Modelng ISP Ter Degn We Da School of Informaton and Computer Scence Unverty of Calforna, Irvne Irvne, CA, US daw1@uc.edu Scott Jordan School of Informaton and Computer Scence Unverty of Calforna, Irvne Irvne, CA, US ordan@uc.edu Atract We model how Internet Servce Provder degn ter rate, ter prce, and network capacty. We rowng and vdeo treamng are condered a e two domnant Internet applcaton. We propoe a novel et of utlty functon at depend on a uer wllngne to pay for each applcaton, e performance of each applcaton, and e tme devoted to each applcaton. For a monopoly provder, e demand functon for each ter derved a a functon of ter prce and performance. We frt gve condton for e ter rate, ter prce, and network capacty at maxmze Internet Servce Provder proft, defned a ucrpton revenue mnu capacty cot. We en how how an Internet Servce Provder may mplfy ter and capacty degn, y allowng er engneerng department to et network capacty, er marketng department to et ter prce, and o to ontly et ter rate. Numercal reult are preented to llutrate e magntude of e decreae n proft reultng from uch a mplfed degn. Index Term Internet Servce Provder, terng, prcng, dmenonng. I. INTRODUCTION The ter offered y Internet Servce Provder (ISP) are dfferentated y er monly prce and er maxmum downtream tranmon rate. In recent year, ISP have egun to market ee ter on e a of e domnant applcaton of each ter ntended ucrer. Mot ISP now offer a ac ter whch ey market a good for we rowng and emal, an ntermedate ter whch ey market a alo good for fle harng, and a hgher ter whch ey market a alo good for vdeo treamng, ee e.g. [1] []. The ter offerng have gnfcant nfluence on e Internet. They affect o applcaton development and applcaton ue. Redental Internet ue n countre w hgh ter rate utantally dfferent an n countre w low ter rate. Mole Internet ue n countre w flat rate prcng utantally dfferent an n countre w uage aed prcng. Internet ue n turn affect what type of applcaton are developed. Thu, o techncal and economc ue have a great mpact on e Internet development. And yet, e reearch lterature provde lttle gudance a to why ISP offer e ter ey do. Mot extng Internet prcng model focu eer on economc ue or on techncal performance ue, ut uually not o. A numer of paper examne Internet prcng ung economc model. The focu on e relatonhp etween uer, ISP, and content provder, ee e.g. [3] [4]. Two-ded model, whch take nto account payment etween uer, ISP, and content provder, are typcally central to e analy. However, Internet archtecture and topology are typcally atracted nto a mple connectvty model. Applcaton are rarely modeled w repect to eer traffc or utlty. Smlarly, congeton and traffc management are rarely condered. A numer of paper examne Internet prcng ung performance model. The focu on uage aed prcng, ee e.g. [5] [6] [7]. Traffc management model whch take nto account uer traffc and congeton control are typcally central to e analy. However, economc apect are typcally atracted nto e revenue generated y e uage aed prcng, and ter choce rarely modeled. A few paper analyze ISP ter degn for monopole. He and Walrand [8] conder Internet ervce offered at multple qualty level and prce, and otan equlrum reult y modelng a game etween uer maxmzng urplu under fxed prce; ey alo conder revenue maxmzaton for a monopoly ISP. Lv and Rouka [9] [10] alo conder Internet ervce offered at multple qualty level and prce, ut aume at uer chooe e hghet ter ey can afford; ey propoe an algorm at attempt to maxmze a monopoly ISP proft under a fxed cot per uer y controllng qualty level and prce. Thee paper model uer wllngne-to-pay olely a a functon of an aggregated ervce qualty (e.g. andwd) and ometme a uer dependent parameter. In contrat, n paper we decompoe uer wllngne-to-pay for Internet acce nto wllngne to pay for two maor applcaton: we rowng and vdeo treamng. Raer an modelng wllngne-to-pay olely a a functon of andwd, we model t a a ont functon of andwd, performance, and e tme devoted to each applcaton. Raer an aumng a unk cot or a fxed cot per uer, we conder a general cot a a functon of network capacty. Raer an conderng only e cot of e ter n uer urplu, we alo conder e value a uer place on tme. The propoed utlty functon general enough to e appled to model w or wout competton etween ISP. Two nterconnected prolem eparated y tme cale are condered. On a tme cale of day, roadand Internet ucrer chooe how much tme to devote to we rowng and vdeo treamng. On a tme cale of mon, ISP chooe what ter to offer, and potental roadand Internet uer chooe ter. We en eek to anwer how a monopoly ISP et ter prce, ter rate and upgrade e underlyng network capacty. The dependence of ISP proft on ter prce, ter rate and network capacty are derved from e model. We how how ISP engneerng and marketng department may cooperate w each oer to fnd near-optmal ter prce, ter rate and network capacty. Th materal aed upon work upported y e Natonal Scence Foundaton under Grant No. 0916085 and 11603.
