pricing internet access - princeton universitychiangm/pricingtalk.pdf · 2010-11-13 · global ip...

South California Symposium On Network Economics, November 11, 2010

Pricing Internet Access -- How To Engineer Your Monthly Bill Mung Chiang, Princeton University

Some 2010 (WSJ) Headlines

1 OCTOBER 19, 2010, 1:09 P.M. ET

3rd UPDATE:Verizon Wireless To Unveil Tiered Data Plan Oct 28

1 TECHNOLOGY2 OCTOBER 15, 2010

FCC Unveils Billing Rules

AT&T Sees Hope on Web RulesExecutive Sees Positive Step in Google-Verizon Proposal on Broadband Regulation

1 E 3, 2010

AT&T's Wireless Pricing Shift Will Test Behavior

1 TECHNOLOGY2 JUNE 2, 2010

AT&T Dials Up Limits on Web Data1 TECHNOLOGY2 MAY 5, 2010

New U.S. Push to Regulate Internet Access

Broadband Plan Faces Hurdles

http://online.wsj.com/public/page/news-tech-technology.html






What Your New Bill May Look Like

paid in part by Apple

Guaranteed express delivery

Usage price $50.99

Time of usage discount $69.88Some of the 45 types of taxes I pay

Why

Pricing can lift the pressure valve off the Internet traffic explosion

White Paper

© 2010 Cisco and/or its affiliates. All rights reserved. This document is Cisco Public Information. of 14

Figure 1. Cisco VNI Forecasts 64 Exabytes per Month of IP Traffic in 2014

For more details, see the paper entitled “Cisco VNI: Forecast and Methodology, 2009–2014.”

Figure 2 shows the components of consumer Internet traffic growth. Of the 42 exabytes per month of consumer Internet traffic that will be generated every month in 2014, nearly 60 percent will be due to Internet video.

Figure 2. Cisco VNI Global Consumer Internet Traffic Forecast

White Paper

© 2010 Cisco and/or its affiliates. All rights reserved. This document is Cisco Public Information. Page 10 of 14

Figure 8. Global Business IP Traffic Will Grow at a CAGR of 21 Percent from 2009–2014

Global IP Traffic Growth: Mobile Mobile video will be responsible for the majority of mobile data traffic growth between 2009 and 2014. As Figure 9 shows, overall mobile data traffic is expected to grow to 3.5 exabytes per month by 2014, and over 2.4 of those are due to mobile video traffic.

Figure 9. Global Mobile IP Traffic Will Grow at a CAGR of 108 Percent from 2009–2014

Issues at Stake

1. Four Questions of Pricing

What to Charge?

Whom to Charge?

How much to Charge?

How to Charge?

2. Universal Coverage

FCC National Broadband Plan

How to improve reach and speed of US broadband access?

Who’s going to pay the $350B bill?

Consumer?

Taxpayer?

Others?

3. Network Neutrality

Different Definitions:

Access/choice

Competition/No monopoly

Equality/No discrimination

Tough Issues:

Efficiency-fairness tradeoffs in parties with conflicting interests

Incentives for innovation and consumer experience

Colors of Neutrality

Red: vertical integration and service limitation

Orange: protocol/user-ID based discrimination

Yellow: usage-based pricing

Green: traffic management and QoS provisioning

Roles of government?

Enable viable competition, or

Regulatory micro-management?

4. ISPs Two Problems

!"# $%&'( )(*(+%,-.*

!"#$% &'()*'+ ,#&-./ 0)(&)$+ 1$2'.*1%)*'+ 3#, '$+ 4.'& )$+ $'*,#&- #5'&)*#& '6#$#"16 +&12'$

7'3)21#& 1$8(4'$6' *3' $'*,#&- 5'&8#&")$6'9:;<)$= &'.')&63 ,#&-. .*4+1'+ &'2'$4' ")>1"1?)*1#$ 1$

6#$%'.*17(' $'*,#&-.@ <)6-1' <).#$ '* )(9AB/ !6'"#4%(4 '* )(9

A:C3)--#**)1 '* )(9

AA/ D1 '* )(9

AE8#64.'+

#$ *3' $'*,#&- &'2'$4' ")>1"1?)*1#$ 7= 4.1$% 4.)%' 5&16' )$+ 8()* 5&16'/ C3'$ '* )(9AF.*4+1'+ *3'

.1"1()& 5&#7('" 74* 6#$.1+'&'+ 1$6#"5('*' $'*,#&- 1$8#&")*1#$9 G=$)"16 5&161$%/ ,3163 1. &##*'+ 1$

=1'(+ ")$)%'"'$*/AH,). 5&#5#.'+ 8#& *'('6#""4$16)*1#$ $'*,#&-. *# &')5 &'2'$4'9

AIJ1"'

+'5'$+'$* 5&161$% 1. 6#$.1+'&'+ 1$ K1)$% '* )(9/AL,3'&' *3' )4*3#&. 5&#5#.' ) "#+'( ,1*3 *1"'

+'5'$+'$* 6#$.4"'& 4*1(1*1'. )$+ )$)(=?' *3' &'2'$4' (#.. *# ) "#$#5#(= MCN +4' *# 1$.488161'$*

1$8#&")*1#$ )7#4* 6#$.4"'& 4*1(1*1'.9

:;0)(&)$+/ K9 OP6#$#"16 <#+'(. #8 Q#""4$16)*1#$ R'*,#&-./S !"#$%&'"() *+&,'"-./ 01-2&%' 3 "4 5%'6,'$-4(% 7,8%."4# -48

94#"4%%'"4#/ C5&1$%'& N47(1.31$% Q#"5)$=/ ABBT9AB

<)6-1' <).#$/ K9 U9 )$+ V)&1)$/ W9/ ON&161$% Q#$%'.*17(' R'*,#&- X'.#4&6'/S :999 ;,+'4-. ,4 !%.%(&%8 <&'%-) "40,$$+4"(-&",4)/ 2#(9 :E/ $#9 L/ 559 ::F: ::F;/ C'59 :;;H9 !%% )(.# <)6-1' <).#$/ K9U9 )$+ V)&1)$/ W9/ ON&161$% *3' M$*'&$'*/S 1$

5+=."( <((%)) &, &1% :4&%'4%&/ Y9 U)31$ )$+ K9 U'(('&/ P+.9/ Q)"7&1+%'/ <!Z <MJ N&'../ :;;H9A:!6'"#%(4/ G9/ [?+)%()&9 !9/ OQ#"5'*1*1#$ )$+ P88161'$6= 1$ Q#$%'.*'+ <)&-'*./S7-&1%$-&"() ,6 >2%'-&",4) ?%)%-'(1/ 2#(9 EA/

$#9 : 559 : E:/ \'79 ABBL9AAC3)--#**)1/ C9/ C&1-)$*/ X9/ [?+)%()&/ !9 )$+ !6'"#%(4/ G9/ OJ3' 5&16' #8 C1"5(161*=/S :999 ;,+'4-. ,4 !%.%(&%8 <'%-) "4

0,$$+4"(-&",4)/ 2#(9 AI/ $#9 L/ 559 :AI; :ALI/ C'59 ABBT9AED1/ C9/ W4)$%/ K9 )$+ D1/ C9/ OX'2'$4' <)>1"1?)*1#$ 8#& Q#""4$16)*1#$ R'*,#&-. ,1*3 ].)%' Y).'+ N&161$%/S J'639 X'59/ J3'

Q31$'.' ]$12'&.1*= #8 W#$% U#$%/ ABB;9AF

C3'$/ W9/ )$+ Y).)&/ J9/ O[5*1")( R#$(1$')& N&161$% 8#& ) <#$#5#(1.*16 R'*,#&- C'&216' N&#21+'& ,1*3 Q#"5('*' )$+

M$6#"5('*' M$8#&")*1#$S/ :999 ;,+'4-. ,4 !%.%(&%8 <'%-) "4 0,$$+4"(-&",4)/ 2#(9 AH/ $#9 I/ 559 :A:I :AAE/ !4%9 ABBL9AHC"1*3/ Y9/ D'1"-43('&/ K9 )$+ G)&&#,/ X9/ O^1'(+ <)$)%'"'$* )* !"'&16)$ !1&(1$'./S :4&%'6-(%)/ 2#(9 AA/ $#9 : 559 T E:/ K)$9

\'79 :;;A9AI<).4+)/ ^9 )$+ 03)$%/ C9/ OG=$)"16 N&161$% 8#& R'*,#&- C'&216'@ P_41(17&14" )$+ C*)71(1*=/S7-4-#%$%4& !("%4(%/ 2#(9 FH/

$#9 I/ 559 THL TI;/ K4$' :;;;9 !%% )(.# N).63)(1+1./ M9/ J.1*.1-(1./ K9/ OQ#$%'.*1#$ G'5'$+'$* N&16' #8 R'*,#&- C'&216'./S

:999@<07 *'-4)-(&",4 ,4 A%&B,'C"4#/ 2#(9 T/ $#9 A/ 559:L: :TF/ !5&9 ABBB9ALK1)$%/ D9/ N)&'-3/ C9/ 0)(&)$+/ K9/ OJ1"' +'5'$+'$* R'*,#&- N&161$% )$+ Y)$+,1+*3 J&)+1$%/S 5',(/ :999 D,EFGGHI "4

(,4J+4(&",4 B"&1 :999@:K:5 A>7! FGGH/ !5&9 ABBT9

A:

Cost

Revenue

Distribution

Bandwidth consumption

Profit margin

Commoditization

New Business Models for ISPs

Avoid commoditization

Offer value-added services beyond connectivity service

Bridge content-pipe divide

Need a new interface between ISP and content/app providers

Innovate pricing

Pricing as Network Management (if timescales match)

Nature of This Talk

Not on specific model/analytic/numerical results

Not an exhaustive overview of pricing literature

Not on non-access Internet pricing or general network economics

A biased path traversing vertices of the problem space

And samples challenges facing the research community

Two-Way Interactions: Subject

Pricing changes technology

Video ads in support of cheap app/content

Technology changes pricing

Heterogeneous wireless platforms

Two Way Interactions: Method

Engineering research benefits from economics research

2-sided, utility model, game, auction, etc.

Economics research benefits from engineering research

Dynamically varying interaction model

Sample Scenarios

5-Party Interactions

Transportation Operator

Distribution Operator

Content/App Producer

Content/App Consumer

Vendors

Basic Benchmark!"#$%&'( )*(+, -&'.#&+

!"#$%&'( )* !"#$"%$&' &( )*+'"#$& ,- %.#&/0.1/% '&% /'2+# */3%&4+# *&'%#&5

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

!"#$%&'( )

/%&'%,'($ (0 !"#$%&'( )12&(34253, $(, 3$6#& "3+,(7#& "($,&(8

!"#$%& '(()%( *+, )(%( &+% -%&.,#$ "-/ +,.0 1,2"3 %-/)(%#( "22%(( '-&%#-%&4 5%%# &, 5%%# "55362"&6,-5#,76/%#( ()2+ "( 86& 9,##%-& )(% 3,2"3 -%&.,#$4&#"::62 5"&&%#-( )-2%#&"6-

;("<% 5"&&%#-( = +%"7> "-/ 36<+& %-/ )(%#( ?)"36&> ,: (%#762% 3%7%3( -,-% @#626-< "-/ A6336-< "##"-<%B%-&(C .+, 5">(.+,B0 D-/ )(%#( 5"> 'E@4 F@ /,%( -,& 5">G -,2,-&#"2&)"3 "##"-<%B%-&

9%#B( "-/ 2,-/6&6,-( 6-23)/% &+% %::%2&( ,:A)-/36-< = %-/ )(%# 5">B%-& A"(%/ ,-2,--%2&6,- "-/ ,- )("<%4 -, #%&"63 (%#762%(,::%#%/ A> &+% 'E@0

H%&.,#$ 6-7%(&B%-& (&#"&%<6%( = 6-2#%"(% 6-3,2"3 -%&.,#$ 2"5"26&>G /%2#%"(% 6- B6//3% B63%2"5"26&>

I2,-&6-)%/JK

8++# %& 1++# %+*.'&5&0C >&#@3 /'2+# %.+ 1#+4$3+ " 8E*"' <+ <&%. " *5$+'% (&# "' "115$*"%$&' 3/*. "3 " 4&9$+"'2 " 3+#9+# %."% 3.$13 %.+ 4&9$+ %& &%.+# /3+#3 '+"#<CG(%% )*+'"#$& H 2$"0#"4I: 6' %.$3 *"3+7 *."#0$'0 %.+ +'2/3+# (&# %.#&/0.1/% 1#+3/4+3 %.+ +'2 /3+# ."3 %+*.'$*"5@'&>5+20+ &( %.+ /3+ &( $%3 &'5$'+ 8E37 >.$*. 4"C <+/'5$@+5C:

D AB8 "% JK:

K

Cost recovery via median-user, 1-sided pricing is challenging

Cost Recovery

!"#$%&$'()*+

,"#$#-&" .#)(/&$0 1(2'&3(-($% 4#55&6&/&%7 89 :;6/( "#-<;$7 =;5 <3(>(33() ;""(55 %# "#$%($%?3(5'/%9 @A4 /(>% B&%= /#B ($) '5(35C $(%B#3D )(03;)(5

4#55&6&/&%7 E9 @A4 ;$) ";6/( "#-<;$7 =;F( (2';/ ;""(55 %#"#$%($%? 3(5'/%9 (&%=(3 -;3D(% ";$ 5'<<#3% %B# "#-<;$&(5 #3#$( 0#(5 #'% #> 6'5&$(55

4#55&6&/&%7 G9 H#%= ";$ )&>>(3($%&;%( %=(&3 <3#)'"%5 !I:1C JI1C%&(5 %# B&3(/(55C 5(% %#< 6#K+? 3(5'/%9 6#%= ";$ 5'3F&F( &> -;3D(%5(0-($%5 ;3( /;30( ($#'0=

