Period Optimization for Hard Realtime Distributed Automotive Systems

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Period Optimization for Hard Real-time
Distributed Automotive Systems

• Abhijit Davare1, Qi Zhu1, Marco Di Natale2,
  Claudio Pinello3, Sri Kanajan2, Alberto
  Sangiovanni-Vincentelli1

1 EECS, UC Berkeley 2 General Motors Research 3
Cadence Research Labs
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Motivation Active Safety Applications
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Design Flow
Application
Architecture
Mapping
Implementation
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Contributions

• In industry today, all stages in mapping are
  typically carried out manually
• Capture the period assignment problem with
  mathematical programming
• Flexibility to add additional constraints for
  system-specific situations
• Construct an approximation to efficiently solve
  the problem
• Iterative approach to reduce approx. error

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System Model

• Tasks allocated to ECUs
• Preemptive execution
• Scheduling static priorities
• Messages allocated to buses
• Non-preemptive transmission
• Scheduling static priorities

• Periodic task/message activation
• No synchronization between ECUs/buses
• Communication
• Read latest data value from buffer
• Overwrite old data values

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Problem Inputs

• System Directed Graph
• Nodes are objects (EITHER tasks or messages)
• Edges are communication links (1-place buffers)

• Resource assignment
• Worst case processing time (not shown)
• Priority
• Utilization bounds
• End-to-End latency constraints

T1
M1
T2
M2
T3
T5
M3
T4
T6
M4
T7
M5
T8
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Problem Statement
Assign activation periods for all tasks and
messages such that
1. Set of objects must be schedulable
2. Stay within utilization bounds
3. Satisfy end-to-end latency constraints
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1. Object Schedulability

• Ensure that all objects are processed before
  their subsequent activations

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2. Utilization Bounds

• Resource utilization
• Fraction of time the resource (either ECU or bus)
  spends processing its objects (either tasks or
  messages)
• Utilization bounds less than 100
• To allow for future extensibility
• Intuition Larger periods ? lower utilization

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3. End-to-End Latency
R1
R2
R3
o1
o2
o3
t1
t2
t3



o1
o2
o3

• For each object in the path, add
• Period (ti)
• Worst case response time (ri)

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Worst Case Response Times
Response time (ri) Processing time (ci)
Interference time (wi)
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Periods and Response Times
Tasks
Messages

• Intuition decreasing the period of an object
• Decreases its own contribution to path latency
• Increases the response times of lower priority
  objects on the same resource

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Approach Mathematical Programming

• What?
• Problem represented with
• Set of decision variables
• Constraints
• Objective function
• Why?
• Modifying an object period affects
• Schedulability of the object
• Utilization of the resource
• Latencies of other paths passing through same
  resource
• Additional constraints due to legacy tasks and
  messages
• Challenge
• Capture the problem and obtain efficient runtimes

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Geometric Programming

• Standard Form
• x (x1, x2, , xn) are positive
• g is a set of monomial functions
• f is a set of posynomial functions
• Sum of monomials
• Variables
• Integer real-valued ? Intractable
• Real-valued ? Efficiently solvable (convex
  programming)

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Approximation

• Rationale
• Exact formulation needs integer variables
  (ceiling function)
• MIGP gives no solution even after 6 hours for
  case study
• Approximate the ceiling function
• Constant parameter 0 ai 1
• Approximated worst case response time si

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Approximation Example

• Impact on r3 as t1 changes
• Lower bound
• ? 0
• Upper bound
• ? 1
• If all ai 1, si ri

r3
t1
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Geometric Programming Formulation

• Sets
• Paths?
• Objects
• Resources

• Parameters
• Computation time c
• Variables
• Periods t
• Approx. response times s

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Iterative Procedure to Reduce Error

• Iteratively change ai
• Parameters
• maxIt max. iterations
• errLim max. permissible relative error between
  r and s

(GP)
(Fixpoint)
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Case Study GM Experimental Vehicle

• Functionality
• 92 tasks
• 196 messages
• Architecture
• 38 ECUs
• 4 buses

• End-to-end latency constraints
• 12 source-sink task pairs
• 222 total paths
• Deadlines range from 100ms to 300ms

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Experiments Manual vs. Period Opt.

• GP feasible with all a 1 in 1st iteration
• Solution time 24s

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Experiments Iterative Procedure

• Max. error reduced from 58 to 0.56 in 15
  iterations
• Avg. error (not shown) reduced from 6.98 to
  0.009

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Conclusions

• Problem
• Period assignment for the design of distributed
  automotive applications
• Approach
• Flexible Approximate period assignment with GP
• Effective Iterate to reduce approximation error
• Results for industrial case studies
• Experimental vehicle 0.56 max. error after 6
  minutes
• Fault tolerant vehicle 45 reduction in average
  path latency

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• Questions?