LDU Parametrized Discrete-Time Multivariable MRAC

and Application to A Web Cache System

Ying Lu, Gang Tao and Tarek Abdelzaher

University of Virginia

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Outline

• Web cache system modeling & identification

• MRAC based on LDU parametrization

• Implementation

• Evaluation

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Examples of Control Theory Application in Computer Science

• Network flow control (TCP/IP - RED)– C. Hollot et al. (U.Mass, INFOCOM 2001)

• Admission control in computing system– J. Hellerstein et al. (IBM, IEEE ISINM 2001 )

• Apache server utilization control– T. F. Abdelzaher et al. (UVA, IEEE TPDS 2001)

• Apache QoS differentiation– C. Lu et al. (UVA, IEEE RTAS 2001)

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System Dynamics and Uncertainties

• Computer systems are dynamic– Current output depends on “system history”

– Queuing delays

• System model parameters are uncertain– software and hardware configuration changes

– workload changes

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Web Caching Architecture

H: hit rate, the rate at which valid requests can be satisfied without contacting the web server

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Differentiated Web Caching

• Requests are classified

• Different class has different level of service

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Caching Differentiation: A Feedback Control Problem

H1 : H2 : … : HN+1 = c1 : c2 : … : cN+1

Hi — average hit rate of classi, ci — QoS specification Si — disk space proportion of content classi

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System Identificationy(k) = Ay(k-1) + Bu(k-1)

y(k) = [y1(k), y2(k)]T

u(k) = [u1(k), u2(k)]T

A, B R2x2

apply a gradient algorithm to estimate the web cache system parameter matrix A & B

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Model Validation

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ImplementationService differentiation in Squid web cache• Timer: manage control loop execution frequency

• Output sensor– measure smoothed average hit rates– report the ratio of hit rates to controller

• Adaptive controller– execute the adaptive control algorithm– output the ratio of space proportions

• Actuator: manage the disk space allocation among classes

• Classifier: classify the requests

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Experimental Setup

• Testbed: – 8 AMD-based Linux machines

connected by 100-MHz Ethernet switch

• Clients: – 6 machines running Surge (a scalable

URL reference generator, a tool that generates realistic web workloads)

– 2 machines per content class

• Modified Squid web cache – cache size : files population = 1 : 33

• Apache web server

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Adaptive Controller Performance

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Conclusions• Web caching systems are dynamic

• System identification is feasible

• On line adaptation is desirable

• An LDU parametrized MRAC is derived for MIMO systems

• MRAC is applied to a web caching system

• Adaptive control is implemented on Squid web cache

• Proportional hit rate differentiation service is achievable despite system uncertainties