Provisioning Content Distribution Networks for Streaming Media Jussara M. Almeida Derek L. Eager Michael Ferris Mary K. Vernon University of Wisconsin-Madison

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

Documents

Provisioning Content Distribution Networks for Streaming Media Jussara M. Almeida Derek L. Eager Michael Ferris Mary K. Vernon University of Wisconsin-Madison