web cache replacements 張燕光資訊工程系成功大學 [email protected]

Web Cache Replacements

張燕光資訊工程系成功大學

[email protected]

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

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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?

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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

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Three Categories• Traditional replacement policies and its

direct extensions:– LRU, LFU, …

• Key-based replacement policies:

• Cost-based replacement policies:

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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.

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Traditional replacement• Least Frequently used (LFU) evicts the

object which is accessed least frequently.

• Pitkow/Recker [78] evicts objects in LRU order, except if all objects are accessed within the same day, in which case the largest one is removed.

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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.

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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.

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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 accesstime since last access. Specifically, objects with higher time since last access are removed first.

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Key-based Replacement• LRU-Threshold [2] is the same as LRU, but

objects larger than a certain threshold size are never cached.

• Hyper-G [78] is a refinement of LFU, break ties using the recency of last use and size.

• Lowest Latency First [77] minimizes average latency by evicting the document with the lowest download latency first.

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Cost-based Replacement• Employ a potential cost functioncost 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 [77] associates a utility function with each object and evicts the one has the least utility to reduce the total latency.

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Cost-based Replacement• Lowest Relative Value evicts the object with

the lowest utility value.

• Least Normalized Cost Replacement (LCN-R) [70] employs a rational function of the access frequency, the transfer time cost and the size.

• Bolot/Hoschka [10] employs a weighted rational function of transfer time cost, the size, and the time last access.

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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.

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GreedyDual• GreedyDualGreedyDual 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 HH is initiated with each cached page p when a page is brought into cache.– H is set to be the cost of bringing the page 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

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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 those of pages that have not been accessed for a long time

• By reducing the H values as time goes on and restoring them upon access the algorithm integrates the locality and cost concerns in a seamless fashion

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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 GreedyDualSize

• The definition of cost depends on the goal of the replacement algorithm costcost is set to – 11 if the goal is to maximize hit ratio – the downloading latencythe downloading latency if the goal is to

minimize average latency – network costnetwork cost if the goal is to minimize the total

cost

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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

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GreedyDual-SizeAlgorithm GreedyDual (document p)

/* Initialize L 0 */

(1) If p is already in memory,

(2) H(p) L + cost(p)/size(p)

(3) If p is not in memory,

(4) while there is not enough room in memory for p,

(5) Let L min H(q) for all q in cache

(6) Evict q such that H(q) = L

(7) Put p into memory & set H(p)L+cost(p)/size(p)

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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:

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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

Wn (np)

Zp

Cs Wb bs

+( )

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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 – ClatClatjj: estimated latency (time) to open connection to server– CbwCbwjj: estimated bandwidth of the connection (in

bytes/second),

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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)

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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.

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Experiment 1

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Experiment 2

WB=8Kb,WN=0.9Kb,CONN=2Kb

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Lowest Relative Value (LRV)• time from the last access tt : 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 ss: This seems to be the most effective parameter that make a selection among documents with only one access

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Distribution of interaccess times, D(t)

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

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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 )2E6t

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Lowest Relative Value (LRV)

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percentage of wrong choices in discarding documents vs # of accesses issued to the document at the moment of the choice

the cache size is 500Mb

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cumulative number of wrong choices in discarding documents vs # of accesses issued to the document at the moment of the choice

the cache size is 500Mb

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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

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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

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

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Bolot/Hoschka’s algorithm’96• Consider following variables:

– ttii, time since the document was last referenced – SSii, the size of the document – rttrttii, the time it took to retrieve the document– ttlttlii, the time to live of the document (i.e. the expected

time until the document will be updated at the remote site, which is also the time interval until the cached document becomes stale).

– Assign a weight to each cached document i Wi = W(ti, Si, rtti, ttli).

• W(ti, Si, rtti, ttli) = 1/ti, documents are replaced according to the time of last reference. This models the LRU algorithm.

• With W(ti, Si, rtt i, ttl i) = Si, documents are cached on the basis of size only

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Bolot and Hoschka's algorithm• Proposed Weight function: • W(ti, Si, rtti, ttli) = (w1rtti+w2Si)/ttli + (w3 +w4)/ti • where w1, w2, w3 and w4 have constant value. • The second term on the right-hand side captures the

temporal locality. • The first term captures the cost associated with

retrieving documents (waiting cost, storage cost in the cache), while the multiplying factor 1/ttli indicates that the cost associated with retrieving a document increases as the useful lifetime of the document decreases.

• ttli is the expiration time provided by web servers

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Bolot and Hoschka's algorithm• There remains to define parameters wi.

