Charging the Internet Without Bandwidth Reservation: An Overview and Bibliography of Mathematical Approaches

Transcription

1 JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 9, -xxx (2003) Chagng the Intenet Wthout Bandwdth Resevaton: An Ovevew and Bblogaphy of Mathematcal Appoaches IRISA-INRIA Campus Unvestae de Beauleu Rennes Cedex, Fance E-mal: Pcng s one of the bggest challenges facng the next geneaton of the Intenet. Even f flat ate pcng s one of the man easons fo the success of the Intenet, the only way to pevent netwok congeston and to dffeentate sevces s to adopt usage-based pcng schemes. We evew n ths pape, fom a mathematcal modelng pont of vew, the pcng schemes wthout esouce esevaton that have been developed n the lteatue. Indeed, an advantage of the absence of esevaton n the Intenet s that netwok management s cheap. Even f accountng and bllng wll ncease ths cost, we beleve that pcng wthout esouce esevaton s the lesse of two evls when costly bandwdth esevaton pocedues ae appled. Keywods: faness, ntenet economcs, optmzaton, pcng, sevce dffeentaton. INTRODUCTION The Intenet s expeencng temendous taffc gowth. A consequence s that eal uses complan that lage data tansfes take too long and that they have no way to mpove ths stuaton by themselves (by payng moe, fo nstance). To cope wth ths congeston, t s possble to develop lnk capactes, but many authos consde that ths s not a vable soluton as the netwok must espond to nceasng demand (and expeence has shown that the demand fo bandwdth has always been ahead of the supply), especally now that the Intenet s becomng a commecal netwok. Futhemoe, ncentves to acheve fa utlzaton between customes s not ncluded n the cuent Intenet (see, fo nstance, [, 2]). Fo these easons, t s suggested that the cuent flat ate fees, whee customes pay a subscpton fee and obtan unlmted usage, be eplaced by usage-based fees [3]. Also, the futue Intenet wll supply dffeent knds of sevces, such as vdeo, voce, emal, ftp, telnet, and html among othes. Each of these applcatons eques a dffeent qualty of sevce (QoS): fo example, vdeo needs vey small delays and packet losses, voce eques small delays but can affod some cell losses, emal can affod delay (wthn a gven bound), whle ftp needs a good aveage thoughput, and telnet benefts moe fom shot ound tp tmes. Some pcng ncentves should exst so that each use does not always need to choose the best QoS fo hs applcaton, and so that the fnal esult s fa utlzaton of bandwdth. On anothe hand, we need to be awae of the Receved Febuay 5, 2002; accepted Mach 6, Communcated by Chu-Sng Yang.

2 2 tade-off between engneeng effcency and economc effcency; ndeed, measuement, fo example, helps mpove the management of the netwok but s costly. In [4], J. Robets classfes pcng schemes n thee categoes, flat ate pcng, congeston pcng, and tansacton pcng, and studes the mpact on QoS (see also othe ntoductoy o ovevew papes [3, 5-8] and [9], whee an nteestng tme-scale methodology and classfcaton s pesented). Anothe classfcaton appoach sepaates schemes nto edge pcng schemes, whee the chage s set only at the edge of the netwok, and node-pe-node pcng schemes. Ou pape dffes fom the pevous ones n that mathematcal models ae dsplayed (when avalable). We classfy the suggestons fo futue Intenet pcng n eght dffeent famles as follows, most of them beng sub-categoes of congeston pcng n [4].. As aleady explaned, a fst goup of people (see, fo nstance, [0, ]) ae those agung that even f the numbe of customes (and the demands) s gowng quckly, the netwok capacty s also adaptng tself to the demand. Futhemoe, f the system has suvved so fa and has known such success, why should we ntoduce a costly bllng model? 2. Fo a second goup of people, ncentve pcng wll be necessay to egulate these vaous levels of qualty of sevce, and some sevces must be guaanteed. As n ATM netwoks, chagng models fo guaanteed sevces, such as voce o vdeo, should be elated to connecton acceptance contol (CAC) [2-6], esouce esevaton and effectve bandwdth theoy [7]. On the Intenet, esouce esevaton may be done usng RSVP [8]. In [9] and [20], esevaton s used and only non-guaanteed sevces ae accomplshed usng best effot technques adapted to the use s wllngness to pay. In [2], CAC and bandwdth esevaton ae appled to loss netwoks; a nce chaactestc of ths appoach s that aval ates fo each class of sevce depend on the connecton fee of the class. A dynamc pogammng method s used to obtan optmal and quas-optmal pces, and t s shown that tme-of-day pcng effcently appoxmates congeston pcng. These esults ae extended n [22] to geneal loss netwoks (non-exponental holdng tmes), and to the case whee the system has po knowledge of connecton tmes, at the aval. In [23], the pcng of elastc taffc flows s elated to outng. 3. Anothe altenatve has been suggested by A. Odlyzko n [24]. The poposal s called Pas Meto Pcng (PMP) snce t s analogous to the Pas Meto System. The netwok s decomposed nto seveal sepaate netwoks, and each netwok, wokng lke the cuent Intenet, has a dffeent connecton fee so that we expect that the most expensve netwoks wll not be less congested. Thus, no QoS s guaanteed, but the model can be easly mplemented wthout huge ovehead. 4. The Cumulus Pcng Scheme (CPS) [25, 26] s also a smple possblty. A contact s negotated between the ISP and the use. Dung peods of tme, the utlsaton s measued, and (postve o negatve) cumulus ponts ae awaded, dependng on whethe the contact s satsfed o not. At a gven tme, exta-fees can be chaged. 5. Anothe goup suggests usng poty pcng, wthout esevaton of esouces (see [27-32] and the efeences theen). Each class s assgned a poty numbe and s seved accodng to ths polcy at each node of the netwok. Poty pcng schemes ae dvded nto two sub-classes:

