PROF. TAJANA SIMUNIC ROSING. Final Exam. Problem Max. Points Points 1 25 T/F 2 10 Esterel 3 20 Petri net 4 20 SDF 5 20 EDF/RM 6 20 LS/power Total 115

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1 CSE 237A WINTER 2012 PROF. TAJANA SIMUNIC ROSING Final Exam NAME: ID: Problem Max. Points Points 1 25 T/F 2 10 Esterel 3 20 Petri net 4 20 SDF 5 20 EDF/RM 6 20 LS/power Total 115 INSTRUCTIONS: 1. Please take a moment to make sure that your test is complete and readable. 2. SHOW YOUR WORK. Partial credit is more easily awarded this way. 3. You may use any handouts available on the CSE237A schedule web page. Everything else is off limits. 4. Please sign the statement below before you begin. HONOR CODE: By signing my name below I hereby certify that I have neither given, nor received assistance in completing this examination.

2 1. [25 pts] True or False a) [10pts] Write if the following statements are True (T) or False (F) Part Statements T/F - Example: My CSE237a project is done. T 1 Cyclic executive RTOS must use preemptive, dynamic schedulers. F 2 Kahn processes use nonblocking FIFOs for communication. F 3 Synchronous data flow graphs are a special case of Petri nets. T 4 Reachability is defined for transitions in a Petri net. F 5 Lamport's vector clocks are strongly consistent. T 6 Total order on events in distributed systems can be obtained with logical clocks. F 7 TTP/C, used in real-time applications, uses binary countdown arbitration. T 8 44kHz A/D converter uses 128 bits in order to avoid aliasing of a signal whose F maximum bandwidth is 22kHz. 9 Scratchpad is used as a replacement for only L2 cache in real time systems. F 10 DSPs are RISC processors used for data intensive applications. F Note: Correct answers (T/F) without reasoning shown will NOT get any credit in parts b, c and d. b) [5pts] Is the statement below True or False? A set of four independent tasks with equal execution times, but where the period of each task is twice as the previous one (T i+1 =2T i ), is guaranteed to be schedulable with rate monotonic scheduling if the maximum utilization for task 1 is less than 25%. True Consider this set of tasks A,B,C,D Task WCET Period=deadline A 1 4 B 1 8 C 1 16 D 1 32 ( ) Thus it is guaranteed to be RM-schedulable.

3 c) [5pts] Is the following statement True or False? Assume an A/D converter supplies samples at 40 khz. When a sample arrives, an interrupt handler will be invoked to process the sample and feed the result to the application. If the interrupt handler executes 100 instructions to process each sample for the application, then 400 application instructions can be executed on a 20 MHz single-processor that executes 1 instruction per cycle. Assume the processor is running only the application and interrupt handler. True. Let x = number of application instructions. 40k(x+100)=20M Thus x=400

4 d) [5pts] Is the following statement True or False? The FSM that accurately represents functionality of the following Esterel code has at most five states. Module test; Input a,b,c, r; Output o; Loop [ await a await b await c ]; Emit o Each r End module

5 2. [10pts] Esterel Draw the FSM that accurately represents the functionality of this code. module Example: input S,A,E; output O; loop abort present A else [ await A await S ] end ; emit O when E end A/ O E / - E / - S / O E / - Ā / - E / - A/ O A / - S / -

6 3. [20pts] Petri Nets Consider the Petri Net defined by the following: P = { p1, p2, p3 } T = { t1, t2, t3 } A = { (p1 t1) (p1 t3) (p2 t1) (p2 t2) (p3 t3) (t1 p2) (t1 p3) (t2 p3) (t3 p1) (t3 p2) } With all weights being one except w(p1 t1) = 2 a) [5pts] Draw the Petri net graph b) [5pts] Let M0 = [1 0 1]. How many times can transition t1 be enabled in subsequent operations of the Petri net? Show why. Never fires. c) [10pts] Let M0 = [2 1 1]. What happens in subsequent operations of the Petri net? Does this Petri net have any special properties given your analysis? YES, see below transition t2 is not live after [0 1 2] as a starting state.

7 4. [20pts] SDF A 2 3 a 6 e B 4 d 8 6 b 4 3 c 2 4 C a) [5pts] Write the incidence matrix. A B C a b c d e

8 b) [5pts] Derive a PASS schedule where A is only executed before B and B is only executed before C. AAAABBCCC c) [5pts] Derive the minimal delay required for the PASS schedule. [ 0, 0, 6, 0, 12 ] d) [5pts] Derive the minimal buffer sizes required for each edge of the SDF for the PASS schedule. [ 8, 12, 6, 24, 12 ]

9 5. [20pts] Task Scheduling: EDF & RM A single processor runs 3 periodic tasks which are defined in the table below. Task WCET Period=Deadline A 2 5 B 1 4 C 2 unknown a) [10pts] Determine the minimum period of task C so that this set of tasks is RM-schedulable. Show the RM schedule in the table below for the first 20 time units assuming first instances of all tasks arrive at time 0. Note: Make sure the period of C is indeed THE smallest and verify the task set is schedulable over the entire hyper-period. Time Task Time Task X=8. The minimum period can be obtained by enumerating period from 1 until it is schedulable. Time Task B A A C B A A C B C Time Task A A B C A B A C C b) [10pts] Show the EDF schedule in the table below for tasks A,B & C, given that A arrives at time 0, B at time 1, and task C at time 2. Assume that task C has a period of 6. If two tasks have the same priority, use alphabetic order to break the tie, e.g. if task A and task B have the same priority, run task A first. Time Task Time Task Time Task A A B C C B A A C B Time Task C A A B C A A C B

10 6. [20pts] List Scheduling For the following problem, assume that multiplication takes 2 ns while addition takes 1ns. O 1 := i 1 *i 2 + i 3 *i 4 O 2 := O 1 + i 5 O 3 := i 6 + i 7 O 4 := O 3 *i 8 a) [3pts] Draw the task graph O 5 := O 2 +O 4

11 b) [5pts] Draw ASAP and ALAP with no resource constraints and calculate the mobility of each operation.

12 c) [5pts] Given the constraint that there are two multipliers and one adder, draw the task graph obtained after using list scheduling algorithm. Assume that LS uses mobility as the metric for determining the task priority. d) [2pts] Assume that each multiplier consumes 1W when operating and each adder consumes 0.4W. What is the maximum power consumption according to the schedule you found in (c)? What is the total energy cost for this schedule? Assume that the power consumption of any idle HW unit is zero. Ans: The maximum power happens in Time = 1 and power consumption = 2.4W (two multiplier and one adder) Total energy consumption is 3 * 1W * 2ns + 3 * 0.4 * 1ns = 7.2nJ

13 e) [5pts] Assume that the peak power consumption cannot exceed 1.5W. Find a schedule based on the list scheduling algorithm that does not violate the power bound. How much later does this schedule finish compared to the schedule in (c)?

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CSE237a Final Exam Winter Prof. Tajana Simunic Rosing. Problem Maximum points Points earned Total 100

CSE237a Final Exam Winter Prof. Tajana Simunic Rosing. Problem Maximum points Points earned Total 100 CSE237a Final Exam Winter 2018 Name: PID: Problem Maximum points Points earned 1 15 2 10 3 15 4 20 5 20 6 20 Total 100 Instructions 1. Write your name on every page. 2. Please make sure your writing is