1. LDU Parametrized Discrete-Time Multivariable MRAC and Application to A Web Cache System Ying Lu, Gang Tao and Tarek Abdelzaher University of Virginia

2. 2 Outline Web cache system modeling & identification MRAC based on LDU parametrization Implementation Evaluation

3. 3 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)

4. 4 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

5. 5 Web Caching Architecture H: hit rate, the rate at which valid requests can be satisfied without contacting the web server

6. 6 Differentiated Web Caching Requests are classified Different class has different level of service

7. 7 Caching Differentiation: A Feedback Control Problem H 1 : H 2 : … : H N+1 = c 1 : c 2 : … : c N+1 H i — average hit rate of class i, c i — QoS specification S i — disk space proportion of content class i

8. 8 System Identification y(k) = Ay(k-1) + Bu(k-1) y(k) = [y 1 (k), y 2 (k)] T u(k) = [u 1 (k), u 2 (k)] T A, B  R 2x2 apply a gradient algorithm to estimate the web cache system parameter matrix A & B

9. 9 Model Validation

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15. 15 Implementation Service 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

16. 16 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

17. 17 Adaptive Controller Performance

18. 18 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