J;%; 1(2'&3() L(%B#3D 5&M( ;$) %3;>>&" >/#B 67 ";33&(3 :#$%($% %(3-5 ;$) "#$)&%&#$5

N'$)&$0 @55'(5 O$)(3 B=;% "&3"'-5%;$"(5 ";$ ;$ @A4 0;&$ -#5% >;F#3()$;%&#$ 5%;%'5 >#3 "#$%($%P

!"#$ #$ %&' ( %)* #$$+), -+' '") .//$"&+01 2('")3 1('( &% 4(-0) !5 4&%')%'4&%'3(4'$678 9:(#0(-#0#'; &< 4&%')%' #%3+3(0 (3)($ 4&+01 2)%)3(') 3):)%+)$$+-=)4' '& /9. ($$)$$>)%'$ (%1'")3)<&3) #%43)($) '(?) 3(')$ (' '")$(>) '#>)6

!"#$%&'( )*!+ ,#-#$.#/0(12 34(51 60(78#2'2'-# 4("%4 $#25(&9 $(2 1:(5$;

7@

78 A0($$, 5#4'&3, )' (06, B!") C(4?)' !3(#% D))1$ '& E'&F (' G:)3; H&&3,I DG/9, JKK8, 9FF)%1#L M6

The Potential of 2-sided pricing

Adding Server by ISP!"#$%&'( )*

+!, -.//'$0 % 1#&2#& ($ '/1 (3$ $#/3(&4

!"# $#%&'()*+,,-.%

/0122(%2)'3(

$).453&%6()&7-'8%'93(4

/0$).453&%

+':%(0%%(-&2;-'%7

<-2: "&=#3&'%&'0%%(-&2;-'%7

!"# 1#%&'()*+,,-.%

!"# ##%&'()*+,,-.%

>%2-3&)*?-5%(

8%'93(4

;.%&)(-3 @!"#$ %&''()* + ,-./-. 0)

(', 01) )-'10.2

!"# 1;%(A%(

6(),,-.;'(%)B%= ,(3B /!"#8%'93(4 ;%(A%(7

!"#$%&'( )5+!, -.//'$0 % 1#&2#& ($ % &#0'($%6 $#/3(&4

3

Localization of trafficImpact on middle mile cost recovery

Distribution by CDN!"#$%&'( )

*'+, #$- "($.#$. -'/.&'01.#- (2#& 3104'" 567

!"#$%&'( )* !"#$% &'%("#$' )*'$+,) ("#$% -'%, %.$ /%0+*"%. *% ,+.1 234 .$*5%'6)

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

!"#$%&'( )

8'-#( 3&(2'-#& /.&#%9/ 2'-#( :&(9($# 4("%.'($ .( 9%$; <!= $#.>(&?/

#$%&"' (!!)"! *+, )!"! '+" -"'.,%& $-/ +,.0 1,2$3 "-/ )!"%! $22"!!(-'"%-"'4 %"5,'" 67/", 8%,67/"% '"%57-$'"! '%$9972

:!$;" 8$''"%-! < +"$6= $-/ 37;+' "-/ )!"%! >)$37'= ,9 !"%672" 3"6"3! -,-" ?%727-; $-/ @7337-; $%%$-;"5"-'!A .+, 8$=! .+,50 B-/)!"%! 8$= (C?4 %"5,'" 8%,67/"% /,"! -,' +$6" $2,-'%$2')$3 $%%$-;"5"-' .7'+ 3,2$3 8%,67/"% ,%'%$-!7'7-; 2$%%7"%

D"%5! $-/ 2,-/7'7,-! 7-23)/" '+" "99"2'! ,9 @)-/37-; <"-/ )!"% 8$=5"-' @$!"/ ,- 2,--"2'7,- $-/ ,- )!$;"

E"'.,%& 7-6"!'5"-' !'%$'";7"! < %$7!"! '%$-!8,%' 2,!'!,9 '%$-!7' 8%,67/"% $-/ 3,2$3 8%,67/"%4 -, %"6"-)" ,99!"'9%,5 67/", 8%,67/"%

B2,-,572 #,/"37-; F"G)7%"5"-'! B!'75$'" "99"2' ,9 %"5,'" 67/", ,- 3$!' 573"H !"2,-/573"H $-/ 57//3" 573" 2,!'! 9,% '%$-!7'7-; $-/'"%57-$'7-; (C?!

(-6"!'7;$'" "2,-,572 "99727"-2= ,9 /=-$572 @$-/.7/'+5$-$;"5"-' %"!)3'7-; 9%,5 ,99!"''7-; %"5,'" 67/",

B!'75$'" /"5$-/ !'75)3$'7,- 9%,5 %"5,'" 67/", $' 3,.8%72"

I2,-'7-)"/JK

F=") ") + *1&$ %- *5% )"#$# ,+'6$* &'%9/$,BF=$ 234) '$0$"(".8 *=$ ("#$% 0%.*$.* +'$ .%*+9/$ *% 0=+'8$ *=$ ("#$% &'%("#$'> 0+7)".8 +.".$--"0"$.* 7)$ %- *=$"' .$*5%'6)B F% $)*",+*$*=$)$ 0%)*)> "* ") .$0$))+'1 *% 8+*=$' #+*+ %.*=") *1&$ %- &%".* *% ,7/*"&%".* *'+--"0 *%

GG

CDN contract and net cost reductionHow to charge between CDN and ISP

Distribution by P2P

!""# $% &""# $#'(()* '+,% &%,", ' -"$.%#/ 0'-'1"0"-$ &#%2+"0$% $3" 45!6 73"- ' &""# $% &""# '&&+)*'$)%- ,+%., )$, -"$.%#/8'- 45! 0'9 :"*):" $% $3#%$$+" $3" '&&+)*'$)%-6 ;3), .', $3" 0')-),,<" +)$)1'$": )- *%<#$=6 >%-1"# $"#08 '- 45! ('*", $3" (<#$3"#*3'++"-1" %( $#9)-1 $% &#":)*$ <," %( &""# $% &""# $"*3-%+%196;3" $"*3-%+%19 *%<+:8 (%# "?'0&+"8 ':: $% )$, +',$ 0)+"2'-:.):$3 *'&'*)$9 -"":, .3)+" #":<*)-1 0)::+" 0)+" *'&'*)$9-"":, )( $#'(()* 1"$, ,3)&&": +%*'++9 (#%0 !@ $% !@6

!"#$%&'%()*+

,-$%$.'- /$*)0'%1 2)3('4).)%&5 67$ 5'*)* .849)& 8%80:5'5 ; )<&)4%80'&')5 $%=>?

=>? -8%%$& @'00 A))4 &$ A))4 A4$B'*)4 ; %$-$%&48-&(80 8448%1).)%&C :)& A))4 &$ A))45:5&).5 @)%)D'& D4$. &E) (5) $D &E) %)&7$49

,5&'.8&) )DD)-& $D A))4 &$ A))4 *).8%* $%085& .'0)C 5)-$%* .'0)C 8%* .'**0) .'0) -$5&5

=%B)5&'18&) )-$%$.'- )DD'-')%-: $D *:%8.'-@8%*7'*&E .8%81).)%& 4)5(0&'%1 D4$.$DD5)&&'%1 A))4 &$ A))4 %)&7$49 50$7*$7%5

,5&'.8&) *).8%* 5&'.(08&'$% D4$. 0$-800:-8-E)* E'1E 5A))* 5)4B'-)5 !E'1E)4 3(80'&:C0$7)4 *)08:+

F8&8 2)3('4)* G(:)4 @)E8B'$4 D$4 5)4B'-)5 (5'%1 A))4 &$ A))4&)-E%$0$1:

=%B)5&.)%&5 -8(5)* @: A))4 &$ A))4 %)&7$49(581)

H(%*'%1 =55()5 >E$(0* -$%&)%& A4$B'*)45 (5'%1 A))4 &$ A))45)4B'-)5 A8: D$4 0$-80 %)&7$49 (5)I >E$(0*&E): 1)& 8 4)D(%* D$4 0$7)4'%1 .'**0) .'0)-$5&5I

>E$(0* )%* (5)45 E8B) &$ A8: (581) -E841)5D$4 &48DD'- %$& (%*)4 &E)'4 -$%&4$0I

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

>%*'+ &""# $% &""# $#'(()* &'$$"#-, '#" -%$ &<2+)*+9 'B')+'2+" '$$3" 45! +"B"+6 4$ .%<+: 2" <,"(<+ $% 1'$3"# $3"," :'$' ,% $3" H@@*%<+: :"*):" .3"$3"# )$ 0'9 0'/" ,"-," $% ',,",, *%-$"-$&#%B):"#, (%# <,)-1 &""# $% &""# ,%($.'#" $% :"+)B"# $3")#'&&+)*'$)%-, $% "-: <,"#,6

!"#$%&'( )*("%+ ,##& -( ,##&

= #$.-85& BJ H##8 IDD H6 J: IKL FM6@6 @)#6 LDCDG6CD N%*3"$8 O68 '-: ;)#%+"8 O68 P;.% 5):": Q'#/"$,R S !#%1#",, N"&%#$8T 2KLF M$(4%80 $D ,-$%$.'-58 B%+6 JU8 -%6 J8 && IKV IIU8S<$<0- LDDI6

U

P2P dynamically changes traffic distribution

Video Multicasting

!"#$%&$'()*+

,-%- .(/'&0() 1'2(0 3(4-5&#0 6#0 5&)(# 7(05&"(7 8$5(7%9($%7 "-'7() 32 0(9#%( 5&)(# 32 %2:(

;'$)&$< &77'(7 =4#'>) 0(9#%( "#$%($% :0#5&)(07 :-2 -$ (?%0-"4-0<( 6#0 :#&$% %# 9'>%&:#&$% '7( #6 %4( 8$%(0$(%@

A#B "-$ %4(7( :0#5&)(07 3( 3&>>()@ =4#'>) &% 3( -7:("&-> '$&5(07-> 7(05&"( -77(779($%@

!"#"$%&'" #(" )&*" +, #(" #$-,,&. ,/+0 -'!0("#("$ &# &) &'.$"-)&'1 +2"$ #&%"3 45 -))"))&'1#(")" 6$+2&!"$) - $"/-#&2"/5 (&1( 789 ,"": #("977 0+;/! &'.$"-)" #(" ,;'!&'1 <-)" -'!&%6$+2" #(" ",,&.&"'.5 +, #(" ='#"$'"#3

!"#$%&'( )*+,-'.('$- /'0#( 1-&#%21 3&(2 4'54 #$0 "($-#$- 1'-#1 -4%- 5( (/#& 6%"76($# -&%$1'-'$5 $#-8(&71

-#&2'$%-'$5 ($ 2%$9 ,("%, :;<= $#-8(&71 1-&#%2#0 3&(2 -4# 6%"76($#

>?

The challenges of scaling up multicast streamingRegulatory issue of bundling

Wireless !"#$%&'( )

*'&#+#,, -%"./%0+ 1#23("#++4 *'1'

!"#$%&'( )*+ !"#$%&"' "( #$))&*) +"%*, &'%*)#"''*#%&"' -"&'%.

/+* ,$.% .#*'$)&" &' "0) ,&.% 1*$,. 2&%+ %+*-"%*'%&$, %+$% #"3-*%&%&"' #,0.%*). -**)&'4-"&'%. &'*((&#&*'%,5 6!"" 7#*'$)&" 89 1&$4)$3:*,"2;< /+* &..0* "( &'*((&#&*'% #"3-*%&%&=*$44,"3*)$%&"' 4"*. :$#> %" ?$))5 ?"%*,&'[email protected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

!"#$%&'( )*

5("%3'($ (6 "%&&'#& /(3#+ '$3#&"($$#"3'($ 7('$3,

#$%&"' (!!)"! *+, )!"! '+" -"'.,%& $-/ +,.0 123 4%,$/4$-/ 5%,62/"%!7""' $' 8$%%2"% +,'"9!

:!$3" 5$''"%-! ; +"$6< )!"%! =)$92'< ,> !"%628" 9"6"9! ; -,' &-,.- ?"%7! $-/ 8,-/2'2,-!@ 5$< %"-' >,% +,'"9A !,7" 5""%A !,7"%"B)2%" 5$<7"-' ', 8,--"8'

(-6"!'7"-' !'%$'"32"! ; %"/)8" '%$-!5,%' 8,!'!

C8,-,728 #,/"92-3 D"B)2%"7"-'! E,8$'2,- '+",%< 7,/"9! C>>"8'! ,> 9,8$'2,- !'%$'"3< ,- 4%,$/4$-/ -"'.,%& /"!23- (/"-'2>< 2-">>282"-82"! 2- 7$%&"' 4$!"/ !,9)'2,-! C!'27$'" "F'"%-$9 8,!'! ', '+" -$'2,-G! 4%,$/4$-/ -"'.,%&!

H$'$ D"B)2%"/ E,8$'2,- ,> 8$%%2"% +,'"9! $-/ (-'"%-"' 4$8&4,-" -,/"!

I)-/2-3 (!!)"! J+,)9/ IKK 8,-!2/"% .$<! ', 275%,6" 9,8$'2,- ">>282"-8<0

8A B#"'"35 -"&'%C KG#* 7$,*.3$' %" L*$#+ J)":,*3CM B#"'"35 -"&'%<")4<N&N&#* .$,*.3$' %" :*$#+ -)":,*3<+%3,<

8A

Heterogeneous wireless networks co-existingMuch more complicated ownership issues

The Four Questions

Q1. How Much to Charge?

From flat rate to usage based (often monthly volume)

Tiered-pricing

Piecewise-linear pricing curves

Control flat-rate part or slope of usage-based part

Flat rate inefficient (e.g., Berkeley INDEX experiment 1998)

Why did it prevail for so long: attract eyeballs AND

Time for Usage-Based Pricing

?

time

Bandwidth demand

Bandwidth supply/$

A Typical Pricing Graph

$

GB

Benchmark

AB

C

D

A Sample of Utility Model

Ui(x) = σiUαi(x)

Uα(x) =x1−α

1− α, α = 1

= log x, α = 1

utility level1/elasticity

x depends on flow and time

Unconstrained Revenue Max.