3 CHARGING THE INTERNET 3 (a) The fst one s posted poty pcng, whee each poty class pce s establshed n advance. In [27], each custome s assgned a quota fo hgh poty packets (followng hs contact), and f hs quota s exceeded, he s chaged a penalty the followng month. In [28], a poty flag s assgned to each packet accodng to the type of sevce, but so s a eject flag fo sevces whch can bea some losses. In [33-35], a dscete tme model s descbed, whee the tme s dvded nto tme slots. Optmal pces ae computed n ode to maxmze the netwok benefts. (b) The second sub-class s non-posted poty pcng, whee the pce of the packet class depends on the taffc level. In [30], an adaptve poty pcng scheme that depends on the context (smla to the pncples gven n [36]) s used. In [32, 37], an optmal ncentve-compatble pcng scheme fo the M/M/ mult-class queue s studed (note that the esult can be easly extended to the M/G/ queue). 6. Bddng fo poty has also been poposed n [38, 39]. The use makes a bd fo each packet, and only bds geate than some cutoff values ae admtted. In [40-42], auctons fo packets ae eplaced by auctons fo bandwdth dung specfc ntevals of tme to educe the management ovehead. Effcency, stablty and faness ssues ae solved not only n the case of one node, but also n the case of nteconnected netwoks. 7. Anothe scheme s the expected capacty theoy developed by Clak [43], whee packets ae flagged n o out and ae seved wthout poty except n the case of congeston, whee out packets eceve a congeston pushback. 8. A last goup of pcng schemes employs chagng fo elastc taffc based on tansfe ates (see also [44]). In Kelly et al. s wok [, 45], the use decdes on hs payment and eceves as the tansmsson ate what the netwok allocates to hm. In Low et al. s wok [2, 46-49], the use decdes hs own ate and pay fo t accodng to the pce computed by the netwok. A vaant of Kelly et al. s wok has been gven by La and Ananthaam n [50, 5], whee the flow ates ae actually contolled by the wndow-based algothm of TCP connectons. A vast lteatue has focused n ecent yeas on the futue Intenet and on the ntegaton of dffeent sevces [24, 27-30, 43, 52-55] as well as on the faness ssue (see, fo nstance, [56-60]). Whch of the dffeent chagng goups wll be mplemented and how pomnent they wll be n pactce can only be guessed. As stated n [30], we beleve that the aguments n favo of smply ovepovsonng the capacty of the Intenet s dangeous n the cuent stuaton. Moeove, capacty esevaton fo some types of sevces s expensve to mplement. We ae, theefoe, bettng that the next pcng scheme wll be pcng wthout bandwdth esevaton. The am of ths pape s to evew cuent woks (and when possble, the mathematcal models) on pcng wthout bandwdth esevaton theoy (fom 3 to 8 n the pevous classfcaton). 2. PARIS METRO PRICING [24] The poposal n [24] s to patton a netwok nto seveal logcally sepaate netwoks (o classes), each havng a fxed facton of the capacty of the ente netwok. All

4 4 netwoks would oute packets accodng to the cuent TCP and UDP. Thee s no fomal guaantee of QoS, but by chagng dffeent ates fo dffeent classes (seved n the same way), t s supposed that the most expensve classes wll be less congested as a esult of self-egulaton and wll then delve bette QoS. The name gven to ths model, Pas Meto Pcng (PMP), s based on the Pas Meto of about 20 yeas ago, whee two classes of cas exsted n tans, but wth exactly the same qualty of seats. As tckets pces wee dffeent, the cas fo the most expensve class wee less congested leadng to bette peceved QoS. The advantage of PMP ponted out by Odlyzko s that, even f no QoS s guaanteed, t would pemt dspensng wth measues, such as RSVP and the complexty, and would etan the smple and cheape cuent model of the Intenet. It s suggested that only a few (3 o 4) subnetwoks would be mplemented to mnmze losses due to not aggegatng all the taffc. PMP chages would be assessed on each packet, and would pobably consst of a fxed chage pe packet and a fee dependng on the sze of the packet. Recently, n [6], Gbbens et al. studed PMP n the case of two Intenet sevce povdes (ISP) competng to maxmze the pofts. In the pape, a use jons the netwok whch maxmzes hs utlty U(θ, ) = V θq /C p, whee V s the postve valuaton of the use, θ s hs pefeence fo lack of congeston (θ s assumed to follow a unfom dstbuton n [0, ]), Q /C s the mass of uses dvded by the capacty (at netwok ),.e., the measue of congeston, and p s the pce pe unt tme chaged by netwok. Netwok then tes to maxmze ts beneft p Q. It s shown that, at the stable pont, the ISP wll not povde multple sevces. By then, they state that PMP may not suvve unde competton (at least f the system follows the gven assumptons). 3. THE CUMULUS PRICING SCHEME (CPS) [25, 26] Lke PMP, CPS s nteestng due to ts mplementaton smplcty. In ths scheme, the use negotates wth the ISP a gven level of utlzaton o a gven QoS dung a peod of tme. Say, fo nstance, that the contact s based on the numbe of packets sent. If ths numbe s V(t) at tme t and s measued between peod [t -, t ], the esultng ove o unde-utlzaton s = t t V ( t) dt x( t t ) wth espect to the expected mean use x pe unt of tme. Defne the thesholds θ n (n = N,, N) such that θ < θ j f < j, and let θ 0 = 0. Also, let θ -(N+) =, and let θ (N+) =. c cumulus ponts (postve o negatve) ae assgned by the ISP to the use dung peod [t -, t ] f θ c < θ c +. n Let Λ n = c = be the sum of the cumulus ponts assgned to the use dung [0, t n ]. The ISP eacts and enegotates the contact f Λ n Θ. The taff functon p(x) pe unt at sevce level x has to be detemned (the total chage s c(x) = xp(x)). Fo convenence, p(x) wll also be used fo exta-fees: f the obseved sevce level s x, the penalty chage s

