provisioning content distribution networks for streaming media jussara m. almeida derek l. eager...

Provisioning Content Distribution Networks

for Streaming Media

Jussara M. Almeida

Derek L. Eager Michael Ferris Mary K.

Vernon

University of Wisconsin-MadisonUniversity of Saskatchewan

Outline

• Problem statement and motivation

• CDN delivery protocols and cost models

• Key results:– unconstrained proxy servers

– Cost-effectiveness of proxy servers

– proxy servers with limited space and bandwidth

• Conclusions and on-going work

Problem: Media CDN Design

Clients

Internet

Proxy Server

Clients

Proxy Server

Origin Server

Scalable streaming protocol: Bandwidth Skimming [EaVZ00]

Each proxy can store a media prefix of size f, 0 f 1

MulticastMulticast

Multicast or Unicast

Goal: insight into value of f that minimizes delivery cost

Motivating Example #1

048

121620

1 10 100 1000 10000Client Request Rate (N )

Requ

ired

Serv

er

Band

wid

th (

B)

BandwidthSkimming(b=2)

Example: 10 proxy servers, client request rate per proxy = 100

(total client request rate = 1000)

cost tradeoff: 10770 proxy streams vs. 12 origin streams

bandwidth needed to serve each client immediately:

Scalable Delivery Protocols

• BWSkim(b):– Proxy and origin use simple Bandwidth Skimming– b: client bandwidth (e.g., b=2 or b=1.2)

• BWSkim/U(b):– Proxy uses Bandwidth Skimming

– Origin uses unicast to the proxy.

• BWSkim+Batch(b):

– If 0 f 1: clients use one unit of bandwidth to batch together for a suffix stream from the origin

BWSkim(b):

BWSkim(2): Streams Requested by Proxy A Clients

Bproxy(f,N,P,b) = ln (1 + f Nproxy/)

Borigin(f,N,P,b) = ln(1+Norigin/)

where: Nproxy = N/P and

PfN

NfNorigin /

)1(

00.10.20.30.40.50.60.70.80.9

1

Time

Pos

itio

n in

Med

ia F

ile Proxy B client stream

f

Prefix merges

Suffix merges

BWSkim/U(b):

BWSkim/U(2): Streams Requested by Proxy A Clients

Bproxy(f,N,P,b) = ln (1 + f Nproxy/)

Borigin(f,N,P,b) = P ln(1+ Norigin/)

where: Nproxy = N/P and

proxy

proxyorigin fN

NfN

)1(

Proxy B client stream

f

Prefix merges

Suffix merges

0

0.2

0.4

0.6

0.8

1

Time

Posi

tion

in M

edia

File

Delivery Cost ModelEach object i: delivery costi = Borigin,i+ P Bproxy,iP: number of proxy servers

: average cost of a proxy stream / average cost of one origin stream

Borigin,i and Bproxy,i depend on:

• fi = fraction of media object i stored at the proxy

• N = total request rate (avg. # of client arrivals per playback duration)

• b = client bandwidth







Unconstrained proxy server: find fi that minimizes delivery costi







Unconstrained proxy server: find fi that minimizes delivery costi

Constrained proxy server: min delivery costi (n objects)

subject to: fi proxy disk space, Bproxy,i max. proxy bandwidth

• Mixed Integer Programming, solved using GAMS library

{fi

}ni

ni

ni

Cost Model Applications• Configuring the CDN:

– protocol delivery cost comparisons• Batching vs. non-batching,• Multicast origin vs. unicast origin• Client bandwidth, b 2 vs b = 1.2.

– proxy content (f) that minimizes delivery cost

– Cost-effectiveness of proxy servers

• Analysis over a wide region of the design space

Proxy Servers with Unlimited Bandwidth and Storage

Unicast Origin Multicast Origin

Protocol Cost Comparison (unconstrained proxies)

P=1 P=10 (Unicast Origin: P 1)

Multicast Origin

0 0.1 0.3

0.50.8

110

100

1000

1000

0

01020

30

40

50

Cos

t In

crea

se

(%)

N/P

0

0.3

0.8

110

100

1000

1000

0

010

20

30

40

50

N/P

0

0.3

0.8

110

100

1000

1000

0

0

10

20

30

40

50

N/P

P=100

• BWSkim (2) is preferred unless P is large and N/P is very small

BWSkim(2) vs BWSkim+Batch(3), each with optimal f: (large system design space)

Optimal f: BWSkim(b) (unconstrained proxies)

f=1 or f=0 is optimal

Proxy servers are cost-effective (i.e., f=1) only if: • Origin uses unicast or P=1 or

• proxy stream is free or costs a very small fraction of cost of an origin stream.