Maximize revenue under hard capacity constraint

Flat rate / Usage fee:

Maximize revenue-capacity cost tradeoff

4

Theorem 3: The optimal pricing scheme that achieves themaximum in (10) is given by setting for each t:

ht! = c"(!

f xtf!)

xtf! = u"

f#1(ht!/!t

f )gt

f! = !t

fuf(xtf!) ! µxt

f!

(11)

The optimal usage fee ht! is the marginal cost c"(!

f xtf!),

which is the same across all flows f , and the optimal flat feegt

f! = uf (xt

f!) ! µxt

f! is flow dependent. The ISP can fully

extract the consumer net-utility from the market if the marginalcost is the same at all data rates (uniform capacity cost). Forconvex cost functions, the ISP leaves behind some consumernet-utility.

C. An Illustrative Example

Consider a monopolist ISP providing connectivity service to10 flows over an access link of capacity C = 10Mbps. Con-sumers associated with each flow are assumed to have utilitiesof the form given in (4) with "f = ", and # = 1/" the commonelasticity of demand across all flows. We generate the utilitylevels !t

f as random variables with uniform distribution inthe range [!0, !1].

0 0.2 0.4 0.6 0.8 10

5

10

15

Inverse elasticity: !

Rev

enue

($)

TotalFlatUsage

0 0.2 0.4 0.6 0.8 10

5

10

15

20


Rf* /R

s*

Fig. 1. Comparison of revenue from flat pricing to usage based pricing atdifferent consumer demand elasticity.

Figure 1 illustrates the average revenue per unit time per unitflow generated by the monopolist ISP with no constraints onthe prices. The flat component of the revenue, which enablesthe monopolist to completely extract the consumer net-utility,increases with decreasing elasticity of demand. The usagecomponent of the revenue decreases with decreasing elasticityof demand. The lower part of Figure 1 plots the ratio of theflat component to the usage component of the revenue as givenby (9), demonstrating the increased reliance on revenue fromflat price at low consumer demand elasticity.The ISP pricing flexibility, in practice, is restricted along

time and across flows. In the following sections, we extendour model to quantify the revenue loss to the ISP and developpricing schemes to mitigate the loss.

IV. TIME CONSTRAINED PRICINGAs discussed in Section I, the common practice today is

for the ISP to price the total data volume, or equivalently, the

average data rate over the longer time horizon T . We modelthis by restricting time variations in rt

f (xtf ) = gt

f + htfxt

f andallow a single price rf = gf + hfxf per flow across all timest " [1, · · · , T ], with xf =

!t xt

f . For hard-capacity constraints,the time-constrained ISP revenue maximization problem, whoseoptimum we denote by R!

t , can be written as:

maximize!

f (gf + hf!

t xtf )

subject to!

f xtf # C, $t

xtf # u"

f#1(hf/!t

f )!t !t

fuf (xtf ) ! gf ! hf

!t xt

f % 0variables gf , hf , xt

f

(12)

The lack of flexibility in varying the price over time canpotentially reduce the ISP revenue. One approach for the ISPis to set the time-independent usage fee hf low enough toensure that the aggregate consumer demand

!f yt

f (hf ) ishigher than the available capacity C. The ISP can then chooseto serve data rates xt

f # ytf(hf ) that maximizes the revenue.

Consider the optimal usage prices in (7) for each time instantthat was obtained as a solution to the revenue maximizationproblem in (5) without time constraints. The solution to thetime-constrained pricing problem (12) can be obtained by firstsetting the usage price to the minimum across time of theoptimal usage prices as given in (7): hf = minht!. Let thedata rates served be given by xt

f = xtf!, the optimal data rates

served in (7) so that the capacity constraint is satisfied. If thetime-independent flat fee gf can be set such that

gf ="

t

!tfuf(xt

f!) ! minht!

"

t

xtf!,

the ISP can generate a revenue of!

t !tfuf(xt

f!), which is the

same as in the case without time constraints. This implies thatR!

t = R!u, with the time-constraint on pricing not impacting

the ISP’s revenue.Note that the ISP could retain the revenue even with time-

constraint on pricing by ensuring that consumer demandsexceed capacity at all times. The price to pay is that ISPhas to drop consumer data packets to limit the data ratesto within the capacity. However, the control exerted by theISP in packet-drop decisions with this approach has attractedregulatory attention [11] and is increasingly infeasible.

A. Time Constrained Pricing without Packet Dropping

An alternative approach for the ISP is to set the usage priceto hf = maxht!, so that the worst case demand is within thecapacity constraint. This ensures that the consumer aggregatedemand is always within the capacity limit, thus avoiding theneed for an explicit packet-drop decision by the ISP. However,capacity is not fully utilized at non-peak times, incurring arevenue loss. To characterize the revenue loss, consider therevenue maximization problem with this approach, with thecorresponding optimal revenue denoted by R !

p.

maximize!

f (gf + hf!

t ytf (hf ))

subject to!

f ytf (hf ) # C, $t!

t !tfuf (xt

f ) ! gf ! hf!

t xtf % 0

variables gf , hf

(13)

α

1− α

Constrained Across Flows

Quantify revenue loss from uniform pricing across flows

More loss if consumer demand is less elastic

Nonlinear pricing (discount at higher rate) mitigates the loss

From first to second degree price discrimination

7

revenue, from uniform price across flows with linear increasein usage, is given by

!r = hC!1 + !"0

1/!

(1!!)B("0,"1)

"

h1/! = B("0,"1)C

B(!0, !1) =# "1

"0(!)1/!f(!) d!

(25)

and the ratio of revenue from flow-restricted pricing ! r torevenue from unrestricted pricing !u is given by

!r

!u= 1 ! "

$1 ! !0

1/!

B(!0, !1)

%(26)

Remarks: Notice that !11/! " B(!0, !1) " !0

1/!. Therefore,!r # !u with equality when all consumers have the sameutility level !0 (!1 = !0). The revenue inefficiency stems fromthe inability of the ISP to charge the flow-dependent flat fee tocapture the net-utility of each flow. The inefficiency is higherwith higher values of " since a larger fraction of the revenue isdependent on the flat fee with higher ", as shown in Theorem 2.The impact of the spread in utility levels on the revenue

can be estimated by noting the following lower bound on therevenue inefficiency.

!r

!u" 1 ! "

$1 ! !0

1/!

!11/!

%(27)

The lower bound can be interpreted as the inverse competitiveratio of the restricted pricing scheme. The revenue inefficiencyis low if the spread in utility levels is low. A large spread inutility levels among flows can, however, result in high revenueinefficiencies.

B. Non-linear Pricing for Loss Mitigation

The price restriction across flows has thus far been modeledas a combination of flat-fee and usage fee, resulting in aprice linear in usage r(!) = g + hy(!). The ISP can incura higher revenue by offering a price that is non-linear inusage without discriminating on a per flow basis. The non-linear price typically takes the form of quantity discounts wherethe price per unit data rate is discounted for higher data ratepurchases. We study the revenue outcome of non-linear pricingin this section by invoking results from second-order pricediscrimination in economics [19].The non-linear price offering is in the form of a “package”

consisting of the data rate y(!) and the price r(!) offered tothe consumers. The package has to be structured in such away that the package y(!), r(!) for a given !, intended fora consumer with utility level !, should indeed be the mostdesirable choice for the consumer. This requirement is referredto as the incentive compatibility and the requirement can beexpressed in terms of the net-utility of consumers as

!u(y(!)) ! r(!) " !u(y(!)) ! r(!), $! % [!0, !1] (28)

In addition, the package has to be structured so that theconsumers derive non-negative net-utility from the package,a requirement that is referred to as the individual rationality,expressed in terms of net-utility of consumers as

!u(y(!)) ! r(!) " 0, $! % [!0, !1] (29)

The revenue maximization problem for the ISP, whose maxi-mum is denoted by !n, can then be written as

maximize# "1

"0r(!)f(!) d!

subject to# "1

"0y(!)f(!) d! # C

!u(y(!)) ! r(!) " !u(y(!)) ! r(!), $! % [!0, !1]!u(y(!)) ! r(!) " 0,

variables y(!), r(!)$! % [!0, !1](30)

In general, we expect !u " !n " !r. Consider a specialcase when consumer utility function is uniformly distributed inthe range [0, 1] so that

f(!) = 1, F (!) = 1 ! !, !0 = 0, !1 = 1 (31)

For this special case, we can state the following result, provedin Appendix C, on the revenue ratios.Theorem 8: Assuming utility functions are alpha-fair (4)

with "f = " for the continuum of flows, and the utility levelsdistributed uniformly as in (31), we have

!r

!n= 2!(1 ! "),

!r

!u= (1 ! "),

!n

!u= 2!! (32)

Remarks: Non-linear pricing allows partial recovery of revenueloss from restrictions on pricing. Under the given distributionof utility levels, revenue from non-linear pricing is no worsethan 50% of revenue from unrestricted pricing.

C. An Illustrative Example

0 0.2 0.4 0.6 0.8 10

5

10

15


Rev

enue

RestrictedUnrestrictedNon−linear

0 0.2 0.4 0.6 0.8 10

0.5

1


Rev

enue

Rat

io

"r/"n"r/"u"n/"u

Fig. 3. Comparison of the ISP revenue from three cases: unrestricted, restrictedand non-linear pricing.

Consider the example in Section III-C. The upper part of Fig-ure 3 plots the revenue from flow-restricted pricing, unrestrictedpricing, and non-linear pricing. The lower part plots the revenueratio between restricted and non-linear pricing, restricted andunrestricted pricing, and between non-linear and unrestrictedpricing. Non-linear pricing allows the ISP to recover lossesfrom restrictions on price differentiation between flows, withthe loss no worse than 50%.

VI. CONCLUSIONThis paper studied access pricing for broadband service

offered by a monopoly ISP. For a single-tier best-effort connec-tivity service, we analyzed an ISP revenue maximization and

Constrained Over Time

Highly inefficient if utility level has large time spread (later) or high elasticity

and no QoS degradation allowed

t(

σtσm )1/αt

σtσm

Ratio of constrained to unconstrained revenue

6

0 1 2 3 4 50.2

0.4

0.6

0.8

1

SpreadR

even

ue R

atio

!=0.1

!=0.25

!=0.5!=0.75

!=0.9

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.2

0.4

0.6

0.8

1


Rev

enue

Rat

io

TheoreticalSimulated

Fig. 2. Comparison of revenue loss from time constrained pricing at differentspread in utility levels and different consumer demand elasticity.

in [!0, !1], we have

E(!(1/!)) =!(1+1/!)

1 ! !(1+1/!)0

1 + 1/", E(!) =

!21 ! !2

0

2

At high values of !1 ! !0, the revenue ratio can be shown tosaturate to

R!p

R!u

=!1E(!(1/!))

!(1/!)1 E(!)

" 21 + 1/"

The revenue loss is plotted against " in the lower part ofFigure 2. Low values of ", indicating high price sensitivity,results in high losses.

V. NON-DISCRIMINATORY PRICING ACROSS FLOWS

In Section IV, we considered restriction over time on theprices rt

f charged by the monopolist ISP. However, the ISPcould discriminate across flows, practicing first-order price dis-crimination [19] to extract the maximum revenue. In practice,the ability of a monopoly ISP to practice such complete pricediscrimination across flows is restricted. The possibility ofregulatory scrutiny and demand for “network neutrality” [5],[6] prevents monopoly ISPs from practicing extensive pricediscrimination. We investigate the revenue loss from such pricerestriction across flows and mitigation of the loss through non-linear pricing.

A. Revenue Loss from Uniform Flow Pricing

The revenue loss from price restriction across flows isincurred due to variations in the consumer utility functions.We simplify the model by removing the time-dependency ofthe utility levels. Unlike the discrete flows we considered in thetime-dependent utility case, here we consider a continuum offlows with the utility levels governed by the density distributionfunction f(!) defined over a range [!0, !1] with the corre-sponding cumulative distribution function F (!) =

! ""0

f(!).With no price restriction, let the price r(!) = g(!)+h(!)x(!)be the ! dependent price charged to a flow with utility level!. The demand function of the consumer facing this price isgiven by y(!) = u"#1(h(!)/!). The revenue maximizationproblem for the ISP in this case is similar to (6), with the ISP

capturing the entire consumer net-utility by setting the flat feeg(!) = !u(y(!)) ! h(!)y(!). The revenue from unrestrictedpricing, which we denote by !u, is then determined by theappropriate usage fee, and is given by

maximize! "1

"0!u(y(!))f(!) d!

subject to! "1

"0y(!)f(!) d! # C

variables h(!)(21)

For alpha-fair utility functions (4), the demand function isgiven by

y(!) = (!/h(!))1/! (22)

The following theorem states the solution to problem (21) inthis case.Theorem 6: Assuming utility functions are alpha-fair (4)

with "f = " for the continuum of flows, the solution toproblem (21) is given by

h1/! = B("0,"1)C

B(!0, !1) =! "1

"0(!)1/!f(!) d!

