Feedback Control Real-Time Scheduling

C. Lu, J.A. Stankovic, G. Tao, and S.H. Son, Design and Evaluation of a Feedback Control EDF Scheduling Algorithm,  IEEE Real-Time Systems Symposium (RTSS'99), December 1999.

Motivation for Feedback control Scheduling Open-loop scheduling paradigms perform poorly

in unpredictable dynamic systems where the workload cannot be accurately modeled

Many complex applications, e.g., robotics and agile manufacturing, are dynamic and operate in a non-deterministic environment where precise workload is not known

Challenging to build real-time systems providing predictable performance in a highly uncertain environment

Feedback control can support the target performance even when the workload varies dynamically via graceful QoS degradation in a closed-loop loop

Motivation

Apply control theoretic approaches to real-time performance management

Feedback control is well known for its robustness, e.g., cruise control or chemical reactor control, in the presence of disturbances Doesn’t need a precise system model

If the precise system model is known, feedback control is not necessary

Dynamically adapt the system behavior to achieve the targe performance (also called set point) in the feedback loop

Feedback Control Concepts

Set-point: Target performance to achieve, e.g., 1% deadline miss ratio

Measured perf: Actual perf, e.g., actual (deadline) miss ratio, measured at the current sampling period

Error = set-point – measured perf = target miss ratio – current miss ratio

ControllerControlled RT System

+

-

Setpoint MeasuredPerf.Error

ControlSignal

Feedback Control Loop

Periodically measure and compare the perf to the set point to determine the error

Controller computes the control signal based on the error and controlled system model

Actuator, e.g., admission controller or QoS manager, change the value of the manipulated variable to control the system

FC-EDF Architecture

Miss Ratio Control Model

At kth sampling instant, miss ratio is:m(k) = m(k-1) + g(k) ∆u(k-1) where m(k-1): miss ratio at the (k-1)th sampling

period g(k): miss ratio gain ∆u(k-1): utilization adjustment by admission

control and QoS adaptation at the (k-1)th sampling period

Miss Ratio Control Model

Instead of considering time-varying miss ratio gain g(k), they took G = maximum (miss ratio/unit load increase)

0.9 1 1.1 1.2 1.3 ...

Load

MissRatio

Miss ratio control is very challengingdue to the nonlinear nature of MR increase!!

Miss Ratio Control Model

Replace g(k) with G m(k) = m(k-1) + g(k)∆u(k-1) → m(k) = m(k-1) + G∆u(k-1)

Take z-transform to convert to frequency domain Convert from time domain to frequency domain You can do arithmetic manipulation rather than

solving (partial) differential equations

Apply z-transform to m(k) = m(k-1) + G∆u(k-1)

M(z) = z-1M(z) + z-1∆U(z)

M(z) = (G/z-1) ∆U(z)

Transfer function T(z) = output/input = M(z)/U(z) = G/z-1

Utilization Control Model

Miss ratio controller itself is not stable MR controller is saturated when utilization is

less than 1 if EDF is used In their later work, they added utilization

controller Utilization controller works when U ≤ 1,

miss ratio controller works when U > 1 Turn on/off util/MR controller when U ≤ 1 Turn on/off MR/util controller when U > 1

Good idea?

Controller Tuning

Given the control model shown in the previous slide, apply Root Locus model to graphically tune the controller in Matlab to support the stability & specified transient performance such as the overshoot and settling time

Feedback performance control in software services

T.F. Abdelzaher, J.A. Stankovic, C. Lu, R. Zhang, and Y. Lu, Feedback Performance Control in Software Services, IEEE Control Systems, 23(3): 74-90, June 2003.

Overview

SW systems become larger and bigger Performance guarantee required, e.g.,

in web-based e-commerce Control theory

Promising theoretical foundation for perf control in complex SW applications, e.g., real-time scheduling, web servers, multimedia control, storage mangers, power management, routing in computer networks, …

Overview

Software performance assurance problems Feedback control problems focused on web

server performance guarantee problems Data centers

SW performance control

Less rigorous guarantees on perf and quality

Most SW eng. research deals with the development of functionally correct SW

Functional correctness is not enough! Timeliness in embedded systems

Correct but delayed action can be disastrous Non-fucntional QoS attributes, e.g.,

timeliness, security, availability, …

Traditional approaches for perf guarantees Worst case estimates of load &

resource availability Recall EDF, RM, DM, Priority Ceiling

Protocol, …

New demand for performance assurance QoS guarantees required in a broader scope

of applications run in open, unpredictable environments Global communication networks enabling online

banking, trading, distance learning, … Points of massive aggregation suffering

unpredictable loads, potential bottlenecks, DoS attacks, …

-> Precise workload/system model unknown a priori Failure to meet QoS requirements -> loss of

customers or financial damages Worst case analysis/overdeisgn could be overly

pessimistic or wasteful Solid analytic framework for cost-effective perf

assurance required

Challenges

How to model SW architecture? How to map a specific QoS problem into

a feedback control system? How to choose proper SW sensors and

actuators to monitor and adjust perf and workloads/resource allocation?

