Real-Time Calculus (RTC) Reading Group I Nan Guan 2013.3.7

About the Reading Group Thursday 18:00~20:00 For schedule see http://faculty.neu.edu.cn/ise/guannan/rtc/ Each time, decide the speaker for the session after the next one Every attendance holds a session Sooner or later …

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

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)

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

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

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

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

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

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

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, …

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

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

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

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

Real-Time Performance Analysis … … Time Time … … Time Time

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

Modeling Inputs/Outputs Inputs Events uncertainty infinity … … Time

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

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

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

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

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

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

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)

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

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

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

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

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

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

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

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

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

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

Modeling and Analysis with RTC Different Components

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