Th paper organzed a follow. Secton II ntroduce e utlty functon and ISP traffc management. Secton III derve uer demand for each ter. Secton IV explan how an ISP may mplfy ter and capacty degn, y decompong e network capacty and ter degn prolem nto ree uprolem for e ISP engneerng and marketng department. Secton V preent numercal reult at llutrate e varaton on e degn w key parameter, a well a e magntude of e decreae n proft reultng from uch a mplfed degn. II. UTILITY AND TRAFFIC MANAGEMENT In ecton, we model uer wllngne-to-pay for Internet applcaton a ont functon of andwd, performance, and e devoted tme. ISP ter degn and uer ter ucrpton are modeled aed on e wllngne-to-pay on a longer tme cale. The domnant applcaton on Nor Amercan fxed acce roadand Internet acce network, a meaured y download traffc volume, are real-tme entertanment, we rowng, and peer-to-peer (pp) fle harng, whch togeer account for approxmately 85% [11]. Real-tme entertanment traffc cont almot excluvely of vdeo treamng. For purpoe of analy, we plt pp nto two uet: pp treamng, whch we aggregate w oer vdeo treamng [1], and pp fle harng, whch we aggregate w we rowng [1]. Alough emal an mportant component of uer wllngne-to-pay, t an ngnfcant urden upon e network, and we mlarly aggregate t w oer fle harng applcaton nto we rowng. We u focu n e remander of paper on two applcaton: we rowng and vdeo treamng. The vat maorty of ucrer are wllng to pay for Internet acce for we rowng, and a porton of ucrer are alo wllng to pay for vdeo treamng. We conder two nterconnected prolem eparated y tme cale. On a tme cale of day, roadand Internet ucrer chooe how much tme to devote to Internet applcaton. On a tme cale of mon, ISP chooe what ter to offer, and potental roadand Internet uer chooe what ter (f any) to ucre to. A. Short term model A dcued aove, e current networkng lterature model uer utlty a a functon of an aggregated ervce qualty, ut doe not conder e tme uer devote to each applcaton. Baed on common oervaton, e devoted tme depend on e ervce qualty and uer charactertc, e.g. how uer value applcaton and er tme. The ervce qualty alo depend on e devoted tme, ecaue more tme mean more nected traffc, whch can affect e network performance n return. We u propoe a novel et of utlty functon at can capture e nteracton etween e devoted tme and ervce qualty. In e frt uecton, we conder uer utlty. In e econd uecton, we defne uer wllngne-to-pay y conderng o utlty and a uer valuaton of tme. 1) Uer utlty We rowng utlty commonly modeled a an ncreang concave functon of roughput [13]. However, uer utlte alo depend on how much we rowng ey do [14]. Defne t a e tme ( n econd per mon) at uer devote to we rowng, contng of t r tme per mon readng we page and e tme pent on watng for em to download. We pot at e perceved utlty y uer for we rowng hould e a functon U of e numer of hour devoted to we rowng per mon, e performance of we rowng, and a uer relatve utlty for we rowng. Utlty r an ncreang concave functon V ( t ) of e tme devoted to t [15], ndependent of e uer [8]. W repect to performance, we rowng an elatc applcaton and u performance often meaured y roughput. However, a uer oervaton of we rowng performance cont of e download tme of we page, raer an drect oervaton of roughput [16], and u e rato r r = t t a more drect meaurement of e we rowng performance; t wll e ncorporated nto a uer wllngne-to-pay when we conder a uer valuaton of tme elow. Uer utlty for we rowng relatve to oer uer modeled ung a cale factor v.the nteracton etween ee factor ha not een tuded; we model uer utlty for we rowng (n dollar per mon) a e product: U = vv t r (1) We mlarly pot at e perceved utlty y uer for vdeo treamng hould e a functon U of e tme devoted to vdeo treamng per mon, e performance of vdeo treamng, and a uer relatve utlty for vdeo treamng. Denote t a e tme (n econd per mon) at uer devote to vdeo treamng. Utlty an ncreang concave functon V ( t ) of e tme devoted to t [15], ndependent of e uer [8]. W repect to performance, vdeo treamng commonly clafed a a em-elatc applcaton; we u model a component of uer utlty y a gmod functon Q ( x ) of e roughput x experenced y vdeo treamng applcaton [17], normalzed o at Q ( ) = 1. Uer utlty for vdeo treamng relatve to oer uer modeled ung a cale factor v. The nteracton etween ee factor ha not een tuded; we model uer utlty for vdeo treamng (n dollar per mon) a e product: U = vv t Q x () ) Uer wllngne-to-pay Uer wllngne-to-pay for we rowng and for vdeo treamng alo depend on er ncome. The cale factor v and v hould o e ncreang w ncome. However e tme devoted ee actvte alo lkely to e vewed a an t opportunty cot. Denote p a e opportunty cot (n dollar per econd) of uer tme, e.g. e mnmum wage uer wllng to accept. We model uer wllngne-to-pay for we rowng and vdeo teamng, repectvely, n dollar per mon a: t t W = U pt, W = U pt (3) Uer wll maxmze er wllngne-to-pay y controllng e tme devoted to each applcaton:
