Web Cache Replacements

1. Web Cache Replacements 張燕光 資訊工程系 成功大學 ykchang@mail.ncku.edu.tw

2. Introduction • Which page to be removed from its cache? • Finding a replacement algorithm that can yield high hit rate. • Differences from traditional caching • nonhomogeneity of the object sizes • same frequency and different size, favor smaller objects if consider only hit rate, • Byte hit rate 2

3. Introduction • Other consideration • transfer time cost • Expiration time • Frequency • Measurement metrics? • admission control? • When or how often to perform the replacement operations? • How many documents to remove? 3

4. Measurement Metrics • Hit Rate (HR): • % requests satisfied by cache • (shows fraction of requests not sent to server) • Volume measures: • Weighted hit rate (WHR): Byte Hit Ratio • % client-requested bytes returned by proxy (shows fraction of bytes not sent by server) • Fraction of packets not sent • Reduction in distance traveled (e.g., hop count) • Latency Time 4

5. Three Categories • Traditional replacement policies and its direct extensions: • LRU, LFU, … • Key-based replacement policies: • Cost-based replacement policies: 5

6. Traditional replacement • Least Recently Used (LRU) evicts the object which was requested the least recently • prune off as many of the least recently used objects as is necessary to have sufficient space for the newly accessed object. • This may involve zero, one, or many replacements. 6

7. Traditional replacement • Least Frequently used (LFU) evicts the object which is accessed least frequently. • Pitkow/Recker evicts objects in LRU order, except if all objects are accessed within the same day, in which case the largest one is removed. 7

8. Key-based Replacement • The idea in key-based policies is to sort objects based upon a primary key, break ties based on a secondary key, break remaining ties based on a tertiary key, and so on. 8

9. Key-based Replacement • LRUMIN: • This policy is biased in favor of smaller sized objects so as to minimize the number of objects replaced. • Let the size of the incoming object be S. Suppose that this object will not fit in the cache. • If there are any objects in the cache which have size at least S, we remove the least recently used such object from the cache. • If there are no objects with size at least S, then we start removing objects in LRU order of size at least S/2, then objects of size at least S/4, and so on until enough free cache space has been created. 9

10. Key-based Replacement • SIZE policy: • In this policy, the objects are removed in order of size, with the largest object removed first. • Ties based on size are somewhat rare, but when they occur they are broken by considering the time since last access. Specifically, objects with higher time since last access are removed first. 10

11. Key-based Replacement • LRU-Threshold is the same as LRU, but objects larger than a certain threshold size are never cached. • Hyper-G is a refinement of LFU, break ties using the recency of last use and size. • Lowest Latency First minimizes average latency by evicting the document with the lowest download latency first. 11

12. Cost-based Replacement • Employ a potential cost function derived from different factors such as • time since last access, • entry time of the object in the cache, • transfer time cost, • object expiration time and so on. • GreedyDual-Size(GD-Size) associates a cost with each object and evicts object with the lowest cost/size. • Hybrid associates a utility function with each object and evicts the one has the least utility to reduce the total latency. 12

13. Cost-based Replacement • Lowest Relative Value evicts the object with the lowest utility value. • Least Normalized Cost Replacement(LCN-R) employs a rational function of the access frequency, the transfer time cost and the size. • Bolot/Hoschka employs a weighted rational function of transfer time cost, the size, and the time last access. 13

14. Cost-based Replacement • Size-Adjusted LRU(SLRU) orders the object by ratio of cost to size and choose objects with the best cost-to-size ratio. • Server-assisted scheme models the value of caching an object in terms of its fetching cost, size, next request time, and cache prices during the time period between requests. It evicts the object of the least value. • Hierarchical GreedyDual(Hierarchical GD) does object placement and replacement cooperatively in a hierarchy. 14

15. GreedyDual • GreedyDual is originally proposed by Young and Tarjan, concerned with the case when pages in a cache have the same size but incur different costs to fetch from a secondary storage • A value H is initiated with each cached page p when a page is brought into cache. • H is set to be the cost of bringing p into the cache • the cost is always nonnegative. • (1) Page with the lowest H value (minH) is replaced and (2) then all pages reduce their H values by minH 15

16. GreedyDual • If a page is accessed, its H value is restored to the cost of bringing it into the cache • Thus the H values of recently accessed pages retain a larger portion of the original cost than the pages that have not been accessed for a long time • By reducing the H values as time goes on and restoring them upon access, GreedyDual integrates the locality and cost concerns in a seamless fashion 16

17. GreedyDual-Size • Setting H to cost/size upon accesses to a document, where cost is the cost of bringing the document and size is the size of the document in bytes • call this extended version as GreedyDual-Size • The definition of cost depends on the goal of the replacement algorithm cost is set to • 1 if the goal is to maximize hit ratio • the downloading latency if the goal is to minimize average latency • network cost if the goal is to minimize the total cost 17

