Translating Offline Schedules into Task Attributes for Fixed Priority Scheduling

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Combining Off-line Schedule Construction and
Fixed Priority Scheduling in Real-Time Computer
Systems

• Radu Dobrin

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Outline

• Real-Time Systems
• Off-line vs. Fixed Priority Scheduling (FPS)
• Problem Formulation
• Application Areas
• Proposed Solution
• Summary

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Real-Time Systems

• Computer systems in which the correctness of the
  system depends not only on the logical
  correctness of the computations performed, but
  also on the time factors (Stankovic et. al.)
• Hard
• no deadlines may be missed (avionics, nuclear
  power plantsetc)
• Soft
• some deadlines may be missed (multimedia
  applications)
• In between
• weakly hard RTS (Bernat et. al.)
• n of m consecutive deadlines may be missed

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Real-Time Systems

• Resources
• one or several processors
• network (if distributed RTS)
• Tasks
• periodic
• an infinite sequence of invocations (instances or
  jobs)
• non-periodic
• aperiodic, sporadic, etc
• Scheduler
• makes the decision which task to execute (on
  which processor) at each point in time based on
  the scheduling policy

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Real-Time Systems

• Scheduling policy
• This talk
• off-line (table driven) scheduling
• pre-runtime allocation of tasks to processors
• priority-driven (on-line) scheduling
• fixed priority scheduling (FPS)
• dynamic priority scheduling (e.g., EDF)

in hard real-time systems
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Off-line (table driven) scheduling

• off-line allocation of time-slots to tasks
• run-time dispatcher selects task from scheduling
  tables

A
B
C
D
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Off-line (table driven) scheduling

• off-line allocation of time-slots to tasks
• run-time dispatcher selects task from scheduling
  tables
• ? misc. complex constraints (instance
  separation, jitter, engineering practice
  constraints )
• ? predictability
• ? determinism
• ? inflexible, task executions fixed
• ? need to know all task attributes before
  run-time

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Fixed Priority Scheduling (FPS)

• schedulability test performed off-line
  guarantees
• on-line servers to handle non-periodic events
• scheduling decisions made at run-time

A
B
C
D
A
B
D
B
C
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Fixed Priority Scheduling (FPS)

• schedulability test performed off-line
  guarantees
• on-line servers to handle non-periodic events
• scheduling decisions made at run-time
• ? widely used (automotive industry, network
  scheduling - CAN)
• ? flexible
• ? simple run-time mechanism
• ? small run-time overhead
• ? ability to handle complex constraints
• ? additional constraints new
  schedulability tests

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Proposed solution

• We want to combine the advantages provided by
  both
• methods that transform off-line schedules into
  attributes for fixed priority scheduling
• execution of fixed priority tasks reenacts
  original off-line schedule at run-time, if
  scheduled by FPS

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Proposed solution
FPS
Off-line scheduling

• ? ability to handle complex constraints ?
  predictability

? simple run-time mechanism ? run-time flexibility
FPS
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Application scenarios
Off-line sched. based system
We have
Our method
FPS schedule
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Application scenarios
FPS system
We have
We want
FPS system
FPS schedule
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Outline

• Real-Time Systems
• Off-line vs. Fixed Priority Scheduling (FPS)
• Problem Formulation
• Application Areas
• Proposed Solution
• Summary

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Off-line to FPS transformation

• Method to transform off-line schedules into
  attributes for fixed priority scheduling
  overview
• Input off-line schedule and target windows
  (feasible time intervals for task executions)
• derive sequences of task executions from
  overlapping target windows
• derive priority inequalities
• solve inequalities by Integer Linear Programming
  (ILP)
• Output minimum number of FPS tasks and priority
  levels

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Off-line to FPS transformation
Target Windows feasible time intervals for
task executions under FPS
ex periodic task with simple constraint (dl)
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Off-line to FPS transformation
Target Windows feasible time intervals for
task executions under FPS
ex periodic task with an instance separation
constraint
A
A
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Off-line to FPS transformation