!u = (1 ! ")#1h1#1/!B(!0, !1) = (1 ! ")#1hC(23)

The above result can be readily shown: The optimal pricestructure in (23) represents the KKT conditions [20] for theoptimization problem in (21).With the ISP restricted to charge a uniform price with linear

increase in usage, the flat component g and the usage rateh do not change with the consumer utility level !. The !-independent usage and flat rate pricing does not allow theISP to capture the consumer net-utility at every utility level,resulting in a revenue loss. The net-utility of a consumer withutility level ! given by !u(y(!))! hy(!) can be shown to beincreasing in !. Given the restriction that the user net-utilitycannot be negative, the ISP has to set the !-independent flat-rate component g to the net-utility of the consumer with theminimum utility level !T $ [!0, !1] that the ISP is willing toserve. Consumers with utility level ! < !T are not served bythe ISP. The threshold utility level !T is then part of the revenueoptimization problem, with higher !T providing a higher flat-fee component from all consumers with utility levels higherthan !T , but also resulting in zero revenue from all consumerswith utility level less than !T . The revenue maximizationproblem with this price restriction, whose optimum we denoteby !r, is given by

maximize! "1

"T(g + hy(!)f(!) d!

subject to! "1

"Ty(!)f(!) d! # C,

g = !T u(y(!T )) ! hy(!T )variables !T , h

(24)

For alpha-fair utility functions of the form in (4), themarginal utility at zero data allocation is infinity, resulting ininfinite penalty for not serving a flow of non-zero utility level.Indeed, we show in Appendix B that !T = !0, so that theISP is better off serving all flows, and further prove that thesolution to (24) is given by the following theorem.Theorem 7: Assuming alpha-fair utility functions of the

form in (4) with "f = " for the continuum of flows, the

Usage fee depends on traffic volume over a fixed period

Two Ways Out

Set price high -> No congestion -> Revenue loss

Set price low -> Overfill capacity -> QoS degrades

How much? What’s the tradeoff?

Set price high -> No congestion -> Sell leftover capacity (later)

Impact of Timescale8

0.5 1 1.5 2 2.5 3

0.85

0.9

0.95

1

1.05

Nor

mal

ized

Rev

enue

0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

!

Aver

age

Rat

e D

ropp

ing

w.o. constraintper−slot constraintlong−term constraint


"f="=0.5

"f="=0.5

Fig. 5. Comparison of the optimal revenue and the average number of packets

dropped for problems (RMP-TC), (RMP-PS) (RMP-LT). Top subfigure: the

comparison betweenVP S

V andVLT

V . Bottom subfigure: the comparison of

the average number of packets dropped E[(σt

fehf

)1

αf − extf ].

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0.75

0.8

0.85

0.9

0.95

1

!

Nor

mal

ized

Rev

enue

Per−Slot, "f="=0.4Long−Term, "f="=0.4Per−Slot, "f="=0.5Long−Term, "f="=0.5Per−Slot, "f="=0.6Long−Term, "f="=0.6

Fig. 6. Impact of flow’s price elasticity on ISP’s optimal revenue. We change

αf = α = 0.4, 0.5, 0.6, ∀f .

a small fluctuation of utility level implies that ISP can more

aggressively lower down its usage-price, thus attracting more

consumer’s traffic rate demand. For example, according to

(13), if

f (σtf ) 1

α is a constant within the time horizon T ,

then ISP can avoid the revenue loss without dropping any

flow’s packets.

0.2 0.4 0.6 0.8 1 1.2 1.4

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

!

Aver

age

Nor

mal

ized

Rev

enue

Per−Slot, u(0.2,1)Long−Term, u(0.2,1)Per−Slot, u(0.3,0.9)Long−Term, u(0.3,0.9)Per−Slot, u(0.4,0.8)Long−Term, u(0.4,0.8)

Fig. 7. Impact of flow’s utility level fluctuation on ISP’s optimal revenue.

αf = α = 0.6, ∀f . Every point in the figure is averaged over 100 random

realizations of σtff,t. We test three cases, i.e., σt

ft,f follows the uniform

distributions u(0.2, 1), u(0.3, 0.9) and u(0.4, 0.8), respectively.

IV. CONCLUSION

This paper studies ISP’s revenue maximization trading

off with QoS measure (in terms of the number of packets

dropped). We consider two QoS time horizons (i.e., short-term

per-slot constraint and long-term packet dropping constraint),

and quantify the tradeoff between QoS protection and revenue

maximization faced by ISP when its pricing has to be “time-

constrained”. In particular, we demonstrate the impact of

consumer’s price elasticity on ISP’s optimal revenue, and show

that in order to mitigate the revenue loss ISP should carry out

a differentiated QoS protection strategy based on consumer’s

price elasticity. We analyze the optimal time-constrained pric-

ing for both cases (short-term per-slot constraint and long-

term constraint) and identify the importance of ISP’s flat-price

in reaping revenue as the QoS protection constraint becomes

loose.

APPENDIX I: PROOF OF PROPOSITION 1

Proof: The optimal revenue VPS for problem (RMP-PS) is

nondecreasing with respect to the value of γ (because of the

increase of the feasible region) until constraint (16) becomes

always slack (e.g., satisfying the sufficient condition provided

in Remark 1) and thus V = VPS .

On the other side, the lower bound ofVP SV is obtained when

γ = 0. Specifically, constraint (20) becomes that(σt

f )1

αf

xtf

=

(σtf )

1αf

xtf

,∀f, t, t when γ = 0. Let t0 = arg maxtσt (we

omit the flow index here for clear presentation). With the

assumption that αf = α, ∀t and σtf = σt,∀f, t, there exists

xt0 = CF . Thus, ISP’s optimal rate allocation can be expressed

as: xt = ( σt

maxtσt ) 1α

CF ,∀t when γ = 0. Therefore, ISP’s

optimal revenue can be expressed as:

VPS =

f

t

σtfuf (xt

f )

= FαC1−α 11− α

(maxt

σt)1− 1α

t

(σt)1α

= V

t(

σt

maxtσt ) 1α

t(

σt

maxtσt ). (34)

APPENDIX II: PROOF OF PROPOSITION 2

Proof: We drop the flow index here for clear presentation.

Constraint (16) requires (σt

h ) 1α ≤ xt + γ,∀t. Therefore, there

exists h1α ≥ maxt (σt)

1α

xt+γ ≥ maxt(σt)1α

xt0+γ ≥ maxt(σt)1α

CF +γ

,

where t0 = arg maxt(σt) 1α (notice that xt0 ≤ C

F because all

flows are symmetric). Thus, according to constraint (15), xt ≤minC

F , (σt)1α

maxt(σt)1α

(CF + γ),∀t. Therefore, by substituting

this expression into ISP’s revenue function (which is equal to

all flows’ sum-utility), we can get:

VPS

V≤

t∈Ω1

σt

t σt

+(C

F + γ)1−α

(CF )1−α

t∈Ω2

(σt)1α

maxt(σt)1α

tσt

maxtσt, (35)

Tight timescale QoS protection -> More revenue loss

Impact of Elasticity

8

0.5 1 1.5 2 2.5 3

0.85

0.9

0.95

1

1.05

Nor

mal

ized

Rev

enue

0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

!

Aver

age

Rat

e D

ropp

ing



"f="=0.5

"f="=0.5

Fig. 5. Comparison of the optimal revenue and the average number of packets

dropped for problems (RMP-TC), (RMP-PS) (RMP-LT). Top subfigure: the

comparison betweenVP S

V andVLT

V . Bottom subfigure: the comparison of

the average number of packets dropped E[(σt

fehf

)1

αf − extf ].

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0.75

0.8

0.85

0.9

0.95

1

!

Nor

mal

ized

Rev

enue

Per−Slot, "f="=0.4Long−Term, "f="=0.4Per−Slot, "f="=0.5Long−Term, "f="=0.5Per−Slot, "f="=0.6Long−Term, "f="=0.6

Fig. 6. Impact of flow’s price elasticity on ISP’s optimal revenue. We change

αf = α = 0.4, 0.5, 0.6, ∀f .

a small fluctuation of utility level implies that ISP can more

aggressively lower down its usage-price, thus attracting more

consumer’s traffic rate demand. For example, according to

(13), if

f (σtf ) 1

α is a constant within the time horizon T ,

then ISP can avoid the revenue loss without dropping any

flow’s packets.

0.2 0.4 0.6 0.8 1 1.2 1.4

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

!

Aver

age

Nor

mal

ized

Rev

enue

Per−Slot, u(0.2,1)Long−Term, u(0.2,1)Per−Slot, u(0.3,0.9)Long−Term, u(0.3,0.9)Per−Slot, u(0.4,0.8)Long−Term, u(0.4,0.8)

Fig. 7. Impact of flow’s utility level fluctuation on ISP’s optimal revenue.

αf = α = 0.6, ∀f . Every point in the figure is averaged over 100 random

realizations of σtff,t. We test three cases, i.e., σt

ft,f follows the uniform

distributions u(0.2, 1), u(0.3, 0.9) and u(0.4, 0.8), respectively.

IV. CONCLUSION

This paper studies ISP’s revenue maximization trading

off with QoS measure (in terms of the number of packets

dropped). We consider two QoS time horizons (i.e., short-term

per-slot constraint and long-term packet dropping constraint),

and quantify the tradeoff between QoS protection and revenue

maximization faced by ISP when its pricing has to be “time-

constrained”. In particular, we demonstrate the impact of

consumer’s price elasticity on ISP’s optimal revenue, and show

that in order to mitigate the revenue loss ISP should carry out

a differentiated QoS protection strategy based on consumer’s

price elasticity. We analyze the optimal time-constrained pric-

ing for both cases (short-term per-slot constraint and long-

term constraint) and identify the importance of ISP’s flat-price

in reaping revenue as the QoS protection constraint becomes

loose.

APPENDIX I: PROOF OF PROPOSITION 1

Proof: The optimal revenue VPS for problem (RMP-PS) is

nondecreasing with respect to the value of γ (because of the

increase of the feasible region) until constraint (16) becomes

always slack (e.g., satisfying the sufficient condition provided

in Remark 1) and thus V = VPS .

On the other side, the lower bound ofVP SV is obtained when

γ = 0. Specifically, constraint (20) becomes that(σt

f )1

αf

xtf

=

(σtf )

1αf

xtf

,∀f, t, t when γ = 0. Let t0 = arg maxtσt (we

omit the flow index here for clear presentation). With the

assumption that αf = α, ∀t and σtf = σt,∀f, t, there exists

xt0 = CF . Thus, ISP’s optimal rate allocation can be expressed

as: xt = ( σt

maxtσt ) 1α

CF ,∀t when γ = 0. Therefore, ISP’s

optimal revenue can be expressed as:

VPS =

f

t

σtfuf (xt

f )

= FαC1−α 11− α

(maxt

σt)1− 1α

t

(σt)1α

= V

t(

σt

maxtσt ) 1α

t(

σt

maxtσt ). (34)

APPENDIX II: PROOF OF PROPOSITION 2

Proof: We drop the flow index here for clear presentation.

Constraint (16) requires (σt

h ) 1α ≤ xt + γ,∀t. Therefore, there

exists h1α ≥ maxt (σt)

1α

xt+γ ≥ maxt(σt)1α

xt0+γ ≥ maxt(σt)1α

CF +γ

,

where t0 = arg maxt(σt) 1α (notice that xt0 ≤ C

F because all

flows are symmetric). Thus, according to constraint (15), xt ≤minC

F , (σt)1α

maxt(σt)1α

(CF + γ),∀t. Therefore, by substituting

this expression into ISP’s revenue function (which is equal to

all flows’ sum-utility), we can get:

VPS

V≤

t∈Ω1

σt

t σt

+(C

F + γ)1−α

(CF )1−α

t∈Ω2

(σt)1α

maxt(σt)1α

tσt

maxtσt, (35)

Less elastic demand -> Sweeter revenue-QoS tradeoff

Importance of Flat Price

7

to the time-constrained price strategy, ISP should only provide

a weak QoS protection if consumer’s price elasticity is high.

Considering the traffic type, Figure 2 also suggests that given

the same packet dropping constraint, best-effort traffic incurs

a smaller revenue loss than real-time video traffic does.

C. Impact of Packet Dropping Constraint on Usage-BasedRevenue

Both short-term per-slot and long-term packet dropping

constraints impose restrictions on ISP’s usage-price, thus in-

fluencing ISP’s usage-based revenue.

Proposition 5: For problem (RMP-PS), let V usagePS =

f (

t xtf )hf denote ISP’s optimal usage-based revenue. If

all flows have the same price elasticity (i.e., ξf = 1αf

=1α ,∀f ), then

V usageP SVP S

≤ 1 − α, and the equal sign is ob-

tained when ISP cannot drop any flow’s rate demand, i.e.,

Γtf = 0,∀f, t. (The proof is in Appendix V.)

Similarly, we also have the following proposition.

Proposition 6: For problem (RMP-LT), let V usageLT =

f (

t xtf )hf denote ISP’s optimal usage-based revenue. If

all flows have the same price elasticity (i.e., ξf = 1αf

=1α ,∀f ), then

V usageLTVLT

≤ 1 − α, and the equal sign is ob-

tained when ISP cannot drop any flow’s rate demand, i.e.,

Γf = 0,∀f .

Notice that the upper bound ofV usage

P SVP S

andV usage

LTVLT

are

both increasing with respect to each flow’s price elasticity.

This is consistent with the intuition that usage-based revenue

is dominant in the entire revenue if consumer has a high

price elasticity. Similar result also appeared in [3]. The exact

values ofV usage

P SVP S

andV usage

LTVLT

with arbitrary packet dropping

thresholds, however, are difficult to derive, and they depend

on the detailed choices of hf (according to (22) and (32)).

Figure 4 shows the comparison betweenV usage

P SVP S

andV usage

LTVLT

.

For both problems, we set the optimal usage-price as hf =mint

σtf

(extf )αf ,∀f according to (22) and (32). Figure 4 shows

thatV usage

P SVP S

decreases when Γtf = γ,∀f, t increases. Mean-

while,V usage

P SVP S

is lower bounded as Γtf = γ → maxf,t∆t

f(12). Specifically,

V usageP SVP S

is lower bounded by the corre-

sponding value ofV usage

V for problem (RMP-TC), where

V usagedenotes the optimal usage-based revenue for problem

(RMP-TC). The intuitive explanation is as follows. If Γtf = γ

is so small that hf = mintσt

f

(extf )αf = maxt

σtf

(extf +Γt

f )αf ,

then hf decreases when Γtf increases, which implies that

ISP can lower down its usage-price more aggressively. As a

result, the value ofV usage

P SVP S

decreases. However, if Γtf = γ

is so large that hf = mintσt

f

(extf )αf > maxt

σtf

(extf +Γt

f )αf ,

then according to our previous description in section III.A,

problem (RMP-PS) has already become equivalent to problem

(RMP-TC). Therefore, there existsV usage

P SVP S

= V usage

V . We can

observe a similar property ofV usage

LTVLT

. The value ofV usage

LTVLT

is lower bounded byV usage

V as Γf = η → maxf

t∆tf.

