1. Proteus: Power Proportional Memory Cache Cluster in Data Centers Shen Li, Shiguang Wang, Fan Yang, Shaohan Hu, Fatemeh Saremi, Tarek Abdelzaher

2. Background A Typical Use Case of Memcached Cluster

3. Background Dynamic Provisioning saves energy by turning off servers when the service level measurements (e.g., response time, # of replicas, etc.) allow. Existing solutions for webservers and databases/DFS does not fit cache clusters due to delay penalties.

4. Outline Load Balance Under Dynamics Smooth Transition Implementation and Evaluation

5. Objectives Balance load distribution in cache tier under dynamics. Minimize data movements during re-balancing transitions. mc1mc2mc3 mc1mc2 mc3mc1mc2

6. Virtual Node Memcache Server Load Balance Under Dynamics Methodology: ₋Consistent hashing. ₋Virtual nodes. mc1 mc2 mc3 mc1mc2mc3

7. Load Balance Under Dynamics Question: 1.In order to achieve our objectives, what is the minimum possible number of virtual nodes? (Provisioning off according to the decreasing order of mc id.) 2.How to construct such consistent hashing ring?

8. Load Balance Under Dynamics Answer 1: (N is the number of cache servers) Proof: denotes the virtual nodes set of cache server if takes over the host range of when turns off. as ‘s host range has to be evenly divided to the other i -1 servers. Then, we constructively show it is possible to achieve this lower bound.

9. Load Balance Under Dynamics Answer 2: (assume the length of the hash ring is 1) For i ← 2~ N For j ← 1~(i-1) Pick any virtual node of server j whose host is large than 1/[i(i+1)]; Insert an virtual node of server i in front of that virtual node of server j, such that exactly 1/[i(i+1)] host range is moved from server j to server i. Please refer to the paper for proof of correctness and complexity analysis.

10. 1/31/411/2 An example 1/2 1/6 1/3 1/12 1/4 mc1 mc2 mc3 mc4

11. Outline Load Balance Under Dynamics Smooth Transition Implementation and Evaluation

12. Smooth Transition Objectives Move only hot in-cache data. ₋A piece of data is “hot” if it has been requested by any user in the past TTL seconds. ₋Even though, a cache server may response for a relatively large key range, only hot in-cache data should be moved. Amortize data movement cost. Bounded transition delay.

13. Smooth Transition Methodology: 1.Each mc server maintains a Bloom Filter digest to record what is in cache. 2.Digests are sent to web servers before provisioning transitions. 3.For subsequent queries during transition, web servers will asks the local digest before query mc servers.

14. Bloom Filter Configuration False positive rate: Counter overflow probability: Minimize Bloom Filter size with given false positive (p p ) and false negative rate(p n ): where

15. Bloom Filter Configuration Take partial derivatives: where Whenwe have Almost always true Hence, optimal solution is reached at minimum possible. whereis Lambert function.

16. Outline Load Balance Under Dynamics Smooth Transition Implementation and Evaluation

17. Implementation

18. Wikipedia Workload Fluctuating workloads create opportunities for energy savings.

19. Response Time Naïve: Re-map the modulo based hash. Consistent: Original Consistent hashing algorithm with n^2 randomly placed virtual nodes. Static: Always keep all servers on.

20. Load Balance The curves show min load over max load among all mc servers under different schemes.

21. Cache Size vs Hit Ratio MEM allocated for each mc server.

22. Energy Saving The energy consumption of the cache cluster is reduced by 23%.