– This goal might be to maximize the hit ratio, or to minimize the perceived retrieval time for a random user, or to minimize the cache size for a given hit ratio, etc.

– expressed as a standard optimization problem, solved using variants of the Lagrange multiplier technique.

• Authors uses the following algorithms– Algo 1: W(ti, Si, rtti, ttli) = w3/ti

– Algo 2: W(ti, Si, rtti, ttli) = w1rtti+w2Si+(w3+w4 Si)/ti

– We express W(ti, Si, rtti, ttli) in terms of bytes, and we take in all cases w1=5000 b/s, w2=1000, w3=10000 bs, and w4=10 s.

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Key-based Replacement (P.4)

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Key-based Replacement• Removal policies is a taxonomy defined

in terms of a sorting procedure. Two phases:– First, it sorts documents in the cache

according to one or more keys (e.g., primary key, secondary key, etc.).

– Then it removes zero or more documents from the head of the sorted list until a criteria is satisfied.

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Williams’s Paper• Undergrad (U):

– About 30 workstations in an undergraduate CS lab from April to October 1995 (190 days), containing 173,384 valid accesses requiring transmission of 2.19GB of static web documents and is representative of a group of clients working in close confines (within speaking distance).

• Classroom (C): – 26 workstations in a classroom containing 30,316 valid

accesses requiring transmission of 405.7MB of static documents.

– tend to make requests when asked to do so by an instructor.

– However results for workloads BR, BL, and G are upper bounds for what real proxies would experience, because a real proxy would probably not cache requests from clients in .cs.vt.edu to servers in .cs.vt.edu.

– workload BR is representative of a cache that is positioned at the point of connection of the Virginia Tech campus to the Internet. Such a cache is useful because it avoids consuming bandwidth

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Williams’s Paper• Graduate (G):

– at least 25 users, containing 46,834 valid accesses requiring transmission of 610.92MB of static web pages for most of the spring 1995 semester.

– representative of clients in one department dispersed throughout a building in separate or in common work areas.

• Remote Client Backbone Accesses (BR): – Every URL request appearing on the Ethernet backbone of

domain .cs.vt.edu with a client outside that domain naming a Web server inside that domain for a 38 day period in September and October 1995, representing 180,132 requests requiring transmission of 9.61GB of static Web pages.

– This workload may be representative of a few servers on one large departmental LAN serving documents to world-wide clients.

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Williams’s Paper• Local Client Backbone Accesses (BL):

– Every URL request appearing on the Computer Science Department backbone with a client from in the department, naming any server in the world, for a 37 day period in September and October 1995, representing 53,881 accesses requiring transmission of 644.55MB of static Web pages. The requests are for servers both within and outside the .cs.vt.edu domain.

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Workload Summary (Paper)Workload

Days Accesses Size(Gb) %Refs %Bytes

U 185 188,674 2.26 graphics graphics

C 95 13,127 0.15 text graphics

G 78 45,400 0.56 graphics graphics

BR 37 227,210 9.38 graphics audio

BL 37 91,188 0.64 graphics graphics

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Experiment Overview• Trace-driven simulation• Compare removal policies, viewed as

sorting problems• Answer:

– 1. Maximum theoretical HR, WHR– 2. Best replacement policy– 3. Effectiveness of second level cache– 4. Effectiveness of partitioning cache by

media type (Question raised by Kwan, McGrath, Reed, Nov. 95, IEEE Computer)

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Simulation Assumptions• Valid Access:

– a legal request– document "passes" the cache (Simulate only

requests with HTTP return code 200.)

• Definition of hit:– In reality, a "hit" is either

• proxy has doc, and doc estimated consistent• proxy has doc, doc estimated inconsistent, and

CONDITIONAL-GET returns no doc(304 not modified)

– But 3 workloads traces lack last-modified times. Thus we use alternate definition:

– Hit = match in URL and size

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Simulation Assumptions• When URL in common log file has

size zero:– If URL appeared earlier with non-zero

size, use last size in simulation– Otherwise URL is probably a dynamic

doc - don’t cache in simulation

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Exp 1: Max Theoretical HR, WHR• Simulate infinite cache (plot 7 day moving

average) • Workload U (undergrad):

– Seasonal variation (e.g., new students in fall access new URLs)

– Cumulative HR=44.9%, WHR=31.4%

• Workload C (classroom):– Did not show high hit rate as expected– Increased HR near exams

• Workload BR (remote clients on backbone):– Hit rates over 90% due to proximity of proxy to

servers

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Exp.1: Max Possible Hit Rate

Semester start, most new users,

so constantly decline

Spring break

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Exp 2: Removal Policy Comparison• Simulate

– cache size = 10% or 50% of max needed of no replacement case

– all primary keys– certain primary/secondary combinations

• Graph U (undergrad):– SIZE superior primary key (with random

secondary)– Secondary key shows only marginal

improvement when primary key has many ties

• Other workloads:– SIZE superior in all workloads

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Ex 2: Primary Key Comparison

(Cache Size = 10% of max needed)

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Ex 2: Primary Key Comparison

(Cache Size = 10% of max needed)

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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

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Exp. 2: Weighted Hit Rate

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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

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• 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.