5 CHARGING THE INTERNET 5 Ψ(x, x ) = c(x ) (c(x) + c(x x)). The followng equements ae nseted n ode to obtan a fa scheme:. p(x) > 0 s monotoncally deceasng; c(x) s monotoncally nceasng. 2. Ψ(x, x ) < 0 f x x, and Ψ(x, x ) = 0 f x = x, so that, due to the penalty chage, the use has an ncentve to ndcate hs tue sevce level equement. Ψ(x, x + δ) s deceasng n δ. 3. Ψ(x, x ) < Ψ(βx, βx ) β Ψ(x, x ) fo β >, meanng that the penalty s hghe fo hgh bandwdths, but smalle popotonally fo the expected ones. Fo nstance, p ( x) = C / x fulflls these equements. It s suggested that no moe than 3-5 thesholds be used. Moeove, the numbe of assgned cumulus ponts should be ndependent of the measuement technque fo detemnng x. Assumng that the stochastc pocess V(t) s n equlbum, and pefomng N ndependent measuements dung each nteval [t -, t ], a confdence nteval of E(V) can be obtaned usng Student dstbuton, at confdence level α, by a standad Monte Calo method. Let ε α,n be the half wdth of the nteval. Then takng θ + θ >2ε α,n wll ensue that, wth pobablty at least α, the numbe of assgned cumulus ponts s not senstve to the measuement technque. 4. Wok by Bohn et al. [27] 4. POSTED PRIORITY PRICING In the wok, Bohn et al. use the 3-bt pecedence feld n the potocol heade to ntoduce potes (fom 0, the lowest, to 7, the hghest) n the taffc as was magned (but not publczed) n the md-80s when the NSFNET backbone was hghly congested. Ths scheme was poposed n [27] as an ntem soluton befoe the Intenet was edesgned to ncopoate potocols wth bandwdth esevaton, but t s woth studyng. Intenet Sevce Povdes negotate wth uses some soft quotas fo the total volume of taffc by specfc IP Pecedence levels: a quota system s ntoduced to dscouage uses fom settng hgh pecedence values thoughout the taffc. Anothe soluton s to buy a total quota whch s a weghted sum of the poty values n ts packets pe unt of tme. They suggest the fomula 6 x = 2 2 Q = α, whee Q s the total quota used by the costume, x s the numbe of packets sent wth poty dung the meteed peod, and α s a paamete geate than (they popose α = 2). Poty levels 0 and ae not consdeed n the fomula because they ae fee, and poty level 7 s eseved fo netwok management. Ths scheme s not dectly elated to pcng, but a pcng scheme can be devsed by the ISP. It can also be seen as a chagng scheme somewhee between the pevous CPS and the next posted poty pcng.

6 6 4.2 Wok by Cocch et al. [28, 29] Ths wok also used the 3-bt pecedence feld n the potocol heade to ntoduce potes. The model s as follows. Let s denote a chaactezaton of the netwok sevce eceved by the th use ( n), and let V (s ) denote the th use s level of satsfacton, expessed n money, wth a gven netwok sevce s (we wll gve some examples late). If the use s chaged an amount c fo that sevce, the oveall level of satsfacton s U = V (s ) c. Each use sends a equest σ (not necessaly nvolvng a call set-up). Let σ = (σ,., σ n ), and let s (σ) be the esultng netwok sevce. Defne n max σ = agmaxσ V = ( s ( σ )) and V max = n = V ( s ( σ as, espectvely, the vecto maxmzng the total satsfacton and the maxmum total satsfacton. As each use s actng selfshly,.e., s tyng to maxmze hs own satsfacton U (s (σ)) = V (s (σ)) c (σ), the system needs to be n Nash equlbum. Fomally, σ s a Nash equlbum f fo all and all ~σ, U (σ) U (σ ~ σ ), whee (σ ~ σ ) s the vecto whee the th coodnate of σ s eplaced by ~ σ. Ths means that use can not alone ncease hs level of satsfacton. A pcng scheme s then sad to be acceptable f σ max s the unque Nash equlbum scheme. It can be easly seen that wthout a pcng scheme,.e., c (σ) = 0, the Nash equlbum s unlkely to be acheved. The scheme s then llustated by means of examples. In [29], a smple two-class model s smulated on two dffeent netwok topologes. The two dffeent classes have dffeent sevce potes at each swtch (o node) of the netwok. Pe-byte pcng s used wth a hghe pce fo the hghest poty. The applcatons consdeed ae e-mal, FTP, Telnet and Voce. The dffeent functons, V, followng the equed QoS, ae V emal = -0. (avg. message delay (sec)) -(% of messages not delveed n loose delay of 5 mnutes), V FTP = 00 (aveage nomalzed thoughput), V Telnet = -(avg. packet ound tp tme (ms))/0, V Voce = -(% of packets not obeyng the tght delay of 00ms)-d/00, whee d s the aveage one-way delay of voce packets (n ms). The equests σ ae meely the poty settngs on the packets. In the mplementaton, each patcula applcaton s assumed to use the same poty settngs. The ange of acceptable pces s gven accodng to the topology of the netwok, but some exst fo a wde ange of netwok condtons. In [28], the same knd of example s used, but n addton to the two sevce potes, thee s a blockng poty, esultng n 4 dffeent classes. Ths stuaton s nteestng, fo some applcatons eque small delays but can affod losses o, convesely, eque no o vey few losses but can affod delays. We then have fou pces pe byte p,j, 0, j, whee the fst bt means that the sevce poty flag s on o off and j gves the status of the no-dop flag. max ))