• first task set with original constraints and
  off-line schedule

• split off-line schedule into target windows

• derive sequences of instances (each start of
  TW)

TW(A)
TW(B)
TW(C)
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Off-line to FPS transformation

• first task set with original constraints and
  off-line schedule

• split off-line schedule into target windows

• derive sequences of instances (each start of
  TW)

A
TW(A)
B
B
TW(B)
C
TW(C)
SEQk
ltA gt
B ordered
ltBAgt
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Off-line to FPS transformation

• first task set with original constraints and
  off-line schedule

• split off-line schedule into target windows

• derive sequences of instances (each start of
  TW)

A
TW(A)
B
B
TW(B)
C
TW(C)
tk
SEQk
ltA gt
B ordered
ltBAgt
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Off-line to FPS transformation

• first task set with original constraints and
  off-line schedule

• split off-line schedule into target windows

• derive sequences of instances (each start of
  TW)

A
TW(A)
B
TW(B)
C
C
TW(C)
SEQk1
ltC gt
A ordered
ltACgt
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Off-line to FPS transformation

• first task set with original constraints and
  off-line schedule

• split off-line schedule into target windows

• derive sequences of instances (each start of
  TW)

• derive priority inequalities to reflect order
  of execution in the sequences

gt priority(B)gtpriority(A)
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Off-line to FPS transformation

• first task set with original constraints and
  off-line schedule

• split off-line schedule into target windows

• derive sequences of instances (each start of
  TW)

• derive priority inequalities to reflect order
  of execution in the sequences

• problem inconsistent priorities for instances
  of same task (not all off-line schedules can be
  expressed by FPS)

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Off-line to FPS transformation

• first task set with original constraints and
  off-line schedule

• split off-line schedule into target windows

• derive sequences of instances (each start of
  TW)

• derive priority inequalities to reflect order
  of execution in the sequences

• problem inconsistent priorities for instances
  of same task (not all off-line schedules can be
  expressed by FPS)

• solution modify the problem
• treat task instances as new tasks artifacts
• which ones?
• potentially many artifacts?

• use Integer Linear Programming to
• solve priority inequalities
• minimize number of artifacts

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ILP formulation
Input - priority inequalities, total nr. of
instances Goal function min G
fps_tasks original_tasks (
instances(Ti) - 1)bi Subject to
constraints transformed from the priority
inequalities 1 create artifacts for
Tis instances bi 0 leave
unchanged Output - bi (which tasks to split)
- priorities for fps_tasks
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Temporal analysis

• transformed FPS tasks execute within derived
  target windows at run-time
• order of execution specified in off-line schedule
  preserved? at run-time, if required by original
  constraints
• ? exact reenaction of off-line schedule by
  adjusting target windows

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So far
Target windows
Offline schedule
input
instance sequences
priority inequalities
FPS tasks
output
guaranteed
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So far

• resolved attribute assignment problem in FPS for
  multiple complex timing constraints
• can be used in CAN scheduling
• scheduling messages with complex timing
  requirements
• better results than processor scheduling
• legacy systems
• upgrade/migrate while preserving constraint
  guarantees
• optimization techniques to minimize costs
• if an off-line schedule exists, we can transform
  it to FPS!

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So far

• FPS
• ability to handle complex constraints
• predictability
• ? simple run-time mechanism
• ? run-time flexibility

v
v
v
?
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Next handling non periodic events?

• Usually done by using FPS servers
• non-capacity preserving
• e.g., background scheduling, polling server
• capacity preserving
• e.g., deferrable servers, slack stealing
• RM based analysis exists
• our task model is not RM based!
• no optimal server exists
• our goal
• use servers to provide good service to
  non-periodic tasks
• use/tweak existing ones?
• develop new ones?
• still guarantee complex constraints on periodic
  tasks

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Using non-capacity preserving servers

• Easy server does not suspend itself
• Off-line
• include server in off-line schedule construction
• together with complex constrained periodic tasks
• derive FPS attributes for both server and
  periodic tasks
• On-line
• if server active and non-periodic request pending
• WCET(server)server capacity
• else
• BCET(server) 0

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Using capacity preserving servers

• Difficult server may execute unpredictable at
  any time during period
• difficult to include in off-line schedule
  construction
• additional interfering instances to the sequences!

