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Q uantitative E valuation of E mbedded S ystems

Q uantitative E valuation of E mbedded S ystems. QUESTION DURING CLASS? Email : qees3TU@gmail.com. FAIL!. Thank you, Robin Wolffensperger en Ruben Lubben!. Exercise: Model a car manufacturing line. Consider a car manufacturing line consisting of. Four assembly robots: A,B,C and D

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Q uantitative E valuation of E mbedded S ystems

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  1. Quantitative Evaluation of Embedded Systems QUESTION DURING CLASS? Email : qees3TU@gmail.com

  2. FAIL! Thank you, Robin Wolffensperger en Ruben Lubben!

  3. Exercise: Model a car manufacturing line Consider a car manufacturing line consisting of... • Four assembly robots: A,B,C and D • A production unit that needs 20 minutes to produce a chassis • A production unit that needs 10 minutes to produce a steering installation • A production unit that needs 10 minutes to produce a breaking system • A production unit that needs 20 minutes to produce a body • Three painting units that each need 30 minutes to paint a body • A production unit that needs 15 minutes to produce a radio • Robot A compiles the chassis and the steering installation in 4 min. and sends it to B • Robot B adds the breaking system in 3 min. and sends it to C • Robot C adds a painted body in 5 min. and sends it to D • Robot D adds a radio in 1 min. and sends the car out of the factory • For safety reasons, there can be at most 3 ‘cars’ between A and C, and only 2 between B and D • Every robot can only deal with one of each of the assembled components at a time

  4. Answer: Model a car manufacturing line Exercise: calculate the first 3 firings of each actor 30min 20min 10min A B D C 5min 3min 4min 1min 15min Disclaimer: no actual car assembly line was studied in order to make this model. 20min 20min 10min

  5. EXERCISE: Simulate a few firings assuming sufficient input tokens. Determine the (max,+) matrix. Determine the max. throughput. Determine a periodic schedule for: µ = MCM µ = 2*MCM µ = 3*MCM as a function of µ Keep your answers for next time!

  6. Quantitative Evaluation of Embedded Systems

  7. Recall the characteristic equations…

  8. or for autonomous systems…

  9. What about this one? Cycles with a 0 execution time cause livelocks But when logging events, this is mathematically okay... y 0 ms

  10. And this one ? A B Theorem: The number of tokens on any cycle is constant! Therefore, every cycle must contain at least one token, otherwise a deadlock occurs. y u C D 2ms 1ms 3ms 4ms

  11. And this one? A B y x1 u C D x2 2ms 1ms x3 3ms 4ms

  12. Reducing rows… A B y x1 u C D x2 2ms 1ms ...but only when assuming: x1(1) = x2(1) which is ok for self-timed execution,but not when reasoning aboutperiodic schedules x3 3ms 4ms

  13. What about reducing columns? A x1 B C x3 y u 2ms 1ms x2 3ms

  14. And back to (max,+) algebra…

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