7 CHARGING THE INTERNET Wok by Hong and Stegltz [3] In ths model, K uses ae assumed to compete fo a esouce (possbly at the gateway of a netwok o dectly at a swtch, fo nstance) fo the same type of taffc, meanng the same type of QoS. Use k wshes to send packets at ate λ k, so that the total ate s Λ = actve k λ k. The QoS pecepton s gven by a functon D(Λ). In [3], the delay epesents the QoS, but othe measues can be consdeed. A utlty functon u k (δ) s assocated wth use k, dependng on the obseved QoS δ. If the pce pe packet s P, use k tansmts hs packets f and only f u k (δ) P. In equlbum, the QoS announced by the netwok must be what the use obseves; that s, the followng fxed-pont equaton must be satsfed: D k : uk ( δ ) P λ k = δ. Unde some assumptons (u k monotoncally deceasng and wth lmt 0 at + and D stctly postve, fnte, contnuous, and monotoncally nceasng), t can be poved that thee s a unque equlbum fo each pce P. The dea s then to choose the pce P that maxmzes the evenue R = PΛ. Some examples ae povded. As extensons, multple potes and tme of day pcng ae dscussed. 4.4 Wok by Mabach [33-35] Ths wok s devoted to DffSev, whee packet classes ae seved accodng to a gven poty. Pces pe sent-packet ae statc. Indeed, t s agued that, by chagng fo all submtted packets, uses have an ncentve to educe the ates dung peods of congeston, as they pay fo lost packets. The mathematcal model consdes a sngle lnk and s as follows. Tme s dscetzed, dvded nto slots. Dung each slot, the lnk has the ablty the seve C packets. It s assumed that packets not seved when the slot s lost. Thee ae N dffeent (and odeed) poty classes, whee s the lowest poty. R uses ae supposed to compete fo lnk access. Let u be the pce chaged fo a class- packet submtted fo access (of couse, u < u j f < j), and let d () be the numbe of class- packets that use submts n a gven tme slot. Use s whole allocaton s gven by the vecto d = (d (),, d (N)). R The numbe of submtted class- packets s d( ) = d = ( ), and d = (d(),, d(n)) s the aggegated allocaton. Let N N be the poty class such that d ( ) < C and = + d( ) C. Packets = wth poty > ae seved (say, wth pobablty P t (, d) = ), those wth poty < ae lost (say, wth pobablty P t (, d) = 0) and those of class ae seved wth pobablty t P (, d) = N ( C d ( )) = + d ( ) Use s thoughput s then.

8 8 x = N = d ( ) P t (, d). A utlty functon U (x ) s assocated wth use. U s assumed to be nceasng, bounded, stctly concave and twce dffeentable. Uses ae assumed to play a non-coopeatve game, whee use chooses allocaton d such that d N = agmax d U ( ) x d = ( ) u. In equlbum, ths happens fo all uses. If we suppose wthout loss of genealty that the total demand at pce u, D(u ), exceeds C, and that D(u ) > 0, then thee exsts an equlbum. If thee s a class 0 such that D(u 0 ) > C > D(u 0 +), then the equlbum s unque. d ( ) = 0 { 0, 0 + }; P t ( 0, d ) u 0 /u 0 +, whee u N+ = max U' (0); and x = D (u ) wth u = u 0 /P t ( 0, d ). In [35], the game s played dynamcally. A gadent algothm s used to pevent oscllatons. In [33], the model s extended to busty taffc. 5. NON-POSTED PRIORITY PRICING 5. Woks by Mendelson and Whang [32], and by Ha [37] The woks descbed hee wee not dedcated to Intenet management. Howeve, even f some ponts ae not elated to ou concen, they ae woth studyng. Mendelson and Whang consde a pcng scheme fo a mult-class M/M/ queue (whch can be easly extended to a M/G/ queue f all job classes have the same coeffcent of vaaton). Avals of class- jobs ( R) to the system eflect the aggegaton of nfntesmal uses job flow. The aval ate s λ. The value functon of class- jobs V (λ ), epesentng the goss value ganed by class- uses pe unt of tme, s assumed to be dffeentable, nondeceasng and concave on λ. λ and the full pce z ae elated n the followng way: λ = D (z) = ( F (z))λ, whee Λ s the maxmum potental aval ate of class and F () s the dstbuton functon of the sevce valuaton. Invetng ths functon, we have V ( λ ) = D ( λ ). Let λ = (λ,, λ R ). The total expected value functon s V ( λ ) = R = V ( λ ). Each class- job s chaactezed by a delay cost of v pe unt of tme. Class- jobs ae assumed to be seved followng an exponental dstbuton wth mean c, and the poty polcy of the seve s assumed to be non-peemptve. It s also assumed, wthout loss of genealty, that the classes ae odeed fom hghest to lowest poty so that the expected aveage delay cost pe unt tme s mnmzed,.e.,