t, t t max W t, t = W + W = U + U p t + t (4) The tme at maxmze uer wllngne-to-pay wll u atfy: t vv rt t = p t = V p vr r t 1 t vv t Q x t = p t = V p vq x 1 t We have u ncorporated o performance and economc factor of e two domnant applcaton. B. Long term model On a tme cale of mon, ISP make decon aout what ter to offer, and potental roadand Internet uer make decon aout what ter (f any) to ucre to. Alough mot ISP offer everal ter, we focu here on only two ter: a ac ter marketed to uer prmarly ntereted n emal and we rowng, and a hgher ter marketed to uer alo ntereted n vdeo treamng. ISP are preumed to eek to maxmze er proft: max 1 1 P1, P, X1, X, ( ) (5) PN + PN C (6) where N 1 and N are e numer of uer ucred to ter 1 and ter repectvely, P 1 and P are e prce of ter 1 and ter repectvely, X 1 and X are e rate of ter 1 and ter repectvely, μ e capacty of e ottleneck lnk n e acce network, and C(μ) e cot per mon for network capacty. On a tme cale of day, roadand Internet ucrer chooe how much tme to devote to Internet applcaton, preumaly y evaluatng er wllngne-to-pay aed on e utlty accrued rough er ue of ee applcaton. However, e ter degn determne e performance of e applcaton, whch n turn affect uer decon aout e tme pent on e applcaton. Performance and tme wll furer affect uer decon aout ter ucrpton n return, a llutrated n Fg. 1. We u nvetgate ee relatonhp n ecton III. hort term long term performance Uer: chooe tme r t, t traffc Network: determne performance r t t, x tme on we/vdeo ter choce cot capacty prcng plan Uer: chooe ter T demand ISP: fnd prcng plan, capacty X 1, X, P 1, P, μ Fgure 1. Relatonhp among an ISP and t ucrer. We focu on e ottleneck lnk wn e acce network. Denote y λ (n t per mon) e total downtream traffc for ucrer wn e acce network. Th aggregate downtream traffc mply e um of demand y each uer: L λ = + tr xt M (7) where L e average ze (n t) of a we page and M e average tme (n econd) pent on readng a we page. A common, we model e ottleneck lnk ung an M/M/1/K queue to etmate e average delay d and lo l a a functon of e traffc λ and e capacty μ. It reman to expre e dependence of applcaton performance upon delay and lo. Suppoe at uer ha ucred to ter and erey otan a ter rate X. For we rowng, utlty depend on performance rough a functon r V t at meaure e relatve value of tme devoted to ( ) readng we page. The rato of tme pent readng we page r to tme pent we rowng, r = t t, can e derved from a TCP latency model [18]; we denote t a a functon TCP of e acce network delay d, acce network lo l, and e uer ter rate X : (,, ) r = t t = TCP d l X (8) r For vdeo treamng, utlty depend on performance rough a gmod functon Q ( x ) of e roughput x experenced y vdeo treamng applcaton. Mot vdeo treamng ue TCP or TCP-frendly protocol and e roughput can e derved from mlar TCP model [19]; we denote t a a functon TCP of e acce network delay d, acce network lo l, and e uer ter rate X : (,, ) x TCP d l X = (9) III. DEMAND FUNCTION In e Unted State and many oer countre, t common at only one or two ISP offer wrelne roadand ervce []. In e remander of e paper, we conder one ISP at monopolze e market. Snce e current academc lterature mlarly analyze a monopoly provder, and here our goal to extend oe model y conderng two clae of applcaton and e tme at uer devote to each, a monopoly model a reaonale tartng pont. To derve e monopolt demand functon at expree e dependence of uer ter ucrpton upon prce and performance, we preume at (1) n e hort term model uer chooe e tme pent on we rowng and vdeo treamng y maxmzng wllngne-to-pay, and () n e long term uer chooe wheer to ucre to roadand Internet acce and f o whch ter to ucre to. Denote uer wllngne-to-pay f ey have ucred to ter y ( W t, t ). Denote e rato of tme pent readng we page y uer n ter y r,, and e roughput of vdeo treamng y uer n ter y x,. Ung (1), (), (4), and (5),, v, v, p t : W( t t ) can e expreed a a functon of ( ) t, t, t W( v, v, p ) vv ( r t) pt vv ( t) Q ( x ) pt = + (10) where t and t can e otaned from (5) gven performance r, and x, n ter. 3
Denote uer ter choce y T = 0,, where T = 0 mean at uer chooe not to ucre. The value of v, v, p t determne a uer choce of ter, a hown n Fg. ( ). Uer wll chooe ter T ff: T arg max (,, t = W v v p ) P. If ere competton etween multple ISP, en a uer would alo have to chooe etween dfferent ter offered y multple ISP. p t v none Ter Ter 1 Fgure. Uer ucre to ter 1 ervce, ter ervce or nong. Denote e total numer of uer n e market y N. Denote e et of uer at ucre to ter y S {(,, t = v v p ) uch at T = }, and e numer of uer at ucre to ter y N = S. Denote e dtruton n e market of uer relatve utlte for we rowng and vdeo treamng and er opportunty cot of tme y a denty functon f(v, v, p t ). The demand functon for each ter gven y: (, t, ) v v p S (,, ) v t t N = N f v v p dv dv dp (11) Accordng to (7), e aggregate traffc n e network can e calculated a