0 0.1 0.3 0.5 0.8

110

100

1000

1000

0

0

0.2

0.4

0.6

0.8

1

Fra

ctio

n St

ored

N/P0

0.3

0.8

1

100

1000

0

00.20.40.60.8

1

Fra

ctio

n S

tore

d

N/P

0

0.3

0.8

110

100

1000

1000

0

00.20.40.60.8

1

Fra

ctio

n S

tore

d

N/P

Multicast Origin, P=1

Unicast Origin, P 1

P=10

Multicast Origin

P=100

Cache Content: BWSkim+Batch(b)(unconstrained proxies)

0

0.3

0.8

1

100

1000

0

0

0.2

0.4

0.6

0.8

1

Fra

ctio

n S

tore

d

N/P

Multicast Origin: P=100

• BWSkim+Batch[/U](3) outperforms BWSkim[/U](2) and the optimal content is prefix caching only if:

– Multicast origin,– Large P (P 10),

– Low N/P (N/P 1),– Intermediate values of ( =

0.1).

Protocol Cost Comparison (unconstrained proxies)

• b=1.2 increases CDN cost by a factor of 1.5 – 3

BWSkim(1.2) compared to best policy with b2: (P=10)

00.

1

0.3

0.5

0.8 1 10 10

010

0010

000

0

50

100

150

200C

ost

In

crea

se

(%)

N/P

Cost-Effectiveness of Proxy Servers

Proxy servers cost-effective if

• the origin server uses unicast

• the file request rate is low

• cost of proxy stream is small fraction of cost of an origin stream

Question: how small?Multicast origin,N 10:

Answer:

~1/P (or less)0

1

2

3

4

5

6

7

8

0 20 40 60 80 100P

Del

iver

y C

ost = 0.1

= 1/P

= 5/P

Proxy Servers with Limited Disk Storage

and Bandwidth

~ 1/P (or less)or Unicast origin

Constrained Proxies: Key Parameters

M: total client arrival rate, in arrivals per T (all files)

Ps: proxy storage capacity, as a fraction of all files

Pb: proxy bandwidth, as a fraction of bandwidth needed if proxy stores all files

– Ps and Pb computed for modern disks, MPEG-2 streams (4 Mb/s)

– Each disk: 44 hours of content and 42 concurrent streams

– Vary M, number & length of files, file popularity skew, # disks:

0.08 Ps 0.68 , Pb 0.02

– Distribute files across the disks to balance the load

Proxy Disk Space & Bandwidth

• Scenario:– 1000 two-hour MPEG-2 (4 Mb/s) movies– 1000 requests / hour at each proxy: M/P = 2000– Zipf distribution of file popularities

Average bandwidth needed for all files = 332 streams

• If proxy has 5 disks:

– Ps = = 0.11 Pb = = 0.63

2000

445332

425

0

0.2

0.4

0.6

0.8

11 22 43 64 85 106

127

File

Fra

ctio

n St

ored

0

0.2

0.4

0.6

0.8

1

1 23 45 67 89 111

File

Fra

ctio

n S

tore

d

True Optimal

(Pb =0.32 (bw)

Near Optimal

(Pb =0.32 )(bw)

(b =2, Ps=34%, M/P =1000, n =128, T =2h)

• Near Optimal Cache Content (contiguous set of full files) yields delivery cost within 0.05% of true optimal for all CDNs studied.

• Optimal Caching Policy for BWSkim/U(b) is full-file caching.