Figure 4 indicates that the flat-part revenue (i.e., flat-price)

is important to ISP’s revenue retention. Specifically, the more

loose the packet dropping constraint, the more heavily ISP has

to rely on its flat-price to achieve the maximum revenue.

0.5 1 1.5 2 2.50.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

!

Rat

io o

f Usa

ge−P

art R

even

ue

Per−Slot, "=0.4Long−Term, "=0.4w.o. constraint, "=0.4Per−Slot, "=0.5Long−Term, "=0.5w.o. constraint, "=0.5Per−Slot, "=0.6Long−Term, "=0.6w.o. constraint, "=0.6

1−"

1−"

1−"

"=0.6

"=0.5

"=0.4

Fig. 4. Comparison of the usage-based revenue ratio between problem

(RMP-PS) and problem (RMP-LT)

D. Tradeoff between Per-Slot and Long-Term ConstraintsFigure 5 shows the comparison of the optimal revenues

and average number of packets dropped among problems

(RMP-TC), (RMP-PS), (RMP-LT). Specifically, the horizontal

axis denotes the packet dropping threshold Γtf = γ,∀f, t

for problem (RMP-PS). Meanwhile, for fair comparison the

packet dropping threshold for problem (RMP-LT) is set as

Γf = η = Tγ. The top subfigure shows the comparison

betweenVP SV and

VLTV . It shows that ISP can always achieve a

smaller revenue loss with long-term packet dropping constraint

than with short-term per-slot constraint (until both problems

(RMP-PS) and (RMP-LT) become equivalent). This result is

consistent with the intuition. Because ISP has a larger flexi-

bility in dropping flows’ traffic rate with long-term constraint,

it can obtain a no smaller optimal revenue.

The downside of long-term packet dropping constraint,

however, is that it can only provide a weak QoS protection.

The bottom subfigure in Figure 5 verifies this point by showing

the average number of packets dropped for the three problems.

Figure 5 presents the tradeoff faced by ISP, i.e., between using

short-term per-slot packet dropping constraint to provide a

strong QoS protection but suffering a large revenue loss and

using long-term constraint to provide a weak QoS protection

but suffering a small revenue loss.

E. Impact of Price Elasticity and Utility Level FluctuationFigure 6 shows the impact of flow’s price elasticity on ISP’s

optimal revenue. Figure 6 shows that ISP will suffer a large

revenue loss if each flow has a high price elasticity (for both

short-term per-slot packet dropping constraint and long-term

packet dropping constraint). These results are consistent with

our previous Remark 4 and Remark 9.

Figure 7 shows the impact of the fluctuation of flow’s utility

level σtff,t on ISP’s optimal revenue. Figure 7 shows that

if each flow’s utility level has a small fluctuation, then ISP

will suffer a small revenue loss. Intuitively this is right since

Ratio of usage price in total revenue drops to a constant as QoS requirement loosens

The constant fraction is less as elasticity decreases

Q2. How to Charge?

Next step: Time dependent pricing

Extension: Congestion dependent pricing

Time-series shaper: from current 24-hour curve to desired shape

Bring “tail” and “mean” (on time axis) closer

How to make it “work”?

Compare with current practice of binary time-dependent pricing

Compare with time-of-usage pricing in utility industry

Key Factors

ISP’s perspective: balance two costs

Cost of worst-case capacity provisioning (capital expenditure)

Cost of “rewarding” users willing to shift their traffic (recurring)

User’s perspective:

“Time elasticity” depends on time sensitivity of traffic

And user’s patience level

How to incorporate user elasticities and optimize price efficiently?

Schematic

Time-Dependent Usage-Based Broadband PricingCarlee Joe-Wong

Department of MathematicsPrinceton UniversityPrinceton, NJ 08544

Email: [email protected]

Mung ChiangDepartment of Electrical Engineering

Princeton UniversityPrinceton, NJ 08544

Email: [email protected]

Abstract—Charging different prices for network connectivityat different times induces users to spread out their bandwidthacross times of the day, thus alleviating capacity constraints. Wedetermine cost-minimizing time-dependent prices for an Internetservice provider (ISP) exploring such an option, using both astatic session-level model and a dynamic session model withstochastic arrival processes. We develop a suite of formulations tohighlight different aspects of the problem, as well as parametrizedestimation of sessions’ time-sensitivity. A key step is choosingthe right representation of the optimization problem so thatthe resulting formulations remain computationally tractable forlarge-scale problems. Using real Internet usage data, we showsimulation results that illustrate the use and limitations of time-dependent pricing. These results demonstrate that optimal prices,which “reward” users for deferring their sessions, often displaysome symmetry, and that changing prices based on real-timetraffic estimates may significantly reduce the ISP’s cost. Thedegree to which traffic is evened out over times of the daydepends on the time-sensitivity of sessions, cost structure of theISP, and amount of traffic not subject to time-dependent prices.The methodology in this paper provides a way to quantify theimpact of time-dependent pricing based on these factors.

I. INTRODUCTIONA. MotivationInternet service providers (ISPs) practicing flat rate pricing

face a dilemma: unlike its cost, ISP revenue does not scalewith consumers’ ever increasing desire for more bandwidth.Usage-based pricing has become an inevitable path as evi-denced by recent news in the industry over the last severalmonths [1], [2]. Yet pricing based on monthly total bandwidthconsumption still leaves a gap open: ISP revenue is based ontotal volume over the long timescale of a month, but its coststructure is dominated by congestion conditions during peakhours. Ideally, the ISP would like total bandwidth consumptionto be spread evenly over times of the day.Time-dependent usage pricing (TDP) charges a user based

on not just “how much” bandwidth is consumed but also“when” it is consumed, as opposed to time-independent us-age pricing (TIP), which only considers monthly consumptionamounts. TDP has the potential to even out time-of-the-dayfluctuations in bandwidth consumption. As a pricing practicethat does not differentiate based on traffic type, protocol, oruser class, TDP also sits lower on the radar screen of networkneutrality scrutiny. In fact, the day-time (counted as part of theminutes used) and evening-time (free) pricing scheme usedby wireless operators for many years is a simple, 2 period

Fig. 1. Overall schematic of time-dependent pricing systems. The focus ofthis paper is on price optimization, the module in the red circle.

TDP scheme. On the other hand, given the “time inelasticity”of demand, it is not clear how much TDP can help, eitherbecause users are impatient or because many applications aretoo time-sensitive. To make TDP work well, research on trafficmeasurement, optimal price determination, and user-interfacedesign must be carried out first. This paper investigates howa monopoly ISP can use TDP to manage network congestion,focusing on the feasibility and efficacy of price determination.Figure 1 summarizes the overall TDP system as a control

loop. This paper zooms in on the center module of determiningoptimal prices, with a brief discussion of basic user profiling.

B. Related WorkThe electricity industry has been developing TDP over the

years, as reflected in Table I’s summary of existing literatureon TDP. We extend these economic analyses to ISPs inseveral non-trivial ways. In focusing on ISPs, we incorporateunique features like stochastic session arrivals and the potentialfor online price adjustments. We also model TDP as usersdeferring part of their Internet usage, rather than the electricitymarket’s model of users choosing the period in which todemand a resource. The following summarizes some keydifferences compared to prior work:

• Most prior work considers the electricity industry, inwhich the bottleneck is resource generation, not transitas for ISPs. This difference requires modeling arrival anddeparture of application sessions in our dynamic model.

• Previous models use the simplified “representative de-mand functions” to estimate resource demand at peak andoff-peak times, while we develop detailed models directly

Some Challenges

General number of time slots (e.g., 48)

User patience function rather than “representative demand function” per time slot

Arrival and departure dynamics

Search for an representation leading to efficient computation

Turns out to be possible

w(p(τ), τ)

Levelling in Action

Impact of Congestion Definition8

TABLE VPRICE AND COST CHANGE, PERIOD 1 DEMAND UNDER TIP

PERTURBATION.

Demand (Mbps) Price Change ($0.10) Cost Change (%)180 2.5806 -8.71190 1.6458 -6.00200 0.7924 -2.88210 0.2302 -0.22230 0.0047 0240 0.1144 -0.01250 0.3433 -0.06260 0.3551 -0.07

Fig. 6. Optimal rewards, static session model.

Fig. 7. Traffic profile, static session model.

out bandwidth consumption fluctuations over a day if usersare too impatient, sessions are too time-sensitive, or the costof exceeding capacity is too low.To measure the even-ing out of traffic, we define residue

spread as the area between a given traffic profile and one withthe same total usage but with usage constant across periods. Ithas units of Gb (session size, in Mbps, multiplied by time, inhours). Figure 7 yields a residue spread of 723.6 Gb with TDPand 939.6 Gb with TIP. The area between the two profilesis 255.6 Gb, so about 8% of traffic is redistributed. Thesenumerical values are large due to summing over an entire day.

Similar demand under TIP and waiting function distribu-tions cause the observed symmetry in optimal prices. Mul-tiplying capacity and demand under TIP by 10 and varying

Fig. 8. Residue spread for different costs of exceeding capacity.

the distributions produces rewards without symmetry, as inAppendix J.One would expect that when exceeding capacity is ex-

pensive, the ISP should even out demand by offering largerewards. Figure 8 shows the residue spread with TDP versusthe logarithm of a, where the cost of exceeding capacity isa max [xi ! Ai]. Residue spread decreases sharply for a "[0.1, 10], then levels out for a # 10. For these values of a, theISP drives demand in all periods almost below capacity.

B. Dynamic Session ModelsWe now simulate the offline dynamic model, with the

same ten waiting function types. We use the waiting functiondistributions from the static model to represent the amount oftraffic arriving in each period. We assume a single bottlenecknetwork, so that the only differences between this and thediscrete static model are a uniform arrival time distributionand usage carrying over into subsequent periods. The networkhas a constant maximum capacity of 210 Mbps.Optimal rewards are given in Fig. 9 and produce a total

daily cost of $43.80. We quantify the intuition that these aregenerally larger than in the static model (Fig. 6), where trafficdid not carry over into different periods; the ISP now has moreincentive to even out traffic. Indeed, rewards finally break the$0.05 barrier in the last simulation. As shown in Fig. 10, traffichas been much reduced in almost all periods; deferred trafficfrom initially overused periods no longer carries over intosubsequent periods. The residue spread decreases dramaticallyfrom 2973.6 Gb with TIP to 723.6 Gb with TDP; the areabetween the two traffic profiles is 2368.8 Gb.For presentational simplicity, we now use 12 periods in the

online dynamic model. Suppose that capacity is 210 Mbps,and that while running the online algorithm, the ISP finds that240 instead of 210 Mbps arrives in period 1. Then optimalrewards for deferring from period 1 increase by about 30%(details of this simulation can be found in Appendix K). TheISP continues to determine optimal rewards for periods 2, 3,etc. These yield an expected cost over the next day of $9.90,which is much smaller than the expected cost with nominalrewards, $29.30. An online adaptation of prices to real-timedata presents a significant cost-saving opportunity to the ISPin this case.

Heavier emphasis on congestion alleviation leads to more levellingEventually saturates at a level determined by user elasticities

Q3. Whom to Charge?

Two sided pricing

Extreme case: 1-800 service of free Internet access

CP interest: Elasticity-cost points just right for volume play !"

!"# $%&'& ()*+', -*%.%/01 2$-34 5/& 63'*34 )/&7#/,'/, -*#8%&'*3

!"#"$% &'(&$#") *$ %+, )*'"' -.*#*$/ 0,'"1 2*"1'$"+ *$)*/3%) *$%, '*44"."$%*&%"' -.*#*$/ 5"%+""$#,$%"$% -.,(*'". &$' "$' 6)".

7,. & /*("$ %,%&1 -.*#" %, #,$$"#% &$ "$' 6)". &$'#,$%"$% -.,(*'".8 %3" )3&." ,4 %3" %,%&1 -.*#"5,.$" 52 "&#3 )*'" 0&%%".)o 9,$%"$% -.,(*'".)8 %3"."4,."8 3&(" & )%&:" *$"$' 6)". 5.,&'5&$' #,$$"#%*(*%2

o 9,$%"$% -.,(*'".) &1), 6$'".)%&$' -.*#*$/#,0-1";*%*") 5"%%". %3&$ "$' 6)".)