follow:,, t,, t r L t Nf ( v, v, p ) x t dv dv dp (1) λ = + (, t, ) v v p S where t, and t, are e amount of tme uer w (v, v, p t ) pent on we rowng and vdeo treamng n ter. They can e otaned from (5). Note at e performance r, r,, x, and x, of each ter depend on e ter rate X 1, X, network lo l and network delay d. Furermore, e lo l and delay d depend on e traffc rate λ ung e M/M/1/K network model. Thu r, r,, x, and x, can e expreed a functon of λ, and (1) u a nonlnear fxed pont equaton n λ. IV. ISP TIER DESIGN In e prevou two ecton, we ntroduced utlty functon for we rowng and vdeo treamng, and derved uer demand for each ter. In ecton, we eek to undertand how an ISP may degn a tered prcng plan and ottleneck network capacty. ISP meod for ter degn are propretary; however, an undertandng of how an ISP may approach ter degn eental for networkng reearch. Our model can provde nght nto prolem, y naturally decompong e M network capacty and ter degn prolem nto ree uprolem for e ISP engneerng and marketng department. Gven e denty functon f(v, v, p t ), e relatve value functon V (t ), V (t ), e vdeo treamng performance functon Q (x ), and an accurate network model, an ISP could calculate e optmal tered prcng plan P 1, P, X 1, X and network capacty μ o a to maxmze t proft, denoted y Proft=P 1N 1+P N C(μ). The frt order condton for optmalty are: Proft Proft Proft Proft Proft,,,, = ( 0, 0, 0, 0, 0) (13) P1 P 1 ρ However, t dffcult for an ISP to drectly calculate e optmal prcng plan and network capacty from (13). Frt, an ISP may not have complete knowledge of all of e requred functon. Second, an ISP may fnd t challengng to ntll e requred cooperaton etween t engneerng department, whch tradtonally focued on network archtecture and performance, and t marketng department, whch tradtonally focued on prcng and demand. Thu, t natural for an ISP to attempt to decompoe e tak of proft maxmzaton etween t engneerng and marketng department. A. Engneerng department determnaton of network capacty An ISP engneerng department typcally ha e prmary reponlty for determnng network capacty. Whle we are not prvy to propretary nformaton aout e operaton of ISP, our undertandng at many ue a dmenonng rule of um: a capacty upgrade cheduled when e load on a network lnk exceed a rehold 1, here denoted y ρ. Thu, gven network traffc λ durng e peak tme perod, an ISP engneerng department may nvet o at network capacty μ atfe: ρ= λ ρ (14) We ak here wheer uch a rule of um appled to e capacty μ of e ottleneck lnk effectvely maxmze proft. Denote e margnal network cot y p μ =dc(μ)/dμ. The optmal choce for ρ would reult n:, Proft PN 1, PN = r = 1, r = + +, ρ r ρ r ρ PN, 1, x PN = = 1, x 1 λ λ + p, (15) x ρ x ρ ρ ρ ρ = 0 We rowng performance n o ter, r and r,, deterorate w network load ρ. Smlarly, vdeo treamng performance n ter, x,, deterorate w network load ρ. However, vdeo treamng performance n ter 1, x, would lkely not change w network load ρ, nce t would lkely e contraned y ter rate X 1. A a reult, any ncreae n load ρ 1 A commonly dcued choce for ρ 0.7. 4
wll reult n uer pendng le tme on o applcaton, and e total traffc λ wll fall. Thu:,, r r x x λ 0, 0, 0, 0, 0 ρ ρ ρ ρ ρ The magntude of ee term, however, depend on e load ρ. The dmenonng rule of um wa aed on oervaton at we rowng performance good when load are elow a rehold, ut egn to deterorate quckly at load aove at rehold. W e ncreang popularty of vdeo treamng, ISP eem to e ung a mlar rule of um for vdeo treamng, ut w a lower rehold. Thu, we conecture at ue of e dmenonng rule of um reult n r /ρ 0, r, /ρ 0, x, /ρ 0 when ρ<ρ, and r /ρ <0, r, /ρ<0, x, /ρ<0 when ρ>ρ. The lat term n (15) a large potve numer when ρ<ρ, and a mall potve numer when ρ>ρ. Thu Proft/ρ a large potve numer when ρ<ρ, near 0 when ρ ρ, and negatve when ρ>ρ. Thu, t appear to e near optmal for an ISP to mantan a network load ρ lghtly maller an ρ. We expect at e amount of u-optmalty wll depend on e choce of e rehold ρ and upon how quckly e performance of we rowng and vdeo treamng change when e load exceed e rehold. We wll nvetgate n ecton V. B. Marketng department determnaton of ter prce An ISP marketng department typcally ha e prmary reponlty for determnng ter prce. Whle we are not prvy to propretary nformaton aout how ey approach tak, we expect at ey attempt to maxmze proft. We preume here at e marketng department take nto account e engneerng department dmenonng rule of um, namely ey aume at μ = λ/ρ. Gven dependence, e optmal choce for P 1 and P would reult n: N1 N p λ = N + P1 + P = 0 ρ Proft P P P P (16) If e ISP ha etmated e market denty f(v, v, p t ), en t can etmate e entvte of demand w prce {N 1/P, N /P } from e demand functon n (11). In cae, t wll lkely conder e performance of we rowng and vdeo treamng {r, r,, x, x, } a fxed,.e. etmate {dn 1/dP, dn /dp } ntead of {N 1/P, N /P }, nce e dmenonng rule of um hould keep e network load contant. Alternatvely, we