Cache Replacement Algorithm

元智大學 資訊工程所 系統實驗室陳桂慧

1999.05.04

Outline

• Exiting document replacement algorithm

• Squid’s cache replacement algorithm

• Ideal

• Problem

Exiting Document Replacement Algorithm

• Least-Recently-Used (LRU) – evicts the document which was requested the

least recently.

• Least-Frequently-Used (LFU) – evicts the document which is accessed least

frequently.

• Size [WASAF96] – evicts the largest document.

• LRU-Threshold [ASAWF95] – is the same as LRU, except documents larger than

a certain threshold size are never cached

• Log(Size)+LRU [ASAWF95] – evicts the document who has the largest log(size)

and is the least recently used document among all documents with the same log(size).

• Hyper-G [WASAF96] – is a renement of LFU with last access time and siz

e considerations;

• Pitkow/Recker [WASAF96] – removes the least-recently-used document, except

if all documents are accessed today, in which case the largest one is removed;

• Lowest-Latency-First [WA97] – tries to minimize average latency by removing the

document with the lowest download latency rst;

• Hybrid, introduced in [WA97], – is aimed at reducing the total latency. – function value : the utility of retaining a given document

in the cache• the smallest function value is then evicted. • a document p located at server s• cs - the time to connect with server s, • bs - the bandwidth to server s, • np - the number of times p has been requested since it was brou

ght into the cache, • zp - the size (in bytes) of document p. • Wb and Wn are constants. Estimates for cs and bs are based on

the the times to fetch documents from server s in the recent past.

p

Wp

s

bs

z

nbW

C n))((

• Lowest Relative Value (LRV), [LRV97] – LRV take into account locality, cost and size of a docu

ment.– function value : the utility of keeping a document in th

e cache. • evicts the document with the lowest value.• the value is based on extensive empirical analysis of trace

data. • Pi - the probability that a document is requested i + 1 times gi

ven that it is requested i times.• Di - the total number of documents seen so far which have b

een requested at least i times in the trace• Pi - estimated in an online manner by taking the ratio Di+1/Di,

• Pi(s) - is the same as Pi except the value is determined by re

stricting the count only to pages of size s.

• 1-D(t) - the probability that a page is requested again as a function of the time (in seconds) since its last request t;

D(t) = .035 log(t + 1) + .45(1-e^(-t/2e6))

• document d of size s and cost c,

• i - the last request to d is the i’th request to it

• t - the last request to d is the was made t second ago

• d’s value in LRV

V(I,t,s) = P1(s)(1-D(t))*c/s if i=1

V(I,t,s) = Pi(1-D(t))*c/s otherwise

Squid’s Cache Replacement Algorithm

• LRU

• When selecting objects for removal, Squid – examines some number of objects and – determines which can be removed and which cannot

• If the object is currently being requested, or retrieved from an upstream site, it will not be removed.

• If the object is ``negatively-cached'' it will be removed.

• If the object has a private cache key, it will be removed

• Finally, if the time since last access is greater than the LRU threshold, the object is removed.

• LRU threshold value is dynamic calculated based on the current cache size and the low and high mark (90% - 95%).– The LRU threshold scaled exponentially between the high an

d low water marks. • the store swap size is near the low water mark, the LRU threshold ↓• the LRU threshold represents how long it takes to fill (or fully replac

e) your cache at the current request rate. ( 1~10 days )

• Squid 1.1 v.s. Squid-2– Squid1.1 cache storage is implemented as a hash table with s

ome number of "hash buckets." • scans one bucket at a time and sorts all the objects in the bucket by thei

r LRU age.

– Squid-2 we eliminated the need to use qsort() by indexing cached objects into an automatically sorted linked list.

• every time an object is accessed, it gets moved to the top of the list.

Ideal

• With the same document size, => removing the document with the lowest do

wnload latency first

• With the same download latency time=> removing the largest document first

• The rate R↑, removing first.

R = Zp / TtotZp - the size of document of p

Ttot - total latency time

Problem

• Hybrid Algorithm

• The contents of squid’s access log– Elapsed time

p

Wp

s

bs

z

nb

WC n))((