How to design controllers for servers?-> This paper focuses on web servers

QoS metrics

Delay metrics Proportional to time: queuing delays,

execution latencies, service response time Rate metrics

Inversely proportional to time Connection bandwidth, throughput, packet

rate

Time-related perf attributes

Can be controlled by adjusting resource allocation Queuing theory can predict perf given a

particular resource allocation or vice versa Queuing theory only works for Poisson

arrival patterns Queuing theory can only predict average perf

even if this assumption holds Arrival patterns in web applications follow

heavy-tailed distribution -> Bursty arrival patterns

Service architecture

Fig. 1 Server architecture: (a) computing model (b) control-orientedrepresentation

Liquid task model

Liquid task model

Ci << Di

Takes Ci units of time to serve request i Di is the max tolerable response time Tolerable response time is finite Service times are infinitesimal

Progress of requests through the server queues ≈ Fluid flow

Service rate at stage k = dNk(t)/dt where Nk is #requests processed by stage k

Liquid task model

Volume at time T≈ #requests queued at stage k = ∫T(Fin – Fk) Fk: service rate at stage k Fin: request arrival rate to this stage

Valves: points of control, i.e., manipulated variables such as the queue length

Liquid model does not describe how individual requests are prioritized

Control theory can be combined with queuing theory or real-time scheduling

Server modeling Difference equation to model web servers

y(k): perf, e.g., delay or throughput, measured at the kth sampling period

U(k): control input at the kth sampling period ARMA (Auto Regressive Moving Average) model

y(k) = a1y(k-1) + a2y(k-2) + … + any(k-n)

+ b1u(k-1) + b2u(k-2) + … + bnu(k-n) n: system order – higher order model is usually (not

always!) more accurate but more complex Transfer function can be derived

Web proxy cache model [4] TCP dynamics [5]

Transfer function

Shows the relation between input and output

Apply z-transform to y(k) in the previous slide

Open loop transfer function vs. closed-loop transfer function

Resource allocation for QoS guarantees Allocate more/less resource =

open/close a valve Need actuators to control resource

allocation or QoS provided by the system

SW system actuators

Input flow actuators Admission control Control queue length, server utilization, … Reject some requests under overload

SW system actuators

Quality adaptation actuators Change processing requirements to

increase server rate under overload E.g., Return abbreviated web page under

overload Tradeoff btwn delay & quality Service level m in a range [0, M] where 0 is

rejection

Resource reallocation actuator Alter the amount of allocated resources Usually applicable to multiple classes of

clients, e.g., dynamically reallocate disk space for differentiated web caching to support the service delay ratio 1:2 between two service classes [4,7]

QoS Mapping

Convert common resource management & SW perf assurance problems to FC problems

Absolute convergence guarantee Relative guarantee Resource reservation guarantee Prioritization guarantee Statistical multiplexing guarantee Utility optimization guarantee

Absolute convergence guarantee

Convergence to the specified problem Overshoot: Maximum deviation Settling time: Time taken to recover the

desired perf

Absolute convergence guarantee

Rate & queue length control Result in linear FC (Flow) rate can be directly controlled by

actuators Queue length can be linearly controlled by

controlling the flow E.g., server utilization control loop

Absolute convergence guarantee

Delay control More difficult Delay is inversely proportional to flow

Queuing delay d = Q/r where Q is queue length & r is service rate

Nonlinear

Relative guarantee

For example, fix the delays of two traffic classes at a ratio 3:1

Hi: measured perf of class i Ci: weight of class i Relative guarantee specifies H1:H2 = 1:3 Set point = 1/3 Error e = 1/3 – H1/H2

Controlled variable: relative delay ratio Manipulated variable: #allocated processes

per class to control connection delay HTTP protocol summary

A client, e.g., a web browser, establishes a TCP connection with a server process

The client submits an HTTP request to the sever over the TCP connection

The server sends the response back to the client Keep open the TCP connection for the Keep Alive interval,

e.g., 15s-> Claim connection delay dominates service response time -> Scheduling can also significantly affect relative delay

ratio, but it is not considered

Relative guarantee in Apache web server

Relative guarantee in Apache web server System identification based on the

ARMA model (Least square method) Also called System Identification (SYSID) in

control theory Randomly change per class process allocations Measure response time

Relative guarantee in Apache web server Perf settings

4 Linux machines run the Surge web workload generator

1 Linux machine runs the Apache web server

Suddenly increase #premium clients by 100 at time 870s

Relative guarantee in Apache web server Perf results

Open Loop

Closed LoopStable?

Related work

ControlWare CPU scheduling Storage management Network routers Power/heat management RTDB

Conclusions

Feedback control is applicable to managing performance in SW systems

Future work Adaptive/robust control Predictive control Apply to other computational systems such

as embedded systems

Adptive Control: Self-Tuning Regulator Dynamically estimate a model of the system

via the Recursive Least Square method Controller will accordingly set the actuators to

support the desired perf.

References (HP Storage Systems Lab)

Designing controllable computer systems, Christos Karamanolis, Magnus Karlsson and Xiaoyun Zhu. USENIX Workshop on Hot Topics in Operating Systems (HotOS), June 2005, pp. 49-54, Santa Fe, NM.

Dynamic black-box performance model estimation for self-tuning regulators, Magnus Karlsson and Michele Covell. International Conference on Autonomic Computing (ICAC), pp. 172-182, June 2005, Seattle, WA.

Autonomic Computing

General, broader research issues regarding self-tuning, self-managing, self-* systems Autonomic computing web site

http://autonomiccomputing.org/

IBM http://www.research.ibm.com/autonomic/

index.html Adaptive Systems Department

Some University Labs

Tarek Abdelzaher: http://www.cs.uiuc.edu/homes/zaher/

Chenyang Lu: http://www.cse.wustl.edu/~lu/

Next class

We will discuss papers from our RTES Lab on feedback control of software system K. D. Kang, J. Oh, Y. Zhou, "Backlog Estimation and

Management for Real-Time Data Services", 20th Euromicro Conference on Real-Time Systems (ECRTS '08), July 2-4, Prague, Czech Republic.

C. Basaran, K. D. Kang, M. H. Suzer, K. S. Chung, H. R. Lee, K. R. Park, "Bandwidth Consumption Control and Service Differentiation for Video Streaming," 17th International Conference on Computer Communications and Networks (ICCCN '08), August 3 - 7, 2008, St. Thomas U.S. Virgin Islands.

Questions?