oerve at ome ISP drectly etmate ee entvte from market urvey and/or prcng tet. The lat term n (16) e mpact of e ter prce on e network cot. Smlarly, f e ISP ha etmated e market denty f(v, v, p t ) and know e tme at uer devote to we rowng and vdeo treamng, en t can etmate e entvte of traffc w prce {λ/p } from (1), now holdng o e performance of we rowng and vdeo treamng and e tme devoted to each {t,, t, } a fxed. Alternatvely, f ISP drectly etmate e entvte of demand w prce, t may alo drectly etmate e entvte of traffc w prce. Thu, e marketng department may attempt to maxmze proft y electng ter prce {P 1, P } ung (16). However, ee prce wll not e optmal nce, rough t relance on e dmenonng rule of um, t preume at optmal performance doe not vary w prce. We wll nvetgate e amount of u-optmalty n ecton V. C. Jont determnaton of ter rate We have preumed aove at an ISP engneerng department taked w determnng network capacty and at an ISP marketng department taked w determnng ter prce. The remanng tak at of determnng ter rate {X 1, X }. We are unure of how mot ISP handle tak. Ter rate affect e performance of we rowng and vdeo treamng, and u affect uer wllngne-to-pay rough (10). Th n turn affect o e demand for each ter rough (11) and e network traffc rough (1). We conecture at ISP u mut nvolve o er engneerng and marketng department n tak. Choong ter rate to atfy Proft/ 1=0 and Proft/ =0 appear to u to e too complex of a tak to e undertaken drectly y an ISP. Thu, we addre determnaton of e rate for each ter eparately n e followng two uecton. 1) Determnaton of ter 1 rate Gven e ue of a dmenonng rule of um, e choce of X 1 hould have lttle effect upon e performance of we rowng and vdeo treamng n ter. Smlarly, e choce of X hould have lttle effect upon e performance of we rowng and vdeo treamng n ter 1. Thu, we aume at:,, r x r x 0, 0, 0, 0 1 1 The partal dervatve of proft w repect to ter 1 rate can en e mplfed to: Q ( x ) Proft N1 r N 1 = P 1 + 1 r 1 Q ( x ) 1 N Q ( x ) r N p λ + P + 1 ( r Q x ) 1 ρ 1 and e partal dervatve of λ w repect to ter 1 rate can e mplfed to: λ λ r λ Q ( x ) = + 1 r 1 Q x 1 The roughput of vdeo treamng n ter 1, x, very lkely to e contraned y ter rate X 1, leadng to x = X 1. The qualty of we rowng, r, an ncreang concave functon of X 1, whle e qualty of vdeo treamng Q (x ) a gmod functon of X 1. On a, we make e followng conecture: Conecture A: There ext an nterval X 1 X 1 X 0, where e qualty of we rowng r very good, ut e qualty of vdeo treamng Q (x ) not derale. Conecture A aed on e common oervaton at e mnmum requred ter rate X 1 for decent vdeo treamng larger an at of we rowng,.e. X 0. Accordng to Fg. 4, Q ha two flat porton. The ntal flat porton (X 1 X 1) correpond to poor vdeo treamng performance under a low ter rate, where Q (x )/ 1 0. Smlarly, r alo ha a flat 5
porton (X 1 X 0 ) correpondng to good we rowng, where r / 1 0. Thu, we can make e followng approxmaton, when X 1 X 1 X 0 : Q x r Proft 0, 0 0 1 1 1 Thu, any choce of X 1 wn X 1 X 1 X 0 can approxmately maxmze proft. One reaonale choce for X 1 : X1 = Wn RTT (17) where Wn e maxmum TCP receve wndow ze and RTT denote a typcal round trp tme. The determnaton of ter 1 rate can u e accomplhed entrely y e engneerng department. The amount of uoptmalty ntroduced y ee approxmaton wll largely depend upon e hape of e functon r (X 1) and Q (X 1), whch we wll nvetgate n ecton V. ) Determnaton of ter rate The determnaton of ter rate more complex, and we eleve t wll nvolve o e engneerng and marketng department. Ung e approxmaton gven n e prevou uecton, e partal dervatve of proft w repect to ter rate can e mplfed to: N1 N p λ = P1 + P ρ Proft (18) We preume here at determnaton of ter rate occur after network capacty and ter prce have een determned a outlned aove. The roughput of vdeo treamng n ter, x,, very lkely to e contraned y ter rate X, leadng to x, = X. The partal dervatve of demand and traffc to ter rate, however, depend on many factor. Defne uer Internet urplu a e wllngne-to-pay mnu e pad ter prce. Denote y S,k e et of uer w equal urplu n ter and ter k (.e. e uer n Fg. on e oundary etween two regon). We propoe two addtonal conecture olely to mplfy etmaton of Proft/ : Conecture B: S 0, << S 1,. Conecture B aed on e common oervaton at mot margnal uer n ter prefer ter 1 to no Internet ucrpton. t t Conecture C: p = p. Conecture C aume at all uer place e ame value p t on er tme. We let p t t e e average value among all p, when calculatng e near-optmal ter rate. Theorem: Baed on ee conecture, Proft/ can e approxmated a follow: mar Proft Nv V t Q X,, mar (, ) ( ) p NQ, X V t p N t X, ρ ρ Q X V t + (19), where, t E( t T ), n ter pend on vdeo treamng, tmar E( t S1, ) = = e average amount of tme uer = e average tme uer ndfferent to ter 1 and pend on vdeo, v = E v S e average relatve treamng, and mar ( 1, ) value placed on vdeo treamng y uer ndfferent to ter 1 and. Proof: