Feedback Control Real-Time
Scheduling: Framework, Modeling,
and Algorithms
Chenyang Lu, John A. Stankovic, Gang
Tao, Sang H. Son
Presented by Josh Carl
Overview
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Motivation and Introduction
Architecture
Performance Specification and Metrics
Control Theory Based Design Methodology
Modeling the Controlled Real-Time System
Design of FCS Algorithms
Experiments
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), AdmissionControl-based
• RM, EDF are Open Loop
– Good in predictable environments with accurate
models
– Bad in unpredictable environments
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
Enter Feedback Control RT Scheduling
• Feedback Control Systems
• Scheduling Framework
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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.”
Task Model
• QoS Levels:
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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 Ti contributes 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:
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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.”
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: Ms and 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.
FCS Architecture
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.
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
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.
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.”
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.
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.”
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.
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.
Profiling
• Run simulator in open-loop.
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.
Experiment A: FC-U Results
Experiment A: FC-M
Experiment A: FC-UM
Experiment A: Open Loop
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).
Experiment B: FC-UM
Experiment B: Open Loop
Final Metrics
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.