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The Challenges of Reflexive Control Systems

Lui Shalrs@uiuc.edu

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Acknowledgement Many have contributed to the collaboration. In

particular, I want to thank Xue Liu, Jin Jeo at UIUC, Tarek Abdelzaher at UVA and Joe Hellerstein at IBM Research

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Web Service Performance Control

Web Servers Application ServersEnd Users

KeepAlive

TImeout

Number of

Threads

MaxClients

DB

ConnectionsFast response cache

MaxRequestsPerChild

ThreadsPerChild

Max simultan. requests

ListenBackLog

URL Cache

EJB threads

JVM heap size

Servlet reload int

Courtesy of Joe Hellerstein, IBM Research

Network based server systems, e.g., Web servers, have now become an integral part of our society.

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Overview In a queueing network, service performance control can

be viewed as a hierarchical control Setting the performance goal at each node

Rout the traffic to the nodes Performance regulation on each node

There are many interesting problems. Among them “Noise” is data Event driven control Reflexivity in control

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Some Interesting Facts Suppose we want to correct a biased coin with Prob(head)= 0.4. We begin by

soldering a small weight to the side of head, and then do some experiments and adjust the weight.

From a control perspective, the transfer function between the change of weight and the change of probability of head manifests itself clearly only when the sample size becomes large.

Fast control actions do not lead to fast convergence Low pass filter, except moving average, won’t work because there is no

noise. Event (sample size) based control action yields better results. Fixed

sample size control typically has random time intervals

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Reflexive Control Normal control system: the plant model is invariant to

control actions

Reflexive control system: the control alters the plant Genetics -> (physique, intelligence) -> mating ->

genetics Laws -> control social behaviors -> changes laws

• Queueing system control is reflexive

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Reflexivity and Uncertainty Uncertainty principle in measurement.

In quantum physics, the act of measurement distorts what we try to observe.

“Uncertainty principle” in reflexive control System. The act of control alters the model used to design

the controller

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The Bright Spot One of the worst that can happen in a network of

servers is performance failure due to congestions.

This turns out to be an easier task Heavy traffic creates long queue Long queue is persistent Low of large number kicks in Allows for fluid approximation Linear model with PI control works well

High performance regulation is reflexive. Why?

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Delay vs Control for M/M/1

1.5 2 2.5 3

5

10

15

20

25

30

delay 1

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Keeping the model relevant

Dref

“Matching” the measured arrival rate with computed service rate e.g., Let µ= + 0.5 will “lock” the system at the point of linearization

Slope = d/dDref = - 4

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Queuing Model Based Control

Measured Delay d

d

Server Queue

Control

Request

Queueing Model

q

Ref Delay Dref

Control of Average Delay

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Experimental Results

-1

0

1

2

3

4

5

6

7

8

9

10

0 500 1000 1500 2000

time (sec)

conn

ectio

n de

lay

G/M/1

G/M/1 with PIcontroller

reference

G/M/1 with P controller

Sha, L., Li, X., Lu, Y., and; Abdelzaher, T. “Queueing model based network server performance control”, the proceedings of IEEE Real-Time Systems Symposium, 2002

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Long Shadow of Reflexivity

Alas, there are still considerable variances The queueing model is a function variances in arrival

time and service time. Good admission control smooth the input variances Good execution time control smooth the execution

time variances Control invalidates queueing model!

Feed forward over-allocates when delay turns lower

Feed forward under-allocates when delay turns higher

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Jumps in Loads In addition to over/under allocation in feed forward errors,

the jumps in arrival process creates another challenge The queue length from previous traffic load takes time

to settle to the new equilibrium queue distribution. Leads to large transients

Whatever the sources of errors, large variance in service time correlates with large variances in queue length

Adding a control term on (Actual_queue_length – expected_queue_length)

Reducing both transients induced by workload changes and variances during steady state

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Comparison of two delay regulators using web trace

)()1

( arg etedtcurrentrefq llKD

)()1

( arg etedtcurrentrefq llKD

)()1

( arg etedtcurrentrefq llKD

Queueing Model Based Feedback Control

Queue Length Model Based Feedback Control

1 arg

1( ) ( )q current t etedref

c l lD

)1

( refq D

Steady state feed forward + delay feedback + model based queue

control

2 ( )refc D d

2 ( )refk D d

Actuator parameters: K: delay control; : multiplicative noise control

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Summary – theoretical problems

Heavy traffic not only cures “reflexivity”, it also allows for fixed time interval control works as well as sample size based control

upside: simple fixed rate linear model works well downside: the fun is gone

Under moderate traffic control, we need to deal with event (sample size) driven control reflexivity

queueing model based feed forward helps but the feed forward both over allocate & under allocate

Optimized supervisory control for networked server set point adjustments

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Summary: Engineering Problems

Poor observability in actual systems: Many queues and I/O states are not visible and not controllable.

Poor actuators: Rejecting individual requests TCP window

adjustment (non-linear, coarse grain actuator in admission control)

Hard to do fine grain control in CPU cycle allocation Nearly no control of I/O bandwidth

Control OS