See Appendx. The frt term n (19) can e nterpreted a e margnal revenue produced y an ncreae n ter rate, f e prce of ter multaneouly ncreaed y e amount at leave e numer of ucrer to ter unchanged. The econd term can e nterpreted a e margnal cot for capacty produced y an ncreae n ter rate requred accommodatng e ncreaed tranmon rate for vdeo treamng. The rd term can e nterpreted a e margnal cot for capacty produced y an ncreae n ter rate requred accommodatng e ncreaed tme pent on vdeo treamng due to an ncreae n qualty of vdeo treamng. The determnaton of ter rate can e calculated from (19) y ettng Proft/ equal to zero. The engneerng department would lkely have knowledge of Q, dq /dx, p μ,, and t, e marketng department would lkely have knowledge of p t, V and t dervatve, and o department mut cooperate to etmate Proft/. The amount of uoptmalty ntroduced y ee approxmaton wll largely depend upon e valdty of Conecture C, whch we wll nvetgate n ecton V. V. NUMERICAL RESULTS In ecton, we explore e magntude of e decreae n proft reultng from e varou ource of u-optmalty dcued n e prevou ecton, and e varaton of e degn w key parameter. We do not compare ee degn to oer degn, nce e current academc lterature doe not conder two clae of applcaton nor e tme uer devote to applcaton, and are u not comparale. A. Magntude of u-optmalty The ue of a dmenonng rule of um, aed on e preumpton of a rehold ρ, may caue gnfcant uoptmalty. To nvetgate, parameter are et a follow: L=750KB [1]; 10 concurrent TCP connecton for we rowng; TCP packet ze = 51B; RTT=100m; M/M/1/K ervce rate = 600Mp and uffer ze = 5, 50, or 100 packet; vdeo treamng ervce aed on TCP w Q (x ) a n []. Fg. 3 how e performance of we rowng and vdeo treamng a a functon of network load. For a 50 packet uffer, ere a farly teep declne n performance of we rowng when ρ>0.97, and n e performance of vdeo treamng when ρ>0.87. Fg. 4 how e performance of we rowng and vdeo treamng a a functon of acce ter rate for a 50 packet uffer when ρ=0.7. The performance of we rowng a concave functon of e ter rate, and farly contant for X>.5Mp. The performance of vdeo treamng a gmod functon of e ter rate; t farly contant at poor performance when X<3Mp, re quckly for 3Mp<X<18Mp, and farly contant at hgh performance when X>18Mp. Thu, 6
alough o we rowng and vdeo treamng performance experence a harp rehold w repect to load, ere much lower change n vdeo treamng performance. Qualty of rowng/treamng 1.0 0.9 0.8 0.7 0.6 0.5 rowng, 5pk treamng, 5pkt rowng, 50pkt treamng, 50pkt rowng, 100pkt treamng, 100pkt 0.0 0. 0.4 0.6 0.8 1.0 Network load Fg. 5 how e percentage of e optmal proft at e mplfed degn acheve under dfferent load rehold ρ. We oerve proft ncreae w ρ untl ρ = 0.85, when e mplfed cheme acheve 98.5% of optmal, and en fall quckly after at. The optmal value of ρ = 0.85 correpond to e load rehold for vdeo treamng a een n Fg. 3. Proft/et proft 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 Fgure 3. The dependence of performance r and Q upon network load ρ. 0.60 0.5 0.6 0.7 0.8 0.9 1.0 Load rehold Qualty of Internet applcaton 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0. 0.1 we rowng vdeo treamng 0.0 0 5 10 15 0 5 Ter rate (Mp) Fgure 4. The dependence of performance r and Q on e ter rate. To gauge e ze of ource of u-optmalty, we compare e optmal choce of capacty, ter prce, and ter rate to oe choen, ung e mplfed cheme under e followng parameter: V (t ) = log(a t + 1) w a = 0.006, o at a uer w t =50 hour/mon [3] wllng to pay $60 for ter 1 [4]; V (t ) = log(a t + 1), w a = 0.0093, o at a uer w t =15 hour/mon [5] wllng to pay an addtonal $0 to move from ter 1 to ter [4]; N=0000; (v, v, p t ) ~ multvarate lognormal w (v /p t, v /p t ) ndependent of p t, f p(p t ) gven y 009 US houehold ncome [6], f(v /p t ) gven y [3], f(v /p t ) gven y [5], and e correlaton etween v /p t and v /p t = 0.5; p μ = $10/Mp/mon [7]; peak traffc = 1.55 tme average traffc [1]; uffer = 50 packet; ρ = 0.7. Tale 1 preent e parameter and proft of e optmal degn (13) and e mplfed degn. The degn match farly cloely, ut e mplfed degn reult n 4.3% le proft. TABLE I. NEAR-OPTIMAL RESULTS AND OPTIMAL RESULTS Smplfed Optmal Prce of ter 1 P 1 $68 $65 Prce of ter P $84 $80 Rate of ter 1 X 1.5Mp.5Mp Rate of ter X 0Mp.Mp Network capacty μ 6.31Gp 6.41Gp Proft $371600 $38880 Fgure 5. Su-optmal proft over optmal proft under dfferent ρ. The dmenonng rule of um e larget ource of u-optmalty n e numercal reult n ecton, and e choce of e rehold e mot gnfcant factor. The determnaton of ter prce contrute addtonal uoptmalty rough t relance on e dmenonng rule of um, whch preume at optmal performance doe not vary w prce. The determnaton of ter rate contrute addtonal u-optmalty rough approxmaton, whch depend upon e hape of e functon r (X 1) and Q (X 1) and upon e valdty of Conecture C. In numercal reult, ee contruton are mnor. B. Varaton of e degn w key parameter