9 CHARGING THE INTERNET 9 v v2 vr L. c c2 cr The dea s to maxmze the expected net value of the jobs pocessed by the system,.e. to fnd R max ( ) ( ), V λ v L λ λ = () whee L s the mean numbe of class- jobs n the system n steady-state. The admnstato sets the pce vecto p = (p,, p R ), whee p s the pce chaged to a class- job. If the class- demand elatonshp (whch s set such that, at equlbum, the magnal value wll be the same fo jonng and o not jonng the system) s V '(λ) = p + v W (λ), then t s poved n [32] that the optmal pce pe class- job s gven by p = R j= DW ( ) j λ u jλ j, Dλ whee W j s the expected delay of a class-j job and λ maxmzes (). λsr In the homogeneous case,.e., c = = c R, we have L ( λ) = + λ S S and S R W ( λ ) = +, whee S S S 0 = 0, S = and. λ j j S = S = We can then explctly get the optmal pces: p = q R k vk λ S S k= k k + R k= k vk λ W q k + λ S k+ k v k+ whee W k = W k s the expected watng tme of a class-k job n the queue and q λ R+ = vr+ = WR+ = 0. The poblem hee s that the pces ae detemned on a centalzed bass, whch s pactcally elevant. Moe specfcally, both the uses and system admnstato know (v, V, c ), but only the uses know the eal class membeshp. To cope wth ths poblem, Mendelson and Whang consde poty-dependent pcng schemes. The dea s to obtan a Nash equlbum,.e., a stuaton whee no use, by unlateally changng hs own equest, can ncease hs own net value. Ths popety s decomposed n ncentve-compatblty, whch means that t s n all uses nteest to classfy the jobs accodng to the coect poty classes, and optmalty, whch means that the esultng aval ates maxmze the expected net value of the system as a whole. Optmalty and ncentve-compatblty ae obtaned when the optmal pces ae used n the homogeneous case and when a class- use decdes not to ente the system f mn {0, p + v W ( λ ( p)) V ( λ )} = 0 j R j and to jon the system othewse. j ' W q k+,

10 0 Unfotunately, ncentve-compatblty s not vald n the heteogeneous case. The pevous posted chagng mechansm should take nto account addtonal nfomaton, such as the actual pocessng tme of the job. We then have a poty and tme-dependent pcng scheme. If we have wth p (t) = A t + (/2)Bt 2 and B = R S v kλk S k= k k a A = S 2 S + R k k= + a S 2 k S k + S 2 k S k, = 2 whee a = vλ c, k k λk then the pcng scheme s optmal and ncentvecompatble. Note that t conssts of a basc chage (coespondng to the lowest poty chage) and a poty suchage (popotonal to the pocessng tme). In [37], A.Y. Ha extends the pevous wok to the case whee sevce equements ae contollable by customes. Then, each custome decdes whethe to equest sevce fom the faclty and, f t s desable, detemnes hs sevce equement. Also nvestgated s the case of the M/G/s pocesso shang queue, fo whch the optmal pces ae found to be two-pats lnea n tme n the system. The fst-come-fst seved M/G/ queue s also studed, and a quadatc pce s also obtaned. 5.2 Wok by Gupta et al. In [30, 62], Gupta, Stahl and Whnston also develop a poty pcng scheme. They fst ague that the posted poty pcng scheme of Bohn et al. may lack an ncentve to povde multple pecedence netwoks (.e., the povdes may not be appopately ewaded), and they pont out that we must look at the context n whch the applcatons ae used, not just categoze them. In [30], a fou poty class model s ntoduced, whee the hghest poty s fo eal-tme sevces wth no toleance of lost packets, the second class s fo eal-tme sevces that ae elatvely toleant to lost packets and the two lowest poty classes fo two levels of best effot sevce (to povde a fne dvson of delay equements). In [62], the numbe of classes s kept geneal. The pce at a patcula seve fo a patcula class s epesented by the followng system of equatons: whee mk ( q) ] D Ω l / DX ] δ j xjlm, (2) mkq = l j

11 CHARGING THE INTERNET mk (q) s the pce of a job of sze q at seve m fo poty class k, X mkq s the aval ate of job of sze q at seve m n poty class k, Ω l s a contnuously dffeentable, stctly nceasng functon of the aval ate X mkq and capacty v m whch povdes the watng tme at a seve m fo poty class l, δ j s the delay cost paamete of consume fo sevce j, x jlm s the flow ate of sevce j fo consume wth poty k at seve m. ]DΩ l /DX mkq ] s the devatve of the watng tme, and j δ j x jlm s the accumulated delay cost of the system. Ths knd of poty pcng pevents the stuaton whee the hghest poty can peempt all the avalable capacty (as noted n [43]) n the case of posted poty of pevous subsectons. In [62], a geneal mathematcal model s ntoduced, and t s shown that ths choce maxmzes a system-wde welfae stochastc allocaton functon. The pces ae computed usng the followng teatve equaton: t+ mk whee t + = αˆ mk + ( α) t, mk α s a eal numbe between 0 and ; the authos suggest takng α = 0.; ˆ mk t+ s the estmated new pce at tme t + usng Eq. (2); s the mplemented pce dung the tme nteval (t, t + ). t mk Many expements wee pefomed usng a smulaton platfom. 6. SMART MARKET: AUCTION IN THE NETWORK 6. Smat Maket of McKe-Mason and Vaan [38, 39] In the pape on the hstoy of the Intenet, cost and pcng [38], McKe-Mason and Vaan ague that posted poty pcng as descbed n secton 4 s not a good soluton. Indeed, f the netwok s at capacty, some uses wth hgh wllngness-to-pay may be unable to access the netwok. Pcng based on the tme of day attempts to acheve ths goal but does not effcently allocate the avalable bandwdth. McKe-Mason and Vaan suggest the use of a smat maket, whch s actually a vaaton of the Vckey aucton. Each packet s gven a bd epesentng the use s wllngness to pay. The packets ae gven a poty at each node of the netwok accodng to ths bd. Usng the Vckey aucton, f the netwok s not congested, the pce s zeo wheeas f thee s congeston, the chage s based on the wllngness-to-pay of the lowest poty packet admtted. Unfotunately, the smat maket concept s not an deal soluton. As noted n [38], the cuent TCP/IP veson would not suppot a smat maket. Moeove, t eques the use of complcated systems to conduct auctons fo ndvdual packets. The model was moe an ncentve fo futhe eseach than a soluton.

