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TECHNISCHE UNIVERSITEIT DELFT Faculteit Elektrotechniek, Wiskunde en Informatica IN4343 – Real Time Systems April 8th 2015, from 09:00 to 12:00 Koen Langendoen Question: 1 2 3 4 5 6 Total Points: 5 10 30 15 20 10 90 Score: • This is a closed book exam • You may use a simple calculator only (i.e. graphical calculators are not permitted) • Write your answers with a black or blue pen, not with a pencil • Always justify your answers, unless stated otherwise • The exam covers the following material: (a) chapters 1-6, 8-9 of the book “Hard Real-Time Computing Systems (3rd ed)” by G. Buttazzo (b) the paper “The Worst-Case Execution-Time Problem” by Wilhelm et al. (except Section 6) (c) the paper “Transforming Execution-Time Boundable Code into Temporally Predictable Code” by P. Puschner (d) the paper “Best-case response times and jitter analysis of real-time tasks” by R.J. Bril, E.F.M. Steffens, and W.F.J. Verhaegh Cheat Sheet IN4343 Real-Time Systems Liu and Layland (LL) bound Hyperbolic (HB) bound RM = n(21/n − 1) Ulub n Y (Ui + 1) ≤ 2 i=1 Response Time Analysis WRi = Ci + BRi = Ci + i−1 X WRi + AJk k=1 i−1 X k=1 w+ = max(w, 0) dX i ≤t2 Ci g(t1 , t2 ) = Processor Demand Tk Ck + BRi − AJk −1 Ck Tk g(0, L) = ri ≥t1 schedulability ∀L ∈ D, n X L + Ti − Di Ti i=1 Ci g(0, L) ≤ L D = {dk |dk ≤ min(H, max(Dmax , L∗ ))} H = lcm(T1 , . . . , Tn ) n X (Ti − Di )Ui L∗ = Polling Server schedulability i=1 1−U RM +P S = Us + n Ulub n Y (Ui + 1) ≤ i=1 response time Deferrable Server schedulability " 2 Us + 1 2 Us + 1 1/n −1 # Ra = Ca + ∆a + Fa (Ts − Cs ) ra Ca ∆a = Ts − ra Fa = −1 Ts Cs " # 1/n Us + 2 RM +DS = Us + n Ulub −1 2Us + 1 n Y Us + 2 (Ui + 1) ≤ 2Us + 1 i=1 response time NP scheduling level-i busy period Ra = Ca + ∆a − C0 + Fa (Ts − Cs ) C0 = min(Cs (ra ), ∆a ) ra Ts − ra ∆a = Ts i X Li Li = Bi + Ch Th Fa = h=1 Bi = max{Cj } j>i response time sik = Bi + (k − 1)Ci + i−1 X sik h=1 Th Ca − C0 −1 Cs l m Ni = LTii + 1 Ch Rik = (sik + Ci ) − (k − 1)Ti Ri = max {Rik } k∈[1,Ni ] Elastic Model utilization ∀i Ui = Ui0 − (U0 − Ud ) EESi where ES = n X i=1 Ei Question 1 [5 points] Determining the worst case execution time of a task lies at the heart of real-time systems. (a) 2 points Provide two reasons explaining the variability observed in practice when measuring the execution time of a task. (b) 3 points Succinctly explain the concept of static timing analysis and hint at how the abovementioned variability is handled. Question 2 [10 points] EDF is known to be optimal for aperiodic task scheduling. The proof by (Dertouzos:1974) starts from an arbitrary feasible schedule σ, which is then transformed through a sequence of steps into the corresponding EDF schedule. (a) 2 points The schedule σ is scanned until a time slot tA is found in which a task JA is scheduled while there exists another task JB having the earliest deadline of all runnable tasks, but that is scheduled later at time tB . Draw a time line visualizing this situation. (b) 2 points Tasks JA and JB are then swapped. Draw the time line after the transformation. (c) 6 points Argue why the transformation step preserves feasibility. Question 3 [30 points] Given the following preemptable periodic tasks scheduled based on the Rate Monotonic Algorithm: τ1 τ2 τ3 τ4 Ci 2 2 3 3 Ti 5 6 18 35 (a) 10 points Demonstrate that this task set is feasible and report the maximum lateness. (b) 8 points Derive the best case response times of the tasks. (c) 4 points When computing the best case response time we must account for the interference from tasks with higher priority. However, we lcannot l m m simply round up as for the worst-case WRi BRi ( Tk ), but must count one occurrence less ( Tk − 1). Explain why this is the case. (d) 8 points Explain what the effects are on the worst and best case response times when task τ2 receives an activation jitter of 1. Question 4 [15 points] Given the following preemptable periodic tasks running under the EDF algorithm: τ1 τ2 τ3 Ci 2 3 3 Di 4 6 8 Ti 6 8 13 (a) 2 points What method can be used to determine the feasibility of the above task set if the deadlines would be equal to the periods? (b) 4 points With the given deadlines, one has to resort to the processor demand criterion. Until what time should the criterion be checked? (c) 9 points Is the task set feasible under EDF? Question 5 [20 points] When mixing periodic and aperiodic tasks one can make use of slack stealing to schedule the aperiodic tasks. Consider the following periodic tasks and aperiodic jobs: τ1 τ2 Ci 1 2 Ti 4 5 J1 J2 ai 2 8 Ci 3 2 (a) 4 points Slack stealing is quite advanced. Comment on its pros and cons when compared to a simple polling server. (b) 8 points Report the response times of the two aperiodic jobs when an RM scheduler is deployed. (c) 8 points Report the response times of the two aperiodic jobs when an EDF scheduler is deployed. Question 6 Despite careful considerations systems may become overloaded due to overruns. (a) 4 points Describe the two types of overruns. (b) 6 points Describe how robust EDF functions. [10 points]