<*44"."$%*&1 -.*#*$/ 4,. "$' 6)".) &$' #,$%"$%-.,(*'".) #&$ *0-.,(" &',-%*,$ .&%") &$' 3"1-."#,(". $"%+,.: #,)%)

79 !"# $%&'& ()*+', -*%.%/01 2$-34 5/& 63'*34 )/& 7#/,'/, -*#8%&'*3

#$ %&&'(')$ () *+'$, -.+%('/+ '$ -)$012+. 3.'-'$,4 '( '0 '23).(%$( () 1$&+.0(%$& #56 )33).(1$'('+0 7).-8%.,'$, (8+ 3.)/'&+.0 )7 -)$(+$( %$& %339'-%(')$0:

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

2$-4 5/& 63'*4 7#/,'/, -*#8%&'* 2/,'*).,%#/

=> L%$&+4 6:4 M8'%$,4 N:4 M%9&+.*%$@4 O:4 O%$,%$4 5:4 JP+(<).@ 6.'-'$, %$& O%(+ ?99)-%(')$ <'(8 M)$(+$( 6.)/'&+. 6%.('-'3%(')$4K=.,#> ?@@@ ?A7B9BC4 ?3.: !>>Q:

Key Factors

EU: utility maximization (of rate, volume, etc)

CP: utility maximization

ISP: max (revenue - bandwidth cost)

Competitive or monopoly ISP

Examine equilibrium behaviors

Single ISP

Inter-connected multiple ISPs

An ExampleV. PRACTICAL CONSIDERATIONS AND ILLUSTRATIONWe derived results for two extreme ISP market conditions,

monopoly and perfect competition. In practice, ISP marketsconditions in many parts of the world are in between the twoextremes. The large capital expenditure required to setup anISP typically results in oligopolistic market structures, wherea few firms dominate the market. In general, oligopolisticmarkets have equilibrium prices and usage in between that ofcompetition and monopoly, and the results in this paper serve asa suitable guideline to analyze the resulting market equilibrium.Under certain models, however, oligopoly markets result innon-intuitive equilibrium [12], in which case such markets willhave to be explicitly analyzed for additional insights.We also assume a flow dependent, route dependent and usage

dependent pricing on the demanded data rates. In practice,pricing is rarely flow or route dependent, and is sometimesbased on total volume of data rather than data rates. Flat-rate pricing models, where prices stay flat up to a thresholddata consumption, are not uncommon either, especially in theU.S. wireline market today. Several papers have addressed thecomparison with usage dependent pricing [13], [14]. Trans-lating prices on data rates to that on volume of data canbe accommodated by considering the time period over whichthe volume of data is calculated, and a multiplexing factorthat captures the effect of the volume of data on capacityrequirements. Imposing flow and route independence on thetraffic is harder to accomplish, and will be the target of futurework.We now provide a simple example to illustrate the de-

pendency of the equilibrium values on the content providerutility functions, under ISP competition and monopoly. Theillustration brings out two salient points related to the rateallocation model. Content provider participation can signifi-cantly increase the data rates under both ISP monopoly andcompetition. Monopoly ISP market conditions dramaticallyreduce the equilibrium data rates in comparison to a competitiveISP market.Consider EU utilities uf (xf ), parameterized by af , !f, of

the form

uf (xf ) =!

af log(xf ) if !f = 1,

af (1 ! !f )!1x1!!f

f if 0 " !f < 1 (16)

and CP utilities vf (xf ), parameterized by bf , "f, given by

vf (xf ) =

"bf log(xf ) if "f = 1,

bf (1 ! "f )!1x1!"f

f if 0 " "f < 1(17)

The utility functions result in end-user demand function y f (pf )and content-provider demand function z f(qf ) given by

yf (pf ) = (pf/af)!1/!f , zf (qf ) = (qf/bf )!1/"f (18)

The elasticities of the demand functions are given by

#E = 1/!f , #C = 1/"f (19)

The assumed utility functions for the EU and CP results inconstant elasticity of demand.We look into a single flow for this illustration and use the

following nominal parameters af = $50, !f = 0.5, bf =

TABLE IBROADBAND PRICING AND USAGE VS. UTILITY LEVEL

af = 50, !f = 0.5, "f = 0.5

bfISP Competition ISP Monopoly

EU Price EU Demand EU Price EU Demand0 $50 1.0 Mbps $100 250 kbps20 $36 2.0 Mbps $71 490 kbps40 $28 3.25 Mbps $56 810 kbps60 $23 4.84 Mbps $45 1.21 Mbps80 $19 6.76 Mbps $38 1.69 Mbps100 $17 9.0 Mbps $33 2.25 Mbps

TABLE IIBROADBAND PRICING AND USAGE VS. UTILITY CURVATURE

af = 50, bf = 50, !f = 0.5

"fISP Competition ISP Monopoly

EU Price EU Demand EU Price EU Demand0.2 $6 63 Mbps $33 2.35 Mbps0.4 $14 13 Mbps $45 1.24 Mbps0.6 $19 7 Mbps $55 824 kbps0.8 $22 5 Mbps $68 547 kbps1.0 $25 4 Mbps $100 250 kbps1.05 $26 3.8 Mbps $151 110 kbps

$50, "f = 0.5. The aggregate capacity cost per Mbps of datarate is assumed to be µf = $50 per month. Table I showsthe equilibrium data rate and the price charged to the end-user at different content-provider utility levels bf . CP does notparticipate in rate allocation when bf = 0. Data rates increasefrom 1Mbps to 9Mbps as bf increases to $100 under ISPcompetition. The end-user price decreases to $17 per month asopposed to the $50 per month paid without content providercontribution. For the monopoly case, the increase in broadbanddata rates and decrease in end-user price is less dramatic, ratesincrease to 2Mbps, and end-user price decreases to $33 forbf =$100.Table II shows the equilibrium data rate, and the end-user

price against "f , the inverse of the CP elasticity of demand.Higher the "f , lower the demand elasticity, indicating lesswillingness to pay. This results in high end-user prices and low

0 20 40 60 80 100−50

0

50

100

150

CP utility level

CP

Gai

n

MonopolyCompetition

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−100

0100200300400500

CP demand elasticity

CP

Gai

n

MonopolyCompetition

Fig. 2. Plot of content-provider gain from participation in rate allocation vs.bf and "f . Content-provider realizes positive gains for high bf and low "funder both ISP competition and monopoly. Gains are limited under monopoly.

V. PRACTICAL CONSIDERATIONS AND ILLUSTRATIONWe derived results for two extreme ISP market conditions,




the form

uf (xf ) =!


af (1 ! !f )!1x1!!f

f if 0 " !f < 1 (16)


vf (xf ) =


bf (1 ! "f )!1x1!"f

f if 0 " "f < 1(17)




#E = 1/!f , #C = 1/"f (19)




af = 50, !f = 0.5, "f = 0.5




af = 50, bf = 50, !f = 0.5





0 20 40 60 80 100−50

0

50

100

150

CP utility level

CP

Gai

n

MonopolyCompetition

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−100

0100200300400500


CP

Gai

n

MonopolyCompetition

Fig. 2. Plot of content-provider gain from participation in rate allocation vs.bf and "f . Content-provider realizes positive gains for high bf and low "funder both ISP competition and monopoly. Gains are limited under monopoly.

CP utility level (or elasticity) increases, EU pays less and demands more

When Will CP See Benefit?

V. PRACTICAL CONSIDERATIONS AND ILLUSTRATIONWe derived results for two extreme ISP market conditions,




the form

uf (xf ) =!


af (1 ! !f )!1x1!!f

f if 0 " !f < 1 (16)


vf (xf ) =


bf (1 ! "f )!1x1!"f

f if 0 " "f < 1(17)




#E = 1/!f , #C = 1/"f (19)




af = 50, !f = 0.5, "f = 0.5




af = 50, bf = 50, !f = 0.5





0 20 40 60 80 100−50

0

50

100

150

CP utility level

CP

Gai

n

MonopolyCompetition

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−100

0100200300400500


CP

Gai

n

MonopolyCompetition

Fig. 2. Plot of content-provider gain from participation in rate allocation vs.bf and "f . Content-provider realizes positive gains for high bf and low "funder both ISP competition and monopoly. Gains are limited under monopoly.Under ISP competition and low enough CP elasticity, CP gains a lot

benefits from the content-provider’s participation, and in factextracts more from the end-user.The monopoly ISP stands to gain in surplus from content-

provider participation at all price restrictions 0 ! q ! q. Whatabout the monopoly price? The equilibrium monopoly price isgiven by

r =µ

(1 " 1/!E)" q(1/!E " 1/!C)

(1 " 1/!E)(26)

where the first term is the monopoly price in the absence ofthe content-provider. It follows that a content-provider less pricesensitive than the end-user (!C < !E) increases the monopolyequilibrium price relative to the case where the content-providerdoes not participate. A more price sensitive content-provider, onthe other hand, decreases the monopoly ISP equilibrium price.Figure 4 is a plot of the end-user and content-provider surplus

in a monopoly market against q for the example illustratedin Section V with af = $50, "f = 0.5, bf = $50, #f =0.5. Figure 5 plots the ISP and the total surplus for the sameexample.In summary, in a monopoly ISP market:• Content provider price restriction below a threshold price

qt ! q results in a drop in the end-user demand belowthat of content-provider demand.

• End user gains in surplus from easing price restriction forq ! qt and loses in surplus for q > qt. The end-usersurplus is maximized at q = qt. With no price restriction,end-user benefits from content-provider participation if thecontent-provider price sensitivity is greater than 1.

• The total surplus increases for q ! qt and decreases forq > qt. The total surplus is maximized at q = qt.

• The content-provider surplus increases at low values ofq if the end-user price sensitivity is sufficiently highrelative to the cost of connectivity. Lowering the cost ofconnectivity reduces the end-user price sensitivity requiredfor the content-provider to gain from participation in rateallocation.

• The content-provider surplus decreases at high values ofq. The value of q at which the content-provider surplus ismaximized is typically different from q t.

• The monopoly ISP price level increases with content-provider participation if the content-provider is less pricesensitive than the end-user and decreases otherwise. Re-gardless of the change in the monopoly ISP price, themonopoly ISP surplus always increases with content-provider participation.

VII. CONCLUSIONWe presented a framework for network data rate allocation by

considering the three-way interaction between end-users, ISPs,and content-providers. It yields quantitative results providinga precise and relevant “language” to structure one of theaspects in the on-going debate about “Network Neutrality”:rate allocation and surplus distribution with content providerpricing. The results from the developed framework indicatethat the Internet connectivity market can benefit from content-provider participation but suffers from monopolistic ISP marketconditions. In addition to the overall connectivity market,

0 20 40 60 80 10020

40

60

80

EU S

urpl

us

Monopoly Equilibrium EU and CP surplus

0 20 40 60 80 10050

60

70

80

CP Price Restriction

CP

Surp

lus

Fig. 4. Monopoly Equilibrium EU and CP Surplus vs. q. End user surplus ismaximized at q = qt, content-provider surplus is maximized at q less than qt.

0 20 40 60 80 10010

20

30

40

50

ISP

Surp

lus

Monopoly Equilibrium ISP and Total surplus

0 20 40 60 80 10050

100

150

200


Tota

l Sur

plus

Fig. 5. Monopoly Equilibrium ISP and Total Surplus vs. q. ISP surplusincreases monotonically. Total surplus peaks at q = qt.

content-providers themselves can benefit from participation, ifthe cost of connectivity is low and the end-users are sufficientlyprice sensitive. Decreasing the cost of connectivity and increas-ing competitiveness in the ISP market, rather than restrictingcontent-provider pricing a priori, appears to be an appropriateset of measures.While we have presented a model that provides a useful tool

to capture the complex interactions involved in the Internetconnectivity market, further work is required to explicitlyincorporate interactions that were abstracted out of this model.For example, a more complete picture will emerge if theinteraction involving content distribution networks and peer-to-peer networks, as well as the transit and peering arrangementsbetween ISPs [16] are incorporated into the model.

APPENDIX A: PROOF OF THEOREM 1

Since yf (pf ), zf (qf ) are monotonically decreasing, the pricestructure pf , qf that maximizes (8) should satisfy pf + qf =µf . Now it is necessarily the case that xf (µf ) = yf (pf ) =zf(qf ). If not, let yf(pf ) < zf (qf ). Then pf > 0 (ifnot, Assumption 2 is violated). This implies that pf can bedecreased by a small amount and correspondingly q f increased

benefits from the content-provider’s participation, and in factextracts more from the end-user.The monopoly ISP stands to gain in surplus from content-

provider participation at all price restrictions 0 ! q ! q. Whatabout the monopoly price? The equilibrium monopoly price isgiven by

r =µ

(1 " 1/!E)" q(1/!E " 1/!C)

(1 " 1/!E)(26)

where the first term is the monopoly price in the absence ofthe content-provider. It follows that a content-provider less pricesensitive than the end-user (!C < !E) increases the monopolyequilibrium price relative to the case where the content-providerdoes not participate. A more price sensitive content-provider, onthe other hand, decreases the monopoly ISP equilibrium price.Figure 4 is a plot of the end-user and content-provider surplus

in a monopoly market against q for the example illustratedin Section V with af = $50, "f = 0.5, bf = $50, #f =0.5. Figure 5 plots the ISP and the total surplus for the sameexample.In summary, in a monopoly ISP market:• Content provider price restriction below a threshold price

qt ! q results in a drop in the end-user demand belowthat of content-provider demand.

• End user gains in surplus from easing price restriction forq ! qt and loses in surplus for q > qt. The end-usersurplus is maximized at q = qt. With no price restriction,end-user benefits from content-provider participation if thecontent-provider price sensitivity is greater than 1.

• The total surplus increases for q ! qt and decreases forq > qt. The total surplus is maximized at q = qt.

• The content-provider surplus increases at low values ofq if the end-user price sensitivity is sufficiently highrelative to the cost of connectivity. Lowering the cost ofconnectivity reduces the end-user price sensitivity requiredfor the content-provider to gain from participation in rateallocation.

• The content-provider surplus decreases at high values ofq. The value of q at which the content-provider surplus ismaximized is typically different from q t.

• The monopoly ISP price level increases with content-provider participation if the content-provider is less pricesensitive than the end-user and decreases otherwise. Re-gardless of the change in the monopoly ISP price, themonopoly ISP surplus always increases with content-provider participation.

VII. CONCLUSIONWe presented a framework for network data rate allocation by

considering the three-way interaction between end-users, ISPs,and content-providers. It yields quantitative results providinga precise and relevant “language” to structure one of theaspects in the on-going debate about “Network Neutrality”:rate allocation and surplus distribution with content providerpricing. The results from the developed framework indicatethat the Internet connectivity market can benefit from content-provider participation but suffers from monopolistic ISP marketconditions. In addition to the overall connectivity market,

0 20 40 60 80 10020

40

60

80

EU S

urpl

us

Monopoly Equilibrium EU and CP surplus

0 20 40 60 80 10050

60

70

80


CP

Surp

lus

Fig. 4. Monopoly Equilibrium EU and CP Surplus vs. q. End user surplus ismaximized at q = qt, content-provider surplus is maximized at q less than qt.