12 2 6.2 Pogessve Second Pce (PSP) Aucton In [40-42, 63, 64], costly auctons fo ndvdual packets ae eplaced wth auctons fo bandwdth dung specfc ntevals of tme. A good analyss of ths scheme based on game theoy s povded, ncludng faness popetes. As stated n [4], n maket-based appoaches, no pecse model need be assumed [...], the selle does not eque a po demand nfomaton. The behavo of the system s then essentally eal-tme, and not model-based. To befly explan how ths aucton woks, consde a sngle esouce of capacty Q and I playes competng fo t. Playe s bd s s = (q, p ), whee q s the capacty the playe s lookng fo and p s the unt pce he s poposng. A bd pofle s s = (s,, s I ). Let s - = (s,, s -, s +,, s I ) be the pofle whee playe s bd s excluded fom the game. Fo y 0, defne Q ( y; s ) = Q qk, pk y k +. The pogessve second pce allocaton ule gves to playe a bandwdth of a (s) = mn(q, Q (p ; s - )) and sets the total cost to be c ( s) = p j[ a j (0; s ) a j ( s ; s )]. j Thus, the hghest bds ae allocated the desed quantty, and the cost s gven by the declaed wllngness to pay (bds) of the uses who ae excluded by s pesence. Assume that playe attempts to maxmze hs utlty u (s) = θ (a (s)) c (s), whee θ s the valuaton functon that playe gves to hs allocaton. Unde some smoothness assumptons on θ and wth a bd fee ε each tme a playe submts a bd, t s stated that f fo all playe bds (v, w = θ (v )) wth ' ' v = sup z : z Q ( θ ( v ), s ) and p j[ a j (0; s ) a j ( z; s )] b ε / θ (0), j whee Q (y; s - ) = [Q pk >y,k q k ] + and b s the budget constant, then convegence, effcency and faness poblems ae solved (the popety n [64] of the equal-bd case (when the total equed bandwdth at ths unt pce s not avalable) does not occu n the PSP scheme). The game s extended n [4, 63] to netwoked auctons, and the same popetes ae obtaned. In ths netwoked game, playes can be aw bandwdth selles, end-uses, o sevce povdes buyng and sellng bandwdth to each othe. Each playe acts n the sngle node case, that s, tes to optmze hs utlty = ( ) j u θ o e a c, whee e j s a functon called the expected bottleneck dependng on the type of playe and c j s the total cost chaged to playe by selle j. +

13 CHARGING THE INTERNET 3 In [65], smultaneous mult-unt descendng-pce auctons (o Dutch auctons) wth dffeent deceasng speeds ae used. Indeed, the authos ague that, among othe dawbacks, n the PSP aucton, each playe splts equally hs bd among lnks, whch mght not be coect (dependng on the congeston levels). The mechansm allows each use to buy the same quantty of bandwdth n all the lnks. Accodng to expemental esults, socal welfae s mpoved wth espect to PSP. In [66], two new aucton schemes ae desgned: the delta aucton, whch allows bds to take place contnuously n ode to pevent addtve setup delays (at each node), and the Connecton-Holde-s-Pefeed-Scheme (CHPS), based on the RSVP potocol, whee holdes of aleady unnng connectons ae pefeed and ae gven a second chance f the actual bds ae exceeded by new ones. 7. EXPECTED CAPACITY [43] In [43], Clak also dscusses how to chage the Intenet. Lke many authos, he examnes moe ssues than he solves. One of hs ponts about poty pcng s the followng: the effect of poty queung s to buld up a queue of lowe-poty packets whch wll cause packets n ths class to be pefeentally dopped due to queue oveflow. Whle dopped packets wll be etansmtted, the ate adaptaton of TCP tanslates these losses nto a educton n sendng packets fo these flows of packets. Moeove he says that thee s no obvous way to elate a patcula poty to a patcula acheved sevce. He then ntoduces hs noton of expected capacty. The mechansm woks as follows. At the netwok access, packets ae flagged (n o out) dependng on whethe the ncomng steam s nsde o outsde of the pofle of the expected capacty (wthout any taffc shapng). When thee s a pont of congeston, out-tagged packets eceve a congeston pushback notfcaton (doppng o explct congeston notfcaton (ECN)). Dung peods of congeston, each sende executes a TCP algothm whch eceves a congeston ndcaton when t exceeds ts expected capacty and stats to send packets that ae flagged out. As noted n [43], ths scheme can also be mplemented n a heteogeneous netwok of mult-povde Intenets, whee coopeatng goups of povdes make contacts to cay each othe's taffc; when too many packets ae maked accodng to the contact, they can be shfted out, o they can be chaged accodng to some fomula. Some dynamc taggng can also be mplemented as s done n the case of smat makets by McKe-Mason and Vaan. Unfotunately, some poblems need to be solved befoe ths scheme can be mplemented effcently. Fst, dependng on the applcaton, the custome can be the sende o the eceve. The scheme pevously descbed woks f the custome s the sende. If he s the eceve, thee s a need to desgn a complex potocol by means of whch the sende s nfomed of the expected capacty contact, whch can be also qute complex (to mantan flexblty of contacts). Second, what about multcast when each eceve has a dffeent expected capacty?

