Kaichen Zhao & Junhan ZhuECE 750 Course Project

PID Control for GPS

Content

Preliminaries 3 min Related Work 1 min Algorithms 5 min

Weighted Round Robin WF2Q+ Control Method

Experiments & Analysis 4 min

Conclusion 1 min

Preliminaries—PID Control

Why do we use PID control:Model FreeEasy to be calculated in

digital systemProportionalIntegralDerivative

Preliminaries—PID Control

Preliminaries—PID Control

Preliminaries—PID Control

Preliminaries—PID Control

Preliminaries—GPS

GPS: Generalized Processor Sharing

Related Works—WRR and WF2Q+

Weighted Round Robin

WF2Q+- The simplest

implementation of GPS. - Each workflow is

allocated a time slice to process task in that flow

- When the time slice is used up, the server terminate the task and move to next flow

- The server will also terminate if there is no task in one workflow though this flow’s time slice hasn’t been used up

- More complicated than Round Robin

- Choose a task with the earliest finish time to transmit

- Still a approximation to GPS

- When implementing, need a virtual clock and a table to track the status of each flow

Related Works

J.A. Stankovic(Univ. of Vriginia):

- Feedback control in task scheduling/WebServer

- They introduce the idea of PID control into EDF

Tarek Ablelzaher(UIUC):

- Control of resource scheduling in complicated (MIMO) system.

- Introduce control theory to software and web system

Parameswaran Ramanathan(UW-Madison):

- Overload management

- He mainly proposed a technique for management of processor overloaded in real-time

control applications.

Algorithms—Control Method

Flow Chart:

Algorithms—Control Method

Utilization Calculation:

Algorithms—Control Method

Flow Chart:

Algorithms—Control Method

Reference Values(Expected Util):If a queue is empty, it will give its band width to other non-empty queues.

Errors:

Algorithms—Control Method

Controller:

W(n)

Implementation

• Three programs

• One application

Experiments & Analysis

Weighted Round Robin WF2Q

Control Method

Weight SettingWorkflow1: 0.1Workflow2: 0.2Workflow3: 0.3Workflow4: 0.4

Experiments & Analysis

Algorithm Flow 1 Flow 2 Flow 3 Flow 4

Ideal 0.1 0.2 0.3 0.4

Weighted Round Robin

0.01016 0.1980 0.2993 0.4011

WF2Q 0.10005 0.19712 0.29989 0.40193

Control Method 0.10010 0.20060 0.30030 0.39940

Utilization Comparison

Experiments & Analysis

Weighted Round Robin WF2Q

Control Method

Weight SettingWorkflow1: 0.1Workflow2: 0.2Workflow3: 0.3Workflow4: 0.4

Experiments & Analysis

Algorithm Flow 1 Flow 2 Flow 3 Flow 4

Weighted Round Robin

33.94 28.59 30.24 25.16

WF2Q 39.66 17.10 10.32 7.30

Control Method 40.12 16.60 10.11 7.37

Average Response Time Comparison

Experiments & Analysis

Algorithm Average Response Time

Variance of Response Time

UtilizationError

Weighted Round Robin

29.56 711.95 0.00396

WF2Q 19.17 1276 0.00497

Control Method 19.17 1213 0.00016

Response Time Comparison

Experiments & Analysis

Algorithm Float point computation number

Branch number

Parameter size

Weighted Round Robin

12 * flow number

5 3 * flow number + 2

WF2Q 14 * flow number

8 3 * flow number + 2

Control Method 16 * flow number

6 5 * flow number + 2

Complexity

Future work

We didn’t research in deep to see how PID parameters will influence the performance

Find better problems to be solved by PID control

Summary

We proposed a new method to implement GPS: Based on the idea of PID control Make schedule decision according

to the error between the real utilization and expected utilization

We did some literature research on related topics: GPS Control theory in RTS

Summary

Compared with two other algorithms by writing three programs and one application

Did some analysis and experiments on control method and two classical methods.

Questions

If you are interested in our work, you are very welcomed to discuss with us or read our report.