18. GreedyDual-Size • Implementation: • Need to decrement all the pages in cache by Min(q) every time a page q is replaced, which may be very inefficient • Improved algorithm is in the next page • Maintaining a priority queue based on H • Handling a hit requires O(log k) time and • Handling an eviction requires O(log k) time since in both cases the queue needs update 18

19. GreedyDual-Size • Algorithm GreedyDual (document p) • /* Initialize L  0 */ • If p is already in memory, • H(p)  L + cost(p)/size(p) • If p is not in memory, • while there is not enough room in memory for p, • Let L  min H(q) for all q in cache • Evict q such that H(q) = L • Put p into memory & set H(p)L+cost(p)/size(p) 19

20. Hybrid Algorithm (HYB) • Motivated by Bolot and Hoschka's algorithm. • HYB is a hybrid of several factors, considering not only download time but also number of references to a document and document size. HYB selects for replacement the document i with the lowest value of the following expression: 20

21. Wb Wn ( ) (np) Cs + bs Zp HYB • Utility function is defined as follows • Cs is the estimated time to connect to the server • bs is the estimated bandwidth to the server • Zp is the size of the document • np is the # of times document has been referenced • Wb and Wn are constants that set the relative importance of the variables bsand np, respectively 21

22. Latency Estimation Algo. (LAT) [REF] • Motivated by estimating the time required to download a document, and then replace the document with the smallest download time. • Apply some function to combine (e.g., smooth) these time samples to form an estimate of how long it will take to download the document • keeping a per-document estimate is probably not practical. • Alternative: keep statistics of past downloads on a per-server basis, rather than a per-document basis. (less storage) • For each server j, the proxy maintains an • Clatj: estimated latency (time) to open connection to server • Cbwj: estimated bandwidth of the connection (in bytes/second), 22

23. Latency Estimation Algo. (LAT) [REF] • When a new document is received from server, the connection establishment latency (sclat) and bandwidth for that document (scbw) are measured , the estimates are updated as follows: clatj = (1-ALPHA) clatj + ALPHA sclat cbwj = (1-ALPHA) cbwj + ALPHA scbw • ALPHA is a smoothing constant, set to 1/8 as it is in the TCP smoothed estimation of RTT • Let ser(i) denote the server on which document i resides, and si denote the document size. Cache replacement algorithm LAT selects for replacement the document i with the smallest download time estimate, denoted di: • di = clatser(i) + si/cbwser(i) Replacement Algorithm 23

24. Latency Estimation Algo. (LAT) • One detail remains: • a proxy runs at the application layer of a network protocol stack, and therefore would not be able to obtain the connection latency samples sclat. • Therefore the following heuristic is used to estimate connection latency. A constant CONN is chosen (e.g., 2Kbytes). Every document that the proxy receives whose size is less than CONN is used as an estimate of connection latency sclat. • Every document whose size exceeds CONN is used as a bandwidth sample as follows: scbw = download time of document – current value of clatj. 24

25. Lowest Relative Value (LRV) • time from the last access t: for its large influence on the probability of a new access • the probability of a new access conditioned to the time from the last access can be expressed as (1 - D(t)) • # of previous accesses i: this parameter allows the proxy to select a relatively small number of documents with a much higher probability of being accessed again • document size s: This seems to be the most effective parameter that make a selection among documents with only one access 25

26. Distribution of interaccess times, D(t) 26

27. Prob. Density function of interaccess times, d(t) 27

28. t 2E6 Lowest Relative Value (LRV) • We compute the probability that a document is accessed again, Pr(i, t, s), as follows Pr(i, t, s) = P1(s)(1 - D(t)) if i = 1 Pr(i, t, s) = Pi (1 – D(t)) otherwise • Pi: conditional probability that a document is reference i+1 times given that it has been accessed i times • P1(s): Percentage of size s with at least 2 accesses • D(t): density distribution of times between consecutive requests to the same document, derived as D(t) = 0.035log(t+1) + 0.45(1 - e ) 28

29. Lowest Relative Value (LRV) 29

30. Lowest Relative Value (LRV) 30

31. Performance from Pei Cao • Use hit ratio, byte hit ratio, reduced latency and reduced hops • reduced latency = the sum of downloading latency for the pages that hit in cache as a percentage of the sum of all downloading latencies • reduced hops = the sum of the network costs for the pages that hit in cache as a percentage of the sum of the network costs of all Web pages • model network cost of each document as hops • Web server has hop value: 1 or 32; we assign 1/8 of servers with hop value 32 and 7/8 with hop value 1 • The hop value can be thought of either as the number of network hops traveled by a document or as the monetary cost associated with the document 31

32. Performance from Pei Cao • GD-Size(1) sets cost of each document to be 1, thus trying to maximize hit ratio • GD-Size(packets) sets the cost for each document to 2+size/536, i.e. estimated number of network packets sent and received if a miss to the document happens • 1 packet for the request, 1 packet for the reply and size/536 for extra data packets assuming a 536-byte TCP segment size. • It tries to maximize both hit ratio and byte hit ratio • Finally GD-Size(hops) sets the cost for each document to the hop value of the document trying to minimize network costs 32

