1. Real-Time Calculus (RTC) Reading Group I
Nan Guan

2. About the Reading Group
Thursday 18:00~20:00
For schedule see
Each time, decide the speaker for the session after the next one
Every attendance holds a session
Sooner or later …

3. About the Reading Group
The speaker may use
White board
Slides …
Other attendance should preview the topic
Important
This is an intensive “course”

4. About the Reading Group
Any people can ask any question during the session, but
Please don’t significantly postpone the progress
(Offline discussions on details are encouraged)
Each session takes up to 2 hours
It can be as short as the speaker wants
(as long as the speaker makes everything clear)

5. About the Reading Group
Share with others if you have good ideas or you are doing something relevant
I have some potential research topics
Talk to me (or Mingsong) if you have interests

6. No Title
“How long does it at most take to walk from your home to this building?”

7. No Title
Approach 1:
Try it for, say, 100 times, measure the time for each time, and find the maximum
Cons?
Pros?

8. No Title Approach 2: Lookup the absolute distance between
Estimate the walking speed

9. No Title Approach 2: Lookup the absolute distance between
Estimate the walking speed
We know physics!
T = S / V

10. No Title Approach 3: Lookup the route distance between
Estimate the walking speed
Consider the traffic, the weather … …

11. No Title Approach 3: Lookup the route distance between
Estimate the walking speed
Consider the traffic, the weather … …
How to calculate?
T = S’ / (V – x)
X: slowdown due to traffic, weather, …

12. No Title
Approach 4:
Approach 5:
Approach 6:
Approach 7: …

13. No Title Approach 1: Try 100 times Approach 2: T = S / V
Experimental approach
Approach 2: T = S / V
Approach 3: T = S’ / (V – x)
Approach 4: …
Approach 5: …
Analytical approach

14. No Title Approach 1: Try 100 times Approach 2: T = S / V
Experimental approach
Approach 2: T = S / V
Approach 3: T = S’ / (V – x)
Approach 4: …
Approach 5: …
Analytical approach
Fundamental
Principle
Refinement

15. We are talking about things on this level
No Title
Approach 1: Try 100 times
Experimental approach
Approach 2: T = S / V
Approach 3: T = S’ / (V – x)
Approach 4: …
Approach 5: …
Analytical approach
We are talking about things on this level

16. Real-Time Performance Analysis… …
Time
Time … …
Time
Time

17. Real-Time Performance Analysis
Questions:
What’s the maximal delay of each event?
Will some buffer overflow? … …
Time
Time … …
Time
Time

18. Modeling Inputs/Outputs
Inputs Events
uncertainty
infinity … …
Time

19. Modeling Inputs/Outputs
Time domain
R(t): the number of arrived events by time t
Time …
Number
Of events
Time

20. Modeling Inputs/Outputs
Time domain
R(t): the number of arrived events by time t
Problem:
can’t handle uncertainty and infinity
NOT analytical
We will come back to this in the future

21. Arrival Curve RTC uses Time-interval Domain
Arrival Curve: α(Δ) = < αu(Δ) , αl(Δ) >
αu(Δ): upper bound arrival curve
αl(Δ): lower bound arrival curve

22. Arrival Curve Arrival Curve au al # of packets max: 1 packet
min: 0 packets
max: 3 packets
min: 1 packet
max: 2 packets
min: 0 packets au al 3 D D D 2 1 D
time t 1 2

23. Arrival Curve Arrival Curve: Exercise: Periodic Events with period=10
Periodic Events with period=10 and jitter=5

24. Arrival Curve Properties of arrival curve: αu(Δ): sub-additive
αl(Δ): super-additive

25. Arrival Curve Where does an arrival curve come from?
From specification:
E.g., Periodic Events with period=10 and jitter=5
From trace (or a number of traces):
Calculate αu(Δ) and αl(Δ) from R(t)

26. Arrival Curve
Exercise: …
Time 1 2 3 4 5 6 7 8 9 10 11 12 13 14

27. Modeling Resource Examples: Full capacity (dedicated resource)
TDMA, e.g., every fourth slot
Flexible pattern
Time
Time

28. Modeling Resource Time domain C(t): the provided capacity by time t

29. Modeling Resource Time domain C(t): the provided capacity by time t

30. Service Curve Service Curve: β(Δ) = < βu(Δ) , βl(Δ) >
βu(Δ): upper bound arrival curve
βl(Δ): lower bound arrival curve

31. Service Curve Properties of service curve: βu(Δ): sub-additive
βl(Δ): super-additive

32. Modeling and Analysis with RTC
Questions:
What’s the maximal delay of each event?
Will some buffer overflow? … …
Time
Time … …
Time
Time

33. Modeling and Analysis with RTC
Questions:
What’s the maximal delay of each event?
Will some buffer overflow?
service curve
output
arrival curve
arrival curve
remaining
service curve

34. Modeling and Analysis with RTC
Questions:
What’s the maximal delay of each event?
Will some buffer overflow?

35. Modeling and Analysis with RTC
Questions:
What’s the maximal delay of each event?
Will some buffer overflow?

36. Modeling and Analysis with RTC
Different Components

37. Modeling and Analysis with RTC
Calculate the output arrival and remaining service curve
Under Fixed-Priority Scheduling