In fnal uecton, we explore e varaton of e mplfed degn w key parameter. Fg. 6 how e dependence of proft upon e margnal network cot p μ. Unurprngly, e cot of capacty decreae and proft ncreae a margnal network cot decreae. The mpact upon e demand for each ter complex. Frt, conder e mpact of p μ on ter prce. The marketng department conder wheer to ncreae or decreae P 1 n repone. If t ncreae P 1, wll reult n uer n S 0 droppng ervce, w a mall decreae n traffc, and uer n S 1, upgradng from ter 1 to ter, w a utantal ncreae n traffc. A a reult, λ/p 1>0 and when p μ decreae, Proft/P 1 ecome potve from (16). Thu, e ISP wll ncreae P 1 to earn more proft. The marketng department wll en conder wheer to modfy P. If t ncreae P, wll reult n uer n S 1, downgradng from ter to ter 1, w a utantal decreae n traffc. A a reult, λ/p <0, and when p μ decreae, Proft/P ecome negatve from (16). Thu, e ISP wll decreae P to earn more proft. Next conder e mpact upon ter rate. Ter 1 rate et y e engneerng department ung (17) whch doe not depend upon p μ. The engneerng and marketng department ontly ue (19) to et ter rate; decreang p μ make Proft/ potve, and u e ISP wll ncreae ter rate X. 7
Snce e prce of ter ha decreaed whle ter rate ha ncreaed, e demand for ter wll ncreae. The ncreae n ter demand outwegh e decreae n ter prce, and u revenue from ter ncreae. Smlarly, e prce of ter 1 ha ncreaed, caung uer to upgrade to ter and caung revenue from ter 1 to decreae. ISP proft/revenue ($) 4.6x10 5 4.4x10 5 4.x10 5 4.0x10 5 3.8x10 5 3.6x10 5 3.4x10 5 3.x10 5 3.0x10 5.8x10 5.6x10 5.4x10 5.x10 5.0x10 5 1.8x10 5 1.6x10 5 1.4x10 5 1.x10 5 ISP proft Revenue from ter 1 Revenue from ter 0 18 16 14 1 10 8 6 4 0 Network cot ($/Mp/mon) Fgure 6. The dependence of proft upon e margnal network cot p μ. Fnally, we explore e effect of ncreang vdeo treamng popularty. To nvetgate, we multaneouly ncreae v and decreae e parameter a n V (t ), o at e average uer tme pent on vdeo treamng ncreae ut er wllngne-to-pay for treamng reman unchanged. Fg. 7 how e network capacty and ter rate a a functon of e average uer tme pent on vdeo treamng. A uer devote more tme to vdeo treamng, Proft/ ecome negatve, and u e engneerng and marketng department wll ontly reduce ter rate X ung (19). Th wll caue ome uer to downgrade from ter to ter 1. Network Capacty (p) 1.0G 10.0G 8.0G 6.0G 4.0G.0G Network capacty Ter rate 30.0M 5.0M 0.0M 15.0M 0.0 10.0M 0 10 0 30 40 50 Average uer' tme pent on vdeo treamng (hour/mon) Fgure 7. Network capacty and ter rate v. vdeo treamng tme. The effect on traffc more complex. For mall ncreae n e average treamng tme, e ncreae n vdeo treamng tme y oe who reman n ter outwegh e very mall reducton n ter ucrpton and performance, and hence reult n an ncreae n traffc. A a reult, e engneerng department ncreae capacty μ accordng to (14). However, for larger ncreae n vdeo treamng tme, e ter ucrpton and performance egn to drop quckly, outweghng e ncreae n vdeo treamng tme y oe who Ter rate (p) reman n ter, and hence reultng n a decreae n traffc, and u a decreae n capacty. VI. CONCLUSION We propoed a model of how an ISP may et ter prce, ter rate, and network capacty y conderng o techncal and economc ue. We rowng and vdeo treamng are modeled y utlty functon dependng on performance, devoted tme, uer valuaton of tme and of applcaton, ntead of only an aggregated ervce qualty (e.g. andwd). A general cot functon dependng on e network capacty ued, ntead of aumng a fxed cot per uer. On a tme cale of day, uer chooe how much tme to devote to applcaton aed on e opportunty cot of er tme. On a tme cale of mon, ISP chooe ter rate and prce, and uer make ucrpton decon. For a monopoly ISP, we derved demand a a functon of ter prce and performance, and condton for e optmal tered prcng plan and network capacty. We en ue our model to anwer how ISP may degn tered prcng plan, whch propretary ut mportant to networkng reearch. Model analy how at e complex ISP proft maxmzaton prolem can e decompoed y e ISP, where e engneerng department et network capacty, e marketng department et ter prce, and ey ontly et ter rate. Numercal reult are preented to llutrate e magntude of e decreae n proft reultng from uch a pole degn taken y e ISP. Alough ISP approache to ee tak are propretary, we hope at model may upport reearch at depend on an undertandng of ter degn. We eleve e frt model preented n e academc lterature of how an ISP may degn ter rate, ter prce, and network capacty at conder two clae of applcaton or e tme uer devote to applcaton. Alough e monopoly cae nteretng n t own rght, an excellent topc for future reearch would e conderaton of market demand and ter degn when ere are multple ISP competng n a market. VII. APPENDIX Proof of eorem: Ung Conecture A:, x r r,, 0, 0, 0, r r, tmar tmar, tmar 0,, where t mar and t mar (rep. tmar and t mar ) are e average tme uer n S 1,, and n ter 1 and repectvely, pend on we rowng (rep. vdeo treamng). Thu, when x, contraned y ter rate X :,,, λ t, N tmarr L, N X + t + + tmar X M The frt term gve e margnal traffc of current ter uer reultng from ncreaed tranmon rate and from addtonal tme devoted to vdeo treamng due to mproved performance. The econd term gve e margnal traffc due to new ter ucrer. By conderng e performance n ter 1 a ndependent of ter rate X : 8