33. Performance from Pei Cao • See Cao’s paper: page 4 33

34. Weighted Hit Rate • Results on best primary key are inconclusive • Most references are from small files, but most bytes are from large files • Why Size? • Most accesses are for smaller documents • A few large documents take the space of many small documents • Concentration of large inter-reference times 34

35. Exp. 3: Partitioning Cache by Media • Idea • Do clients that listen to music degrade the performance of clients using text and graphics? • Could a partitioned cache with one portion dedicated to audio, and the other to non-audio documents increase the WHR experienced by either audio or non-audio documents? • Simulate • cache size = 10% of max needed • two partitions: audio and non-audio 35

36. Exp. 4: Partitioning Cache by Media • In Experiment 4, • a one-level cache with SIZE as the primary key • random as the secondary key • three partition sizes: dedicate 1/4, 1/2, or 3/4 of the cache to audio; • the rest is dedicated to non-audio documents. 36

37. Exp. 4: Partitioning Cache by Media 37

38. Exp. 4: Partitioning Cache by Media 38

39. Problems to solve • Certain sorting keys have intuitive appeal. • The first is document type. A sorting key that puts text documents at the front of the removal queue would insure low latency for text in Web pages, at the expense of latency for other document type. • The second sorting key is refetch latency. To a user of international documents, the most obvious caching criteria is one that caches documents to minimize overall latency. • A European user of North American documents would preferentially cache those documents over ones from other European servers to avoid using heavily utilized transatlantic network links. Therefore a means of estimating the latency for refetching documents in a cache could be used as a primary sorting key. 39

40. Problems to solve • caching dynamic documents. Cache is only useless for dynamic documents if the document content completely changes; otherwise a portion but not all of the cached copy remains valid. • allow caches to request the differences between the cached version and the latest version of a document. 40

41. Problems to solve • For example, in response to a conditional GET a server could send the “diff" of the current version and the version matching the Last-Modified date sent by the client; or a specific tag could allow a server to “fill-in“ a previously cached static “query response form." • Another approach to changing semi-static pages (i.e., pages that are HTML but replaced often) is to allow Web servers to preemptively update inconsistent document copies, at least for the most popular. 41

42. RandomizedStrategies • These strategies use randomized decisions to find an object for replacement. 42

43. Randomized Strategies RandomizedStrategies • 1. RAND • This strategy removes a random object. • 2. HARMONIC [Hosseini-Khayat 1997] • RAND uses equal probability for each object, HARMONIC removes from cache one item at random with a probability inversely proportional to its specific cost cost = ci/si. 43

44. Randomized Strategies RandomizedStrategies • 3. LRU-C and LRU-S[Starobinski and Tse 2001]. • LRU-C is a randomized version of LRU. Let Cmax={c1,…cN} be the maximum of the access costs of all N objects of a request sequence. Let ĉi = ci/cmax be the normalized cost for object i. When an object i is requested, it is moved to the head of the cache with probability ĉi; otherwise, nothing is done. 44

45. Randomized Strategies RandomizedStrategies • LRU-S uses the size instead of the cost. Let smin={s1,…sN} be the size of the smallest objects among the N documents, and di=smin/sibe the normalized density of object i. • LRU-S acts as LRU with probability di; otherwise the cache state is left unmodified. • Furthermore, Starobinski and Tse [2001] proposed an algorithm which deals with both varying-size and varying-cost objects. • The following quantities were defined: Upon a request for object i, this algorithm performs the same operationas LRU with probability and with will leave the cache state unmodified. 45

46. Randomized Strategies RandomizedStrategies • 4. Randomized replacement with general value functions [Psounis and Prabhakar 2001]. • This strategy draws N objects randomly from the cache and evicts the least useful object in the sample. The usefulness of a document can be determined by any utility function. After replacing the least useful object, the next M(M < N) least useful objects are retained in memory. • At the next replacement, N − M new samples are drawn from the cache and the least useful of these N−M and M previously retained is evicted. The M least useful of the remaining are stored in memory and so on. 46

47. Randomized Strategies RandomizedStrategiesSummary 1. Randomization presents a different approach to cache replacement. 2. Randomized strategies try to reduce the complexity of the replacement process without sacrificing the quality too much. 47

48. Admission control • If we store the response in cache or not? • First time not save 48

49. Admission control • heuristic to make this decision: the most frequently accessed objects recently will most likely be accessed again. The words “frequently” and “recently” imply that access frequency of objects and a decay function applied on frequency are needed. • an extra space called URL memory cache is introduced to store URLs and the associated access frequency of the requested objects. 49

50. Admission control • If the requested object is cacheable, the process of storing the object in disk cache is delayed until the same object is accessed again. (Or we can say that cacheable objects are not stored in disk cache unless they have been accessed before. ) • Since the access stream is infinite, the size of URL cache must be limited. A replacement policy is also needed in URL cache. 50