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60


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Problems to solve• Certain sorting keys have intuitive appeal.

– The first is document typedocument 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 latencyrefetch 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.

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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.

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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.

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Admission control• If we store the response in cache or not?

• First time not save

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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.

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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.

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Admission control: operations • Cache hits:

– The operations are similar to the original algorithm.

– In addition to unused non-cacheable objects and hot objects in memory cache, the cacheable objects without disk copies are also the candidates for replacement in memory cache.

– Consider the case that a copy of the requested object exists in memory cache but not in disk cache.

• The reference count associated with the requested object in memory cache is incremented by one and the data is then stored in disk cache.

• If the evicted objects from memory cache are cacheable, its URL along with its reference count is then stored in URL cache.

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Admission control: operations • Cache misses for cacheable objects :

– If the requested object is cacheable, the caching algorithm checks if its URL is not recorded in URL cache.

• Replacement operations are performed for allocating enough space for holding the requested object.

• The URL of the replaced object is now stored in URL cache along with its reference count.

• The replacement operations in URL cache must be performed. • The evicted URLs from URL cache are released. • The requested object itself is not stored in disk cache at this moment.

Thus, no replacement in disk cache is needed. – If the URL of the requested object is in URL cache,

• its associated record in URL cache is removed, the requested object is stored in disk cache, and the reference count is set to one.

• Similarly, the replacement operations in disk cache must be performed. The URLs of the evicted objects from disk cache are stored in URL cache and again the replacement operations in URL cache are performed.

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Admission control: operations • Cache misses for no-cacheable objects :

– For a cache miss, if the object is non-cacheable, the operations are similar to original algorithm. If the evicted object from memory cache is cacheable and it does not exist in disk cache, its URL along with the reference count is stored in URL cache.

– Notice that the proposed approach may lose some possible hits on the disk cache when objects are accessed the second time. However, it removes all the disk activity that disk cache stores the objects that will not be accessed again before evicted.

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Admission control • Efficient Management of URL Cache

– A separate hash table similar to that in memory/disk cache is used in URL cache to support efficient search for the URL of requested object.

– The MD5 of URL is employed as the search key.

– We employ a replacement policy that is based on the URL access frequency.

– The least frequently accessed entry in URL cache is first selected for replacement.

– A priority queue with access frequency as the key is a suitable implementation for such replacement policy.

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Admission control • Efficient Management of URL Cache

– Each entry of the URL cache records the MD5 of URL, access frequency, and a few pointers for facilitating priority queue and hash table data structures.

– The required memory space for each entry in URL cache is constant.

– The size of hash table and priority queue itself is small and does not depend on the number of entries hashed, thus can be ignored.

– Based the size of the UC trace we studied in this paper, keeping all the URLs of the requests from one-day period in URL cache is reasonable. This accounts for 400k URLs. Therefore, assuming 80 bytes is needed for each entry in URL cache, 32 MB of the memory space is needed for the URL cache.

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hit ratio h(S)

0.55

0.6

0.65

0.7

HR

CHU

heff(S)

h(S)

1 2 4 8 16 32

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Removal frequency• On-demand: Run policy when the

size of the requested document exceeds the free room in a cache. (take time to do the removal)

• Periodically: Run policy every T time units, for some T.– If removal is time consuming

• Both on-demand and periodically: Run policy at the end of each day and on-demand (Pitkow/Recker [13]).

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On-demand• Two arguments suggest that overhead of

simply using on-demand replacement will not be significant. – First, the class of removal policies maintains a

sorted list. If the list is kept sorted as the proxy operates, then the removal policy merely removes the head of the list for removal, which should be a fast and constant time operation.

– Second, a proxy server keeps read-only documents. Thus there is no overhead for “writing-back" a document, as there is in a virtual memory system upon removal of a page that was modified since being loaded.

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How many to remove• Removal process is stopped when

the free cache area equals or exceeds the requested document size.

• Replace documents until a certain threshold (Pitkow and Recker's comfort level) is reached.

web cache replacements 張燕光 資訊工程系 成功大學 [email protected]

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web cache replacements 張燕光資訊工程系成功大學 [email protected]