λ 1 N 1 tmarr L N1 tmarr L tmar x + M M Ung Conecture B, a margnal ncreae n X prmarly caue ome margnal uer to upgrade from ter 1 to ter, w e total numer of ucrer remanng contant: ( N1+ N) N1 N 0 = Thu, we have e followng approxmaton for λ/ : ( λ λ ) λ, 1+ t, N, = N X + t + tmar X It reman to fnd expreon for N / and t X to get an expreon for Proft/ n (18). We preumed at ter prce have already een determned accordng to (16). Thu:, Proft N p Xt mar = 0 = N P P1 P P ρ An ncreae n ter rate wll ncreae uch margnal uer wllngne-to-pay for vdeo treamng n ter. Thu: N, NPro W > P P 1,,,,, ( mar ),, ( 1 mar ) = NPro W + X W X > P P X, Wmar 1 = NPro W + X W X > P P X 1 NPro W > P P X W W = X W, mar mar ( ), mar N N,, = = v mar V t Q X P P Ung Conecture C, e average tme uer n ter pend on vdeo treamng can e etmated from (5) ung: t,, t, 1 p v V t Q X = p t = V, v Q ( X ), Thu, gven p t and v,, t X can e expreed a:, ( ) ( ) X v Q X Q X V t, t Q X V t t 1 p =V X, =, ( ) Thu, we can derve e fnal expreon for Proft/ n, (19) y replacng λ/, N / and t n (18). REFERENCES [1] AT&T, U-Vere prcng, http://www.att.com/u-vere/hop/, acceed Apr. 30, 01. [] Cox Communcaton, Cox Internet prcng, http://ww.cox.com/redental/nternet.cox, acceed Apr. 30 01. [3] A. Gold and C. Hogendorn, Tppng n two-ded market w aymmetrc platform, Telecommuncaton Polcy Reearch Conference, 011. [4] J. Muaccho and D. Km, Network platform competton n a twoded market: Implcaton to e net neutralty ue, Telecommuncaton Polcy Reearch Conference, 009. [5] M. Chang et al., Prcng roadand: Survey and open prolem, Second Internatonal Conference on Uqutou and Future Network (ICUFN), 010. [6] P. Hande et al., Prcng under contrant n acce network: Revenue maxmzaton and congeton management, IEEE Infocom, Mar. 010. [7] S. Shakkotta et al., The prce of mplcty, IEEE Journal on Selected Area n Communcaton, vol. 6, no. 7, pp. 169-176, Sep. 008. [8] Lnha He and Jean Walrand, Prcng dfferentated Internet ervce, IEEE Infocom, Mar. 005. [9] Qan Lv and George N. Rouka, An Economc Model for Prcng Tered Network Servce, IEEE ICC 009. [10] Qan Lv and George N. Rouka, Internet Servce Terng a a Market Segmentaton Strategy, IEEE GLOBECOM 009. [11] Sandvne Incorporated, Gloal Internet phenomena report 01, Techncal report, Fall 01. [1] Yong Lu, Yang Guo, Chao Lang, A urvey on peer-to-peer vdeo treamng ytem, Peer-to-Peer Networkng and Applcaton, vol. 1, no. 1, Mar. 008. [13] W. Wang, M. Palanwam, and S. H. Low, Applcaton-orented flow control: Fundamental, algorm and farne, IEEE/ACM Tranacton on Networkng, vol. 14, no.6, pp. 18 191, Dec. 006. [14] John Muaccho, Jean Walrand, WF Acce Pont Prcng a a Dynamc Game, IEEE/ACM Tranacton on Networkng, vol. 14, no., pp. 89-301, Apr. 006. [15] Han U Gerer, Gerard Pafum, Utlty Functon: From Rk Theory to Fnance, Nor Amercan Actuaral Journal, Jul. 1998. [16] O. Ormond, J. Murphy, and G.-M. Muntean, Utlty-aed ntellgent network electon n eyond 3G ytem, IEEE Internatonal Conference on Communcaton (ICC), 006. [17] P. Hande, Z. Shengyu, and C. Mung, Dtruted rate allocaton for nelatc flow, IEEE/ACM Tranacton on Networkng, vol. 15, no.6, pp. 140 153, Dec. 007. [18] N. Cardwell, S. Savage, and T. Anderon, Modelng TCP latency, IEEE Infocom, pp. 174-1751, Mar. 000. [19] J. Padhye, V. Frou, D. Towley, and J. Kuroe, Modelng TCP roughput: A mple model and t emprcal valdaton, ACM SIGCOMM, 1998. [0] Nchola Economde, Net Neutralty, Non-Dcrmnaton and Dgtal Dtruton of Content Through e Internet, Journal of Law and Polcy for e Informaton Socety, vol. 4, no., 008. [1] Wete Optmzaton LLC, Average we page ze eptuple nce 003, http://www.weteoptmzaton.com/peed/tweak/averagewepage/, acceed Aprl 30, 01. [] S. Weer and V. Veeraraghavan, Dtruted algorm for rateadaptve meda tream, INFORMS Telecommuncaton Conference, Dec. 007. [3] Georga Tech Reearch Corporaton, GVN' 10 WWW uer urvey, 1998, avalale at http://www.cc.gatech.edu/gvu/uer_urvey/urvey- 1998-10/graph/ue/q0.htm. [4] G. Roton, S. Savage, and D. Waldman, Houehold demand for roadand Internet ervce, Fnal report to e Broadand.gov Tak Force Federal Communcaton Common, Fe. 3, 010. [5] Burtmeda.com, Onlne vdeo content & advertng vdeo preference, hat and acton n Q4 011, Oct. 011, avalale at http://www.urtmeda.com/pdf/urt_meda_onlne_nght_011_11. pdf. [6] Unted State Cenu Bureau, Money ncome of houehold, 009, 009, avalale at http://www.cenu.gov/compenda/tata/01/tale/10690.pdf [7] CCS Leed Network Soluton, UK leaed lne prcng, http://www.uk-leaed-lne.co.uk/prce.html, acceed Apr.30 01. 9