14 4 8. CHARGING FOR ELASTIC TRAFFIC BASED ON THE TRANSFER RATE [, 2, 45, 46, 48] 8. Wok by Kelly et al. The model pesented hee make t possble to combne dffeent elastc taffc [, 36, 45], whee the ates ae popotonal to the wllngness of each use to pay. The model s as follows. Consde a set of J esouces wth a capacty of C j fo esouce j. A oute s a non-empty subset of J, and R s the set of possble outes. Let A j = f j and 0 othewse, and defne A as A = (A j ). If each oute s assocated wth a use, let U (x ) be the utlty functon of the use when the flow ate s x fo use. U s assumed to be an nceasng, stctly concave and contnuously dffeentable functon. Let U = (U (.), R) and C = (C j, j J). Fom the system pont of vew, the dea s to maxmze R U ( ) (3) x subject to Ax C and x 0. Fom the use pont of vew, the dea s to maxmze w ( ) U w (4) λ ove w 0; hee, the flow ate s x = w λ, whee w s the amount that use s wllng to pay pe unt of tme and λ s the chage pe unt of flow and unt of tme fo use. Assume that the netwok knows w = (w, R) and attempts to maxmze R w log (5) x subject to Ax C and x 0. Ths last assumpton s vey convenent because t makes t possble to compute optmal flow ates vey easly. Indeed, t s shown n [, 36, 45] that thee always exst vectos λ, w and x satsfyng w = x /λ R such that w maxmzes (4), x maxmzes (5) and x s the unque soluton maxmzng (3). It s also shown that the vecto of ates x pe unt chage s popotonally fa; that s, f x 0 and Ax C, and fo any othe feasble vecto x, the aggegate popotonal change s zeo o negatve: R w x x x 0. Even f solvng ths poblem s mathematcally tactable, the maxmzaton of (5) needs to be done on a centalzed bass, whch s ndesable. In the followng, how to poceed on a decentalzed bass s explaned. Consde the system of dffeental equatons d dt x ( ) ( ) ( ) ( ) t = K w, t x t µ j t (6) j

15 CHARGING THE INTERNET 5 whee µ j ( t) = p j s: j s x s ( t) s the shadow pce pe unt flow though j and p j (t) s the devatve of the ate at whch a cost n ncued at esouce j when the load though t s y. The motvaton behnd these equatons s as follows. If esouce j geneates a contnuous steam of feedback sgnal at ate yp j (y) when the total flow though esouce j s y; then that esouce j sends a popoton x /y of these feedback sgnals to a use wth a flow of ate x though esouce j; and that use vews each feedback sgnal as a congeston ndcaton equng some educton of flow x. It s, then, a flow-contol algothm. It s shown usng Lyapunov functons that the system of dffeental equatons has a unque value x such that x = w / j µ j abtaly closely appoxmates the optmzaton of poblem (5). Some stochastc petubatons of Eq. (6) ae also analyzed n [45]. Eq. (6) shaes seveal chaactestcs wth TCP but also pesents seveal dffeences as ponted out n []. In TCP, congeston s ndcated by dopped o maked packets. Thee ae, then, two multplcatve effects. In addton, t s shown that multple TCP can be modeled by the system of dffeental equatons 2 d m m x ( t) x = + ( t) µ j ( t) (7) dt 2 2 T T 2m j and can be vewed as actng as f the utlty functon of use s 2m actan xt, T 2 m whee T s the ound tp tme fo the connecton of use and m s a paamete whch would nte ala be multpled by m, the ate of addtve ncease, and make /2m the multplcatve decease facto n Jacobson s TCP algothm. The stable pont s then such that x m = T 2( p p ) / 2, whee p = j p j. Note that ths concluson cannot be eached when uses o the netwok have outng choces. Each custome can use ntellgent agents [67] n ode to optmze hs wllngness to pay accodng to the netwok congeston status. In [50, 5], the necessay feedback to the uses who adjust the ates s based on wndow-based congeston contol, whch s pactcally easy when connectons use TCP. The method s poved to gve optmal values. It s shown that the soluton solves the same poblem than the one of Kelly et al. Othe mplementatons of the scheme ae pesented n [68-7] whch gve some scenaos and algothms fo use adaptaton and netwok feedback sgnals fo flow contol.

