1. 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

2. Motivation: Active Safety Applications
[Source: G. Leen, D. Heffernan, “Expanding Automotive Electronic Systems”, IEEE Computer, 35(1), 1/02, pg ]

3. Design Flow Allocation Priorities Mapping Periods Implementation
Application
Architecture IR
Sensor
Wheel
Fusion
Task
Object
ID Task
Brake
Actuator
Throttle
Nav.
150 ms
225 ms
(Messages)
ECU1
ECU2
ECU3
ECU4
CAN1
CAN2
Allocation
Priorities
Periods
Mapping
Implementation

4. 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

5. System Model Tasks allocated to ECUs Messages allocated to buses…
ECU
Message 1 2
Bus
Tasks allocated to ECUs
Preemptive execution
Scheduling: static priorities
Messages allocated to buses
Non-preemptive transmission
Periodic task/message activation
No synchronization between ECUs/buses
Communication
Read latest data value from buffer
Overwrite old data values
Task
Message
1-place
Buffer

6. Problem Inputs System: Directed Graph ECU1 CAN1 ECU2 ECU3 T1 M1 T2 M2
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
ECU1
CAN1
ECU2
ECU3
100 ms
280 ms T1 M1 T2 M2 T3 2 1 3 4 5 T5 M3 T4
[0.7]
[0.6]
[0.8]
[0.5] T6 M4 T7 M5 T8

7. Assign activation periods for all tasks and messages
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

8. 1. Object Schedulability
Ensure that all objects are processed before their subsequent activations oi
Period (ti)
Response Time (ri)
Interference from other objects on the same resource

9. 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

10. 3. End-to-End Latency For each object in the path, add… … …
End-to-End Latency t1 r1 o1 t2 r2 o2 t3 r3 o3
For each object in the path, add
Period (ti)
Worst case response time (ri)

11. Worst Case Response Times
Pre-emption (pi)
Blocking (bi) + Pre-emption (pi)
Response time (ri) = Processing time (ci) + Interference time (wi)
Tasks
Messages

12. 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

13. 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

14. 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)

15. Approximation Rationale Approximate the ceiling function
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 ≤ αi ≤ 1
Approximated worst case response time: si

16. Approximation Example
Task
Priority c t T1 1 3 t1 T2 2 8 T3 20
Impact on r3 as t1 changes
Lower bound:
 = 0
Upper bound:
 = 1
If all αi = 1, si ≥ ri r3 t1

17. Geometric Programming Formulation
Sets
Paths:
Objects:
Resources:
Parameters
Computation time: c
Variables
Periods: t
Approx. response times: s  =
Minimize the sum of approx. response times
Meet end-to-end latency deadlines
Transformed equations for approx. response times
Ensure schedulability
Meet utilization bounds
Lower and upper bounds for periods

18. Iterative Procedure to Reduce Error
Iteratively change αi
Parameters
maxIt – max. # iterations
errLim – max. permissible relative error between r and s
Start
all αi = 1;
ItCount = 0;
ItCount++;
(s, t) = GP(α);
Calculate r;
ei = (si – ri)/ri;
αi = αi - ei No
 = 1
max(|ei|) < errLim OR
ItCount > maxIt
End
Yes
 = 0.6
(GP) t s r
(Fixpoint)

19. 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

20. Experiments: Manual vs. Period Opt.
GP feasible with all α = 1 in 1st iteration
Solution time: 24s

21. 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%

22. Conclusions Problem Approach Results for industrial case studies
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

23. Questions?