks
• Such that
– functional model semantics are preserved
– each block finish in time for the follower blocks
– memory usage is minimized
Undoing the Task: Moving Timing Analysis back to Functional Models
M. Di Natale, H. Zeng
Thank you!
Initial discussion on the example problems
[3] M. Di Natale and H. Zeng, “Task implementation
of synchronous finite state machines,” in Proc. the
Conference on Design, Automation, and Test in
Europe, 2012.
[4] H. Zeng and M. Di Natale, “Schedulability
Analysis
of
Periodic
Tasks
Implementing
Synchronous Finite State Machines,” in Proc. 23rd
Euromicro Conference on Real-Time Systems,
2012.
Undoing the Task: Moving Timing Analysis back to Functional Models
M. Di Natale, H. Zeng
Baseline (Single-Task) Implementation
The generated code
runs in the context of a 1
ms task (gcd), but
reactions do not occur
every 1ms
e1=2ms
e2=5ms
e1/{action1();o1}
0.25
i1
S1
i2
e2/{action2();o2}
in
o2
e1/{action3();o1} 2
0.1
0.3
o1
S2
1
S3
0.15
om
A single task forces the
execution of all the
actions at the same
priority level
e2/{action4();o2}
Simple periodic model: Worst-case exec time of a reaction to any event –
Undoing the Task: Moving Timing Analysis back to Functional Models
deadline at 1ms – quite pessimistic
M. Di Natale, H. Zeng
Partitioned (Multi-task) Implementation
Applicable if the priority of a
transition is determined by
the corresponding event
e1=2ms
e2=5ms
i1
i2
e1/{action1();o1}
0.25
S1
o1
o2
e2/{action2();o2}
0.3
in
e1/{action3();o1}2
0.1
e2=5ms
1
om
S3
0.15
e1=2ms
S2
e2/{action4();o2}
One task for each event rate.
• Priority of transitions is
handled by task priorities
• Single reaction execution by
an “inhibit signal”
• Atomicity (state consistency)
by deadlines.
Undoing the Task: Moving Timing Analysis back to Functional Models
M. Di Natale, H. Zeng