Feedback Control Real-Time Scheduling: Framework, Modeling, and Algorithms

1. Feedback Control Real-Time Scheduling: Framework, Modeling, and Algorithms Chenyang Lu, John A. Stankovic, Gang Tao, Sang H. Son Presented by Josh Carl

2. Overview • Motivation and Introduction • Architecture • Performance Specification and Metrics • Control Theory Based Design Methodology • Modeling the Controlled Real-Time System • Design of FCS Algorithms • Experiments

3. Motivation and Intro • Static vs. Dynamic Scheduling • Knowledge of task set and time constraints • Example: Rate Monotonic (RM) • Dynamic: Resource Sufficient/insufficient • Example: Earliest Deadline First (EDF), Admission-Control-based • RM, EDF are Open Loop • Good in predictable environments with accurate models • Bad in unpredictable environments

4. Soft Real-Time Systems • New soft real-time applications • Open and unpredictable environments • Examples: Online trading, e-commerce, agile manufacturing • Resource requirements and arrival rates not known, but the system still has performance guarantees. • EDF and RM fail miserably in these applications

5. Enter Feedback Control RT Scheduling • Feedback Control Systems • Scheduling Framework • Architecture • Performance specifications • Design methodology • “In contrast to ad hoc approaches that rely on laborious design/tuning/testing iterations, FCS enables system designers to systematically design adaptive real-time systems with established analytical methods to achieve desired performance guarantees in unpredictable environments.”

6. Task Model • QoS Levels: • Each QoS level j (0 ≤ j ≤ N-1), higher QoS=more CPU and more Value • Di[j]: the relative deadline • EEi[j]: the estimated execution time • AEi[j]: the (actual) execution time • Vi[j]: the value task Ticontributes if it is completed at QoS level j before its deadline Di[j]. • For periodic tasks: • Pi[j]: the invocation period • Bi[j]: the estimated CPU utilization Bi[j] = EEi[j] / Pi[j] • Ai[j]: the (actual) CPU utilization Ai[j] = AEi[j] / Pi[j] • For aperiodic tasks: • EIi[j]: the estimated inter-arrival-time between subsequent invocations • AIi[j]: the average inter-arrival-time that is unknown to the scheduler • Bi[j]: the estimated CPU utilization Bi[j] = EEi[j]/Eii[j] • Ai[j]: the (actual) CPU utilization Ai[j] = AEi[j] / AIi[j] • “A key feature of our task model is that it characterizes systems in unpredictable environments where task’s actual CPU utilization is time varying and unknown to the scheduler.”

7. Control Variables • Controlled Variables • Performance metrics controlled by the scheduler. • Defined over window ( (k-1)W, kW), W=sampling period, k=sampling instant • Miss Ratio, M(k)=deadline misses/completed & aborted tasks • Utilization, U(k)=% of CPU busy time in window • Value, V(k) • Performance References: Msand Us • Manipulated Variables: What can be changed by the scheduler • Total estimated utilization B(k)=ΣiUi[li(k)], li=QoS level • U(k) and B(k) are different values (actual vs. estimated), and U(k) bounded to 100%, B(k) is not.

8. FCS Architecture

9. Control Loop • Monitor: Measures controlled variables (M(k) and/or U(k)) and sends data to the controller. • Controller: Compares actual data to estimated data and changes control input accordingly (DB(k)). • QoS Actuator: Changes total estimated requested utilization at each sampling instant k according to the control input by adjusting QoS levels. • Basic Scheduler: EDF or Rate/Deadline Monotonic.

10. Performance • Regular metrics (average miss ratio and average utilization) don’t work. • Stability: “Miss ratio M(k) and utilization U(k) are always bounded for bounded references” – don’t want to stay at 100%. • Transient-state response: • Overshoot: Mo=(Mmax-MS)/MS, Uo=(Umax-US)/US • Settling Time = TS • Steady-state Error = ESM or ESU= Difference between average values in steady state and its corresponding reference. • Sensitivity = SP = Robustness of the system with regard to workload or system variations. • Loads: Step-load, Ramp Load

11. Design Methodology • “A system designer can systematically design an adaptive resource scheduler to satisfy the system’s performance specifications with established analytical methods in control theory.” • 1. Specify the desired dynamic behavior with transient and steady state performance metrics. • 2. Establish a dynamic model of the real-time system for the purpose of performance control. • 3. Based on 1 and 2 apply established mathematical techniques of feedback control theory to design FCS algorithms that analytically guarantee the specified behavior.

12. Modeling • Utilization • Misses • GA=worst case utilization ratio, GM=worst case miss ratio, DB=change in total estimated requested utilization, A(k)=total (actual) requested utilization, Ath(k)=Utilization Threshold • “Property 1: At any instant of time, at least one of the controlled variables (U(k) and M(k)) does not saturate in a real-time system.”

13. Design (abbreviated) • At each sampling instant k, the Controller computes a control input DB(k), the change in total estimated requested utilization based on an error ratio. • Error ratios (E(k)): • EM(k)=Ms-M(k) • EU(k)=Us-U(k) • Control Input: DB(k)=KPE(k), KP=tunable parameter. • Controller Goal: (1) guaranteed stability, (2) zero steady state error, (3) zero sensitivity to workload variations, and (4) satisfactory settling time and overshoot.

14. Derivations and z-transforms later… • “In summary, given the system parameters, the worst-case utilization ratio GA, and the miss ratio factor GM, we can directly derive the control parameter KP…to guarantee a set of performance profiles including stability, zero steady state error, and a satisfactory range of transient performance.”

15. Three Algorithms • FC-U: Feedback Utilization Control • Periodically samples the utilization, computes a change in total estimated utilization, assigns new QoS levels. • “FC-U guarantees that the miss ratio M(k)=0 in steady state if its reference Us ≤ Ath.” • Achieves excellent performance (M(k)=0) in steady state if utilization reference is correct. • FC-M: Feedback Miss Ratio Control • Utilizes a miss ratio control loop to directly control miss ratio. • Does not depend on any knowledge about the utilization bound. • It can always achieve low miss ratio, therefore is more robust in the face of utilization threshold variations. • FC-UM: Integrated Utilization/Miss Ratio Control • Best of both worlds but more complicated. • Uses the most conservative of the control inputs.

16. Experiments • On a simulator called FECSIM. • Two task sets: • Some built in randomness in the tasks. Tasks have 3 QoS levels. • QoS Actuator: Highest-Value-Density-First • Sampling window is 0.5 sec.

17. Profiling • Run simulator in open-loop.

18. Performance Reference Settings and Experiment A • System Settings • Experiment A: Arrival Overload • SL(0,150%) • Ga’=2 (execution time factor) – average execution time is twice the estimation.

19. Experiment A: FC-U Results

20. Experiment A: FC-M

21. Experiment A: FC-UM

22. Experiment A: Open Loop

23. Experiment B: Arrival/Internal Overload • Same as experiment A, plus the average execution times vary every 100 seconds. • First and second change: 57.5% increase for every task. • Last change: 75% decrease for every task. Underload situation. • Shortened settling time by manually setting B(0)=80% (estimated requested utilization).

24. Experiment B: FC-UM

25. Experiment B: Open Loop

26. Final Metrics

27. Conclusions • FCS algorithms can provide: • Stability with arrival overload and internal overload. • System miss ratio and utilization stay close to the corresponding performance reference. • Satisfactory settling time and low overshoot in transient state.