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Using capacity preserving servers

• Difficult server may execute at any time during
  period
• difficult to include in off-line schedule
  construction
• additional interfering instances to the sequences!

A
TW(A)
B
S
TW(B)
C
C
TW(C)
SEQk1
ltC gt
A ordered
ltACgt
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Using capacity preserving servers

• Solution
• take into account potential interference?
• pessimistic over constraining the LP
  formulation
• provide users set of deadlines to prevent
  undesired interference
• assign server highest feasible priority while
  guaranteeing completion before new deadlines

dl(B)
A
TW(A)
B
S
S
TW(B)
C
C
TW(C)
SEQk1
ltC gt
A ordered
ltACgt
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Example
constraints (for LCM)


polling server (S,T6,C1)
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Example
constraints (for LCM)


polling server (S,T6,C1)
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Example
constraints (for LCM)


polling server (T6,C1)
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Inequalities
prio(S)gtprio(C)
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Inequalities
prio(S)gtprio(C)
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Inequalities
prio(S)gtprio(C)
prio(A)gtprio(C)
prio(C)gtprio(B)
prio(S)gtprio(B)
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Inequalities
prio(S)gtprio(C)
prio(A)gtprio(C)
prio(C)gtprio(B)
prio(S)gtprio(B)
prio(B)gtprio(C)
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Inequalities
prio(S)gtprio(C)
prio(A)gtprio(C)
prio(C)gtprio(B)
prio(S)gtprio(B)
prio(B)gtprio(C)
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Inequalities
prio(S)gtprio(C)
prio(A)gtprio(D)
prio(C)gtprio(B)
prio(S)gtprio(B)
prio(B)gtprio(C)
prio(A)gtprio(B)
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Inequalities
prio(S)gtprio(C)
prio(A)gtprio(D)
prio(C)gtprio(B)
prio(S)gtprio(B)
prio(B)gtprio(C)
prio(A)gtprio(B)
prio(A)gtprio(S)
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Inequalities
prio(S)gtprio(C)
prio(A)gtprio(C)
prio(C)gtprio(B)
prio(S)gtprio(B)
prio(B)gtprio(C)
prio(A)gtprio(B)
prio(A)gtprio(S)
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Inequalities
prio(S)gtprio(C)
prio(A)gtprio(C)
prio(C)gtprio(B)
prio(S)gtprio(B)
prio(B)gtprio(C)
prio(A)gtprio(B)
prio(A)gtprio(S)
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Inequalities
prio(S)gtprio(C)
prio(A)gtprio(C)
prio(C)gtprio(B)
prio(S)gtprio(B)
prio(B)gtprio(C)
prio(A)gtprio(B)
prio(A)gtprio(S)
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Example
FPS tasks
Off-line scheduled tasks
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Example
J1
J2
J2
S (prio 4)
A (prio 5)
A
A
B (prio 2)
B
B
B
C1 (prio 3)
C1
C1
C2 (prio 1)
C2
C3 (prio 1)
C3
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Example
J1
J2
J2
S (prio 4)
A (prio 5)
A
A
B (prio 2)
B
B
B
C1 (prio 3)
C1
C1
C2 (prio 1)
C2
C3 (prio 1)
C3
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Example
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Example
guaranteed
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Conclusions and future work

• Conclusions
• Transforming off-line scheduled tasks into FPS
  tasks to reenact original off-line schedule at
  run-time
• create artifacts if attribute inconsistency
• ILP used to minimize the number of artifacts
• non-periodic events handled by existing FPS
  servers
• periodic servers include into off-line schedule
  construction
• capacity preserving servers provide means to
  use while guaranteeing periodic task constraints
• Ongoing work
• include fault tolerant aspects

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