0 20 40 60 80 10010

20

30

40

50

ISP

Surp

lus

Monopoly Equilibrium ISP and Total surplus

0 20 40 60 80 10050

100

150

200


Tota

l Sur

plus

Fig. 5. Monopoly Equilibrium ISP and Total Surplus vs. q. ISP surplusincreases monotonically. Total surplus peaks at q = qt.

content-providers themselves can benefit from participation, ifthe cost of connectivity is low and the end-users are sufficientlyprice sensitive. Decreasing the cost of connectivity and increas-ing competitiveness in the ISP market, rather than restrictingcontent-provider pricing a priori, appears to be an appropriateset of measures.While we have presented a model that provides a useful tool

to capture the complex interactions involved in the Internetconnectivity market, further work is required to explicitlyincorporate interactions that were abstracted out of this model.For example, a more complete picture will emerge if theinteraction involving content distribution networks and peer-to-peer networks, as well as the transit and peering arrangementsbetween ISPs [16] are incorporated into the model.

APPENDIX A: PROOF OF THEOREM 1

Since yf (pf ), zf (qf ) are monotonically decreasing, the pricestructure pf , qf that maximizes (8) should satisfy pf + qf =µf . Now it is necessarily the case that xf (µf ) = yf (pf ) =zf(qf ). If not, let yf(pf ) < zf (qf ). Then pf > 0 (ifnot, Assumption 2 is violated). This implies that pf can bedecreased by a small amount and correspondingly q f increased

Model net neutrality via CP price restriction

Monopology ISP Case Relax the price

restriction -> Impact on

surplus and its distribution

Competitive ISP Case

Charging CP (1) increases EU surplus(2) leaves ISP surplus the same

(3) increases CP surplus if EU elasticity high compared to connectivity cost

0 10 20 30 40 5050

60

70

80

90

100

EU

Sur

plus

Competition Equilibrium surplus

0 10 20 30 40 50100

105

110

115


CP

Sur

plus

Fig. 3. Competitive Equilibrium end-user and content-provider surplus vs.q. End user surplus increases with q and content-provider surplus peaks at avalue of q less than the equilibrium value q.

lower is the end-user price sensitivity required for the contentprovider to benefit from participation in rate allocation. Thecontent-provider surplus can be seen to be maximized at avalue of q less than the equilibrium price q. Figure 3 is aplot of the end-user and content-provider surplus against q forthe example illustrated in Section V with af = $50, !f =0.5, bf = $50, "f = 0.5.In summary, in a competitive ISP market:• The participation of the content-provider in rate allocationincreases the end-user surplus, and the total surplus, whilethe ISP surplus remains unchanged.

• The content-provider can increase surplus through partic-ipation in rate allocation if the end-user price sensitivityis sufficiently high relative to the cost of connectivity.

• Lower cost of connectivity reduces the end-user pricesensitivity required for the content-provider to gain fromparticipation in rate allocation.

B. Net Neutrality in a Monopoly ISP Market

Consider now the monopoly ISP case. The end-user sur-plus SE

M (q), content-provider surplus SCM (q), the ISP surplus

SIM (q), and total surplus ST

M (q) are given by

SEM (q) = u(y(r ! q)) ! (r ! q)y(r ! q) (22)

SCM (q) = v(y(r ! q)) ! qy(r ! q)

SIM (q) = (r ! µ)y(r ! q)

STM (q) = u(y(r ! q)) + v(y(r ! q)) ! µy(r ! q)

where r = r(q) is the price charged by the monopoly ISP as afunction of the content-provider price restriction.To quantify the surplus behavior, we need to evaluate r(q).

To simplify the exposition, we assume that the end-user andcontent-provider utility functions are such that the elasticitiesof demand #E and #C are fixed and greater than 1. For lowvalues of q, it is apparent that the content-provider’s demandz(q) exceeds the end-user demand y(r! q). The monopoly ISP

determines the price r(q) through the following maximization

maximize!

f (r ! µ)(y(r ! q))variables r " 0 (23)

resulting in r(q) = !Eµ!1!E!1 . As q increases, the content-provider

demand falls until it equals the end-user demand generated bythe monopoly determined price r(q). This threshold price, q t, atwhich the two demands are equal, can be determined by solvingy(r(qt)!qt) = z(qt). It can be verified that qt # q, where q isthe equilibrium content-provider price under no restriction. Forq > qt, the monopoly ISP can maximize revenue by equatingthe two demands so that r(q) = y!1(z(q)) + q. We have

r(q) =

"!Eµ!1!E!1 if q # qt

y!1(z(q)) + q if qt < q # q(24)

The first-order derivatives can be shown to be given by thefollowing theorem.Theorem 5: Assuming fixed #C , #E, the partial deriva-

tives of the surpluses SEM (q), SC

M (q), SIM (q), ST

C(q) with re-spect to q, for 0 # q # q, is given by:

$SEM (q)$q

=

"y!E

!E!1 if q # qt

! p(q)y!C

q!E if qt < q # q

$SCM (q)$q

=# y

µ!q [(v"(y) ! q)#E ! (µ ! q)] if q # qt

!y else

$SIM (q)$q

=

"y if q # qt

y!C

q [µ ! q(1 ! 1/#C) ! p(q)(1 ! 1/#E)] else

$STM (q)$q

=

"y!E

(µ!q) (v"(y) + µ!!E q

!E!1 ) if q # qt

! y!C

q (p(q) + q ! µ) if qt < q # q

where p(q) = r(q) ! q is the end-user price under content-provider price restriction q, and y = y(p(q)) is the end-userdemand at price p(q).It is clear that the ISP surplus increases with q. For q # q t,

the content-provider surplus increases provided the end-userprice sensitivity is sufficiently high relative to the cost ofprovisioning capacity as in the competitive market case. Forq > qt, the surplus decreases. The total surplus increases forq < qt and decreases for q " qt, as it can be shown thatp(q) + q " µ.The end-user surplus increases for q # q t and decreases for

q > qt. To quantify the surplus at q = q, we re-write themonopoly price structure given by (15) as

p =µ

(1 ! 1/#E)! q(1 ! 1/#C)

(1 ! 1/#E)(25)

Notice that the first term on the right hand side is the monopolyprice in the absence of content-provider participation. Thepresence of the content-provider reduces the end-user priceand increases the end-user surplus, provided that the content-provider has an elasticity of demand greater than 1. If we allowcontent-provider elasticity of demand #C < 1, then the end-userfaces increased prices due to content-provider participation!When the content-provider is highly price insensitive, with anelasticity of demand #C < 1, the monopoly ISP reaps all the

Inter-ISP Pricing

2

ISPs as a supply chain and apply the revenue sharing contract[7] to it. The essence of the contract is that the dominant ISPrequires a transit-price lower than its marginal traffic deliverycost. Meanwhile, to compensate its revenue loss, the dominantISP claims a lump-sum sharing of the other ISP’s income.In spite of the simplicity, this contract can incentive ISPs tocooperate so that the social revenue is maximized.

To evaluate the revenue sharing contract, we also analyzethe noncooperative model where each ISP selfishly maximizesits own revenue. In particular, the Stackelberg game fits wellas a model here because the dominant ISP on the traffic chaincan naturally be considered as the game leader who determinesthe transit price prior to the decision of the follower ISP3. Wequantify the social revenue loss due to the noncooperation.Building upon the noncooperative model, we design a revenuedivision scheme for the revenue sharing contract with theasymmetric Nash Bargaining Solution (NBS) [8]. Specifically,the equilibrium of the noncooperative model is used as the“threat point”, and both ISPs expect to be better off comparedto the game equilibrium if they agree to cooperate.

A. Related WorksMultiple ISPs pricing in one-sided market has been exten-

sively studied. For example, [4] studied the equilibrium ofpricing competition among ISPs and obtained the social opti-mality with the repeated game. However, the social optimalityalone cannot guarantee that each individual ISP will be betteroff. [11] focused on the peering strategy used by local ISPs,but it may be of no economic interest for an ISP with largeconsumer size to establish peering relationship with anotherISP with a small consumer size [16]. [12] used Shapley valueto model selfish ISPs’ routing and interconnecting decisions.[13] proposed multiple ISPs to share revenue proportional totheir local costs. Neither [12] and [13] considered the socialrevenue optimality and the relevant social revenue loss. Onthe other hand, [1] studied the optimal pricing structure andrate allocation for a single representative monopolistic ISP in atwo-sided market, but did not analyze the interaction betweenISPs.

The rest of the paper is organized as follows. We describethe network model and two-sided market in section II. Wedevelop a revenue sharing contract for ISPs to achieve theoptimal social revenue in section III. We propose a nonco-operative model for comparison in section IV. We use theasymmetric NBS for revenue division in section V and developa distributed procedure to implement the bargaining process.Figure 1 summarizes the different focuses of sections III, IVand V and the logic flow among them.

II. NETWORK SCENARIO AND TWO-SIDED MARKET

We consider a scenario of two interconnected ISPs as shownin Figure 2. Table I lists main notation used in this paper.Traffic originates from CP (whose access service is provided

3The provider/client relationship is the most stable business outcome if oneparty has a high reliance on the interaction arrangement and the other doesnot [3].

!"#"$%"&'()*+$,&-.$/*)-/&0.*'.-+)1&*"#"$%"&2)34&5'"-4&6667

8.$9-..:"*)/+#"&2.;"1&<+/(=+)'";&:.'+/+.$'&5'"-4&6>7

!"#"$%"&;+#+'+.$&=)'";&.$)'?22"/*+-&8@A&5'"-4&>7

'.-+)1&*"#"$%"&1.'' B*.:.'";&*"#"$%"&;+#+'+.$

C/(*")/&:.+$/D

Fig. 1. Different focuses of sections III, IV and V, and the logic flow amongthem.

Fig. 2. The solid arrows denote the charging directions. ISP 1 charges CPusing the usage-price hcp and flat-price gcp. ISP 2 charges EU using theusage-price heu and flat-price geu. In addition, ISP 2 charges ISP 1 fortraffic delivery by using the transit-price π.

by ISP 1) and terminates at EU (whose access service isprovided by ISP 2). Both ISP 1 and ISP 2 aim to maximizetheir own revenues. ISP 1 uses the combination of usage-price hcp and flat-price gcp to charge CP. Meanwhile, ISP2 uses the combination of usage-price heu and flat-price geu

to charge EU. ISPs 1 and 2 have their own marginal costsc1 and c2 for traffic delivery, respectively. In particular, weassume ISP 2 is dominant and can determine the transit-priceπ charged to ISP 1 prior to ISP 1’s decision. For example,ISP 2 provides connectivity to a large population size of EUsand thus is more powerful in determining the transit-price thanISP 1. Therefore, ISP 2 (ISP 1) is the leader (follower) in thefollowing noncooperative game analyzed in section IV. Noticethat the model can also capture the opposite scenario, i.e., ISP1 is dominant and determines the transit-price π paid to ISP 2prior to ISP 2’s decision, for example ISP 1 provides accessto a very popular CP.

We model CP’s service rate provisioning and EU’s trafficrate demand (in terms of the effective data rate) as follows.Given ISP 1’s prices (hcp, gcp), CP decides its service rate bysolving the following problem

(CP-P): maxy≥0

σcpucp(y)− hcpy − gcp, (1)

where y denotes CP’s service rate provisioning and σcp

denotes CP’s utility level (e.g., σcp indicates the popular-ity of the content). A common example of utility functionis ucp(y) = 1

1−αcpy1−αcp , 0 < αcp < 1. In this case,

CP’s service rate provisioning function can be expressed as:

TABLE INOTATION LIST

Symbol Definitionσcp, σeu utility levels of CP and EU

cp = 1αcp

, eu = 1αeu

CP’s and EU’s price elasticitieshcp, gcp usage-price and flat-price used by ISP 1heu, geu usage-price and flat-price used by ISP 2c1, c2 marginal costs of ISP 1 and ISP 2

π transit-price used by ISP 2 to charge ISP 1

Biased position on traffic delivery chain

Cooperative:Revenue sharing contract: dominant ISP asks for transit price lower than

marginal traffic delivery cost, plus lump-sum sharing of other ISP revenue

Non-cooperative: Quantify lost social revenue

Asymmetric NBS to improve both ISPs

Non-cooperative and Bargaining 5

ISP 2 determines its traffic rate equal to xe and its transit-priceequal to πe. As a response to ISP 2’s decisions, ISP 1 requiresits traffic rate equal to xe exactly.

Let Res denote the corresponding social revenue at the non-

cooperative equilibrium. We can quantify the social revenueloss as follows.Proposition 2: Assume that αcp = αeu = α, then Re

sR∗

s= G,

where

G = (1− ασcp

σeu + σcp)

1α−1 σeu + (2− α)σcp

σeu + σcp. (17)

(Proof in Appendix III).We can further characterize the revenue ratio G as follows:

Proposition 3: Assume αcp = αeu = α, then the revenueratio G in (17) is increasing with σeu and decreasing withσcp. (Proof in Appendix IV).Remark: In the Stackelberg model, ISP 2 is the game leaderwhich has the dominant position and determines the transit-price prior to ISP 1. As a result, the utility level of EU (whoseaccess service is provided by ISP 2) can be fully exploited.Therefore, revenue ratio G is increasing with σeu. In contrast,in the Stackelberg model, ISP 1 is the follower which can onlyoptimize its traffic amount in response to ISP 2’s decision. As aresult, the utility level of CP (whose access service is providedby ISP 1) is poorly exploited. In fact, CP could have produceda larger revenue if ISP 2 charges ISP 1 more appropriately.Therefore, the revenue ratio G is decreasing with σcp.

Figure 3 shows the decreasing (increasing) property of therevenue ratio G = Re

sR∗

swith σcp (σeu) under different values

of αcp = αeu = α.Proposition 4: In the special case of αcp = αeu = α, therevenue ratio G is increasing with α when 0 < α < 1. (Proofin Appendix V).Remark: The noncooperative behaviors of ISP 1 and ISP 2adversely impact the effective traffic rate from CP to EU, andthus result in a social revenue loss compared to the optimalone (i.e., R∗s corresponding to the optimal traffic rate x∗).Notice that in the noncooperative model, ISP 1 charges CPwith c1+πe, which is different from that in the revenue sharingmodel. However, the social revenue loss decreases when CPand EU become more price inelastic. Therefore, ISP’s revenueratio G is increasing with α4.