Optimal vs. Near Optimal BWSkim(b) Proxy Content

(unicast origin, constrained proxies)

Optimal Content for BWSkim (b)


00.20.40.60.8

1

1 26 51 76 101

126

File

Frac

tion

Stor

ed

00.20.40.60.8

1

1 25 49 73 97 121

File

Fra

ctio

n St

ored

00.20.40.60.8

1

1 27 53 79 105

File

Fra

ctio

n St

ored

00.20.40.60.8

1

1 27 53 79 105

File

Fra

ctio

n St

ored

Pb 1

P=10, =0.1,(cap), M/P=100

Pb 1

P=10, =0.3,(cap), M/P=100

Pb 1 ,

P=100, =0.1,(cap), M/P=100

Ps = 34%, n=128, T=2h

Pb=0.32

P=10, =0.1, (both),

M/P=1000

• Full file caching is the most cost-effective

• Less popular files are cached as either Pb decreases or or P increases.

• BWSkim/U(b) is more cost effective than BWSkim+Batch/U(b+1)

• BWSkim+Batch/U(b+1): prefix caching, cost improves up to 8%

(BWSkim/U(2), Pb1, Ps=34%, n =128, T =2h)

0

0.2

0.4

0.6

0.8

1

1 21 41 61 81 101

121

File

Fra

ctio

n S

tore

d

M/P = 1000

(unrealistic Pb )

0

0.2

0.4

0.6

0.8

1

FileF

ract

ion

Sto

red

M/P = 100

(realistic Pb )

• Arbitrarily setting values for proxy bandwidth leads to unrealistic and non-optimal results

Unrealistic Proxy Bandwidth Assumption


• BWSkim/U(1.2) increases the delivery cost by up to a factor of three

(same for unconstrained proxies)

Cost Increase of BWSkim/U(1.2) (unicast origin, constrained proxies)

0.08

5

0.34

1010

010

00

1000

0

0

0.2

0.4

0.6

0.8

1

Cos

t R

atio

PsM/P

Ratio of delivery cost for BWSkim/U(2) to cost of BWSkim/U(1.2)

Cost Increase of BWSkim(2) vs. BWSkim+Batch(3):

• BWSkim+Batch(3) and prefix caching is preferred only if:• large P, moderately small Pb

• a large number of the popular files have N/P 1 and• cost of proxy stream is very small or zero

• In all other scenarios: BWSkim(b) + full file caching is optimal

0.131

0.321Pb=

10

100

1000

1000

0 1 10 100

0%

20%

40%

60%

80%

100%

Co

st

Inc

rea

se

(%

)

M/P P

BWSkim(2) vs. BWSkim+Batch(3)(multicast origin, constrained proxies)

= 0, Ps=34%

Optimal Content for BWSkim+Batch(3)

(multicast origin, constrained proxies)

0

0.2

0.4

0.6

0.8

1

1 18 35 52 69 86 103

120

File

Frac

tion

Stor

ed

0

0.2

0.4

0.6

0.8

1

1 19 37 55 73 91 109

127

File

Frac

tion

Stor

ed

Pb 1

P=10, (cap) Pb =0.32

P=10, (bw)

0

0.2

0.4

0.6

0.8

1

File

Frac

tion

Stor

ed

Pb 1

P=100, (cap)

Ps=34%, = 0

• BWSkim+Batch(b) caches primarily prefix files.

• Less popular data is cached as either Pb decreases or or P

increases.

Protocol Cost Comparison (constrained proxies)

Cost Ratio for Origin Unicast vs. Origin Multicast:

( = 0)

• Multicast origin significantly reduces delivery cost unless

- Total request rate per proxy, M/P, is small or P 1

10100

100010000 1

10100

123456789

10

Cos

t F

acto

r

M/P P

60 64

Conclusions• Scalable multicast delivery involves new cost trade-offs

• Simple delivery cost models can yield significant insight

• Insights:

• BWSkim(b) is preferred over BWSkim+Batch(b) unless

- P is large and N/P is very small

• BWSkim+Batch(3) system: prefix caching is optimal

• BWSkim(b): f=0 or f=1; f=1 only if • the origin server uses unicast

• the file request rate is low (N 1)

• cost of proxy stream is small, i.e., ~1/P (or less)

• Multicast origin greatly decreases CDN cost if M/P 10

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