Figure 4 shows the increasing property of G with α =αcp = αeu under different values of σcp and σeu. We alsoplot the lower bound 2

e (i.e., the bottom dash-dot line) forboth the case of α→ 0 and σcp →∞ and the case of α→ 0and σeu → 0.Remark: Based on Proposition 4, we can show the lowerbound of the revenue ratio G as

G = limα→0

G = (1e)

σcpσeu+σcp

σeu + 2σcp

σeu + σcp. (18)

4Similar conclusions also appeared in [2]. Specifically, Theorem 4 [2]quantified the revenue loss due to ISP’s inability to charge the time-dependentusage-price to EU (thus the network resource may not be fully utilized).Theorem 4 [2] indicated that revenue loss due to this “time-constrained” pricedecreases as EU is more price inelastic.

0 10 20 30 40 50 60 70 80 90 1000.7

0.75

0.8

0.85

0.9

0.95

1

!cp

Rev

enue

Rat

io

0 1 2 3 4 5 6 7 8 9 100.7

0.75

0.8

0.85

0.9

0.95

1

!eu

Rev

enue

Rat

io

"=0.5"=0.7

"=0.01

"=0.01"=0.5

"=0.7

Fig. 3. Performance of the revenue ratio G =Re

sR∗

s. Top Subfigure: ratio

G decreases with CP’s utility level σcp. We fix EU’s utility level σeu = 1,and fix both ISPs’ marginal costs c1 = c2 = 1; Bottom Subfigure: ratio Gincreases with EU’s utility level σeu. We fix CP’s utility level σcp = 1, andfixed both ISPs’ marginal costs c1 = c2 = 1. Dash-dot line denotes the valueof 2

e .

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.7

0.8

0.9

1

Rev

enue

Rat

io

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.7

0.8

0.9

1

!cp=!eu=!

Rev

enue

Rat

io

"cp=1 "cp=10

"cp=100

"cp=0.1

"eu=10 "eu=1"eu=0.1

"eu=0.01

Fig. 4. The revenue ratio G =Re

sR∗

sincreases with consumer’s price

inelasticity (notice that the price elasticity = 1α ). Top Subfigure: We fix

EU’s utility level σeu = 1, and fix both ISPs’ marginal costs c1 = c2 = 1;Bottom Subfigure: We fix CP’s utility level σcp = 0.5, and fix both ISPs’marginal costs c1 = c2 = 1. Dash-dot line denotes the value of 2

e .

Specifically, there exists G→ 1 when σeu →∞, and G→ 2e

when σeu → 0. These results verify the increasing property ofG with σeu. Meanwhile, there exists G→ 2

e when σcp →∞,and G→ 1 when σcp → 0. These results verify the decreasingproperty of G with σcp.

We also show the upper bound of the revenue ratio G to be

G = limα→1

G = 1, (19)

i.e., the price inelasticity can mitigate the revenue loss.

V. REVENUE DIVISION BASED ON THE ASYMMETRICNASH BARGAINING SOLUTION

A. Sufficient Conditions for Both ISPs to Be Better Off

The revenue sharing contract provides incentives for bothISPs to achieve the optimal social revenue cooperatively. How-

7

0 2 4 6 8 10 120.4

0.6

0.8

1

Opt

imal

Rev

enue

0 2 4 6 8 10 120.35

0.4

0.45

0.5

w1

!"

ISP 2’s Equilibrium RevenueISP 1’s Optimal Revenue

ISP 1’s Equilibrium Revenue

ISP 2’s Optimal Revenue

the lower bound of condition (22)

the upper bound of condition (22)

Fig. 5. Revenue division scheme with asymmetric NBS. CP and EU’s utilitylevels σcp = σeu = 1. αcp = αeu = 0.4. Both ISPs’ marginal costsc1 = c2 = 1. We fix ISP 2’s bargaining power w2 = 0.5. Top subfigure: theoptimal revenues of ISP 1 and ISP 2 with different ISP 1’s bargaining powerw1. Both ISPs are better off compared to the noncooperative equilibrium.Bottom subfigure: the optimal revenue division factor θ∗ with different ISP1’s bargaining power w1. The value of θ∗ satisfies condition (22) strictly.

package. Figure 6 shows the performance of the proposedbargaining procedure. Since ISP 1 uses the bisection methodto search the optimal value of λ, the proposed procedure canconverge within log2

λ−λ iterations with a tolerance error .

Distributed Bargaining Procedure for Two ISPsInitialization: ISP 1 initializes λ and λ, and sets λ = λ, ISP2 sets Flag = 1.Iteration: Repeat step (1) and step (2) until ISP 1 and ISP 2reach an equilibrium.step (1) ISP 1’s decision procedure:

1: If Flag = 1 is received, then ISP 1 updates λ = λ. IfFlag = −1 is recieved, then ISP 1 updates λ = λ. IfFlag = 0 is received, ISP 1 knows that ISP 2 has acceptedthe offer and the algorithm can stop.

2: ISP 1 first calculates λ = 12 (λ + λ), θ = minR∗

s−r1R∗

s−

w1λ , 0, and then sends the offering package (θ, λ) to ISP

2.step (2) ISP 2’s decision procedure:

1: ISP 2 receives ISP 1’s offering package (θ, λ) and calcu-lates γ = w2

λ + r2R∗

s.

2: If θ − γ ≥ , then ISP 2 replies ISP 1 with Flag = 1. Ifθ− γ ≤ −, then ISP 2 replies ISP 1 with Flag = −1. If− < θ− γ < , then ISP 2 replies ISP 1 with Flag = 0.

End

D. Limitation of the Revenue Sharing Contract and TriggerStrategy

The revenue sharing contract also has the following lim-itation. Each ISP has to share its income with the otherISP truthfully. However, in practice, some ISP may find itprofitable to lie and deviate from the contract, e.g., reportingits income less than the true value. One method to avoid thismisbehavior is to design a cheat-proof mechanism to guarantee

0 5 10 150.4

0.6

0.8

1

Opt

imal

Rev

enue

s

0 5 10 1510

20

30

40

50

!

0 5 10 15−1

0

1

Flag

Iteration Index

ISP1’s Optimal Revenue

ISP2’s Optimal Revenue

Fig. 6. Performance of the proposed distributed procedure. We set both ISPs’minimum requirements as the game equilibrium, i.e., r1 = Re

1, r2 = Re2.

We fix both ISPs’ bargaining power as w1 = 1, w2 = 0.5. CP and EU’sutility levels σcp = σeu = 1, αcp = αcp = 0.4, their marginal costsc1 = c2 = 1. Top Subfigure: optimal revenues (R∗

1 , R∗2) of ISP 1 and ISP

2. Middle Subfigure: dual price λ. Bottom Subfigure: the value of Flag.

the correct operation of the revenue sharing contract. The“trigger strategy” in the repeated game theory can be usedhere. Specifically, each ISP announces a threat message whichstates that it will turn back to the noncooperative model foreverif any misbehavior (e.g., untruthful report of the income) of theother ISP is detected8. Therefore, each ISP considers whetherit is profitable to cheat in the contract, and faces a tradeoffbetween gaining a short-term large revenue and losing itsoptimal revenue in long-term. Specifically, each ISP (say ISP1) will check the following condition:

∞

t=0

δtR∗1 ≥ R1 +∞

t=1

δRe1 (25)

where R1 denotes ISP 1’s short-term large revenue by violat-ing the contract (e.g., reporting its income less than the truevalue). Usually there exists R1 ≥ R∗1 ≥ Re

1. The discountparameter δ (0 ≤ δ ≤ 1) represents ISP 1’s emphasis onits future revenue. Obviously, if condition (25) is met, thenit is nonprofitable for ISP 1 to violate the revenue sharingcontract. Condition (25) implies that if the discount parameterδ ≥ bR1−R∗

1bR1−Re

1, then ISP 1 bearing its long-term revenue in mind

will strictly adhere to the revenue sharing contract without anyincentive to deviate. Similar analysis is applicable to ISP 2.

VI. CONCLUSION

We study the revenue sharing among interconnected ISPsthat jointly delivery traffic from CPs to EUs. We first use therevenue sharing contract to coordinate both ISPs’ objectivesso that the optimal social revenue can be achieved. Nonco-operation between two ISPs inevitably incurs a social revenueloss, and our results quantify that the loss decreases (increases)with the utility level of customer whose access is provided

8For example, if ISP 1 finds that R∗1 < Re

1, then it is reasonable for ISP1to believe that ISP 2 violates the contract.

Stackelberg model: EU-facing ISP is the leader

Example of asymmetric bargaining converging to global optimum

Q4. What to Charge?

Different services -> Different prices

New service types:

Package service

User-specific service

Emergency service

New Connectivity Services

Create new class of services: Scavenger class of service

Fill in the leftover capacity. Particularly helpful for wireless

Minimum utility level needed to recover revenue loss due to constraint over time

$5/month data plans

No guarantee on near-instantaneous access

Precise QoS depends on how crowded $5/month plan users are

Paris Metro Pricing

Differential prices -> Differential services

Origin: Odlyzko 2000...

Survey: Walrand 2008...

Recent development: Chiu Lui et al. 2010...

Pricing Across Hetero Wireless

Co-existence of multiple wireless platforms owned by different ISPs:

3G/4G, Femto, WiFi

Price bundling: pricing for stickiness

Price differentiation: offload licensed band congestion

Interaction with interference management on technological plane

Mobility and hand-off support

May enable the dissolution of cellular industry’s vertical mode

From Theory To Practice

Model/Analysis is Only 1 Step

Data, Data, Data

Prototyping proof-of-concept

Field trial and industry adoption

Public education and policy impact

NECA-EDGE Lab whitepaper June 2010

TUBE

Time-dependent Usage-based Broadband-price Engineering

Measurement

Price optimization engine

User interface

User profiling

Recommendation

Wireless extension

TUBE Architecture

!"#$"%&'%&$

!"#$%&'()*'+%

()*+,-.*/0$102,0%$

304&/,4$5%',6%$

#&,6%$.04$78.2%$$ #&,6%$9)4.:%;<&$

78.2%$"=06$>%.89&%+%0:$

102,0%$

,-.(/-0%1.2-/3'4-.%

TUBE Architecture

!"#$$

"%&'%&$

""()*("$

*+,-$.+!$-/01/%$$

223$

-/01/%$

#4567/$

#%&8$

957:$

;%<$"%&'%&$

#=>?%5$@=/A8%&$

!"#$%&'()*'+%

B:CD1E=C7/$

-/01/%$

9%5F7&?$"5=CGC>G$$$$$$

.3,H"$

#8I01/G$

JKL#!$

@*H($

LMLN$

223$

*+,-$J7DDO$-/01/%$

L/A&71A$

3%'1>%$

@**#$

*+,-$$

P185%&$

P1&%F=88$

J7/5&78$

!"#$%,-./0().(1-)%

TUBE UI

!"#"$%&' ($")"$"#*"+' ,+%-"'./+01$2' 30%4+4*+'

51#0.&2'*%6'789:;'

8<=>?'

($/*"'

!"#$%"&%'()*+,%-.%

TUBE UI

!"#$#"#%&#'()#%#"*+( ,'*-#(./'01"2( 30*4'4&'(

5601(!/+10(

5601(!/+10(!"#$#"#%&#'(

714$2(8.#%(0.#(6'*-#("#*&.#'(9(((:;(1$(0.#(<1%0.+2(&*=(

5==+/&*41%'("#>6/"#(/<<#?/*0#(*&&#''(01(0.#(@%0#"%#0(

ABB!( ABB!3( 3C2=#( )11-+#(D1/&#(

5==+/&*41%'(?1(%10("#>6/"#(/<<#?/*0#(*&&#''(01(0.#(@%0#"%#0(

!E!(5=='( F/%?18'(,=?*0#( ,G!(

!"#$#"#%&#'(

5==+2(

5++18($1++18/%-(*==+/&*41%'($"1<(( 5HI!H(01( (!H(

!"#$%"&%'()*+,%-.%

TUBE UI

!"#$%&'(")*+,&-+%.%+%/0%"&1%/%+#2& 3)#4"40"&

-+(0%&

!"#$%"&%'()*+,%-.%

TUBE UI

!"#$%$&%'()*+*)*,&*%' -%#.*'/0%"1)2'3*,*)#4'

!"#$#%#&'()*$")+,-#.'

56('

-7('

869('

/00&)%1-#.'()*$")+,-#.'

2345'36'(7*)8.'9:'

Utility Function/Demand Function/Elasticity construction from empirical data and proxies

Different speed tiers/service offerings impact elasticity a lot

Substantial statistical challenges

NECA-Princeton Surveys and Polls to ISPs

Data Collection and Analysis

Partners

Data sources and deployment outlets:

NECA

AT&T

Small ISPs

Princeton trial user base

Acknowledgements

Sangtae Ha, Carlee Joe-Wong (Princeton)

Rob Calderbank, Prashanth Hande, Hongseok Kim (Formerly P)

Raj Savoor, Steve Sposato and group (AT&T)

Victor Glass and group (NECA)

Junshan Zhang (ASU)

Yuan Wu, Danny Tsang (HKUST)

What We Need (Most)

Challenges in Access Pricing Study

Model/theory on

User profiling: utility and irrationality

ISP cost and cooperation/competition in inter-ISP scenarios

Theory falsification by data

Start with falsifiable theory

Market impact by deployment

Start with small user base trials

Your Research Changes Your Bill

paid in part by Apple

Guaranteed express delivery

Usage price $50.99

Time of usage discount $69.88Some of the 45 types of taxes I pay

1!

Wireless Interference Management: From Theorems To Deployments

Mung Chiang Princeton University

ONR January 21, 2010

http://scenic.princeton.edu

Theory Practice



pricing internet access - princeton universitychiangm/pricingtalk.pdf · 2010-11-13 · global ip...

Documents