16 6 8.2 Wok by Low et al. In [2, 46, 48] Low et al. study the same knd of poblem than Kelly et al. nvestgated (manly fo ABR n ATM netwoks athe than fo TCP on the Intenet), and they obtan vey smla solutons. The man dffeence s that n Low et al. s wok, uses decde on the ates and pay, wheeas n Kelly et al. s wok, uses decde on the payments and eceve what the netwok allocates. In addton, they use a decentalzed algothm to set pces accodng to changng netwok condtons. As n the pevous subsecton, we have a set L of undectonal lnks of capactes c l, l L, a set S of souces chaactezed by utlty functon U s (x x ) concave, wth an nceasng tansmsson ate x s. The system s wllng to maxmze s S U ( ) s x s ove x s subject to capacty constants. The poblem s also decomposed, and the followng synchonous algothm s used n [48]. Each lnk eceves the ates x s (t) f s s oute s though lnk l. 2. Each lnk l calculates ts pce p l (t + ) fo a unt of bandwdth (n ode to optmze the benefts obtaned) usng the gadent pojecton algothm p l (t + ) = [p l (t) + γ(x l (t) c l )] +, (8) whee γ s a stepsze. 3. Each lnk communcates p l (t + ) to each souce whose oute s though lnk l. Then, the algothm fo each souce s as follows:. Each souce s fed back the pce p s = L(s) p l whee L(s) s the set of lnks that s uses. 2. The souce then chooses then ts tansmsson ate x s (n an nteval (m s, M s )) whch maxmzes ts beneft: U s (x s ) p s (t) x s. 3. These ates x s (t + ) ae sent to the lnks whch agan calculate new pces, and so on. The algothm appoaches a pce vecto (p l, l L) that algns ndvdual and system optmalty wth faness popetes. In [46], the gadent pojecton method s eplaced wth the Newton method, whch typcally conveges much faste. Eq. (8) s, then, eplaced wth l + + l ll l p ( t ) = [ p ( t) + γ H ( t)( x ( t) c )], (9) l whee H s a Hessan matx (see [46] fo detals). In [47], the equaton s eplaced wth p ( t l l + l l l l + ) = [ p ( t) + γ ( α b ( t) + x ( t) c )], (0) whee α l s a constant and b l (t) s the buffe backlog at lnk l.

17 CHARGING THE INTERNET 7 The model s extended to the asynchonous case, whee the updates at the souces and the lnks ae not synchonzed, whch bette esembles ealty of lage netwoks. The communcaton between souces and lnks s also geatly smplfed as follows. In [2], the lnks estmate souce ates usng local nfomaton wthout omttng the optmalty popety. In [47, 72], communcaton fom lnks to souces s accomplshed usng the poposed ECN (Explct Congeston Notfcaton) bt n the IP heade. These modfcatons lead to a flow contol scheme called REM (Random Ealy Makng), a vaant of RED, and a stochastc veson of the pevous algothm: lnk l maks an avng packet wth pobablty m l (t) = Φ -p l (t) (wth Φ > ). Ths leads to m s (t) = Φ -ps(t). Invetng ths equaton, p s s s (t) s estmated by pˆ ( t) = logφ ( mˆ ( t)) whee mˆ s ( t) s the facton of maked packets (known by usual acknowledgement). The stablty, pefomance and obustness of ths veson of the algothm s studed n [73] usng a contnuous tme veson of the dynamcs. 9. CONCLUSIONS In ths pape, we have suveyed usage-based pcng schemes wthout bandwdth esevaton, wth an emphass on mathematcal models. All these schemes have the own advantages, angng fom mplementaton smplcty to faness. An nteestng poblem would be to compae (mathematcally and n pactce) the espectve costs and benefts on a smple netwok n ode to see one whch s lkely to pefom the best. Othe ssues ae also woth studyng. Fst, an nteestng aea of eseach s the pcng of Weghted Fa Queung schemes. Accodng to Clak [43], ths mechansm would only acheve local equalty nsde one swtch. Ths ases seveal questons. Fo example, n the multcast case, what does congeston along one path as to do n esponse to congeston along anothe? Ths also shows that the multcast case [74-76] needs moe attenton, whch t eceved n [77], whee pcng adaptaton based on tansfe ates s appled to multcast flows and faness popetes ae obtaned. Futhemoe, as ponted out n [78], the optmalty paadgm s not a panacea; moe attenton needs to be pad to achtectues and stuctues. REFERENCES. F. P. Kelly, Mathematcal modellng of the ntenet, n Poceedngs of the Fouth Intenatonal Congess on Industal and Appled Mathematcs, 2000, pp S. H. Low, Optmzaton flow contol wth on-lne measuement o multple paths, n Poceedngs of the 6th Intenatonal Teletaffc Congess, 999, pp P. Dolan, Intenet pcng s the end of the wold wde wat n vew? Communcatons & Stateges, Vol. 37, 2000, pp J. W. Robets, Qualty of sevce guaantees and chagng n multsevce netwoks, IEICE Tansactons on Communcatons, Vol. E8, 998, pp L. A. DaSlva, Pcng of QoS-enabled netwoks: a suvey, IEEE Communcatons Suveys & Tutoals, Vol. 3, M. Falkne, M. Devetskots, and I. Lambadas, An ovevew of pcng concepts fo boadband IP netwoks, IEEE Communcatons Suveys & Tutoals, Vol. 3, 2000.

18 8 7. T. Hendeson, J. Cowcoft, and S. Bhatt, Congeston pcng, payng you way n communcaton netwoks, IEEE Intenet Computng, Vol. 5, 200, pp B. Stlle, P. Rechl, and S. Lenen, Pcng and cost ecovey fo ntenet sevces: pactcal evew, classfcaton, and applcaton of elevant models, Netnomcs, Vol. 2, 2000, pp P. Rechl and B. Stlle, Nl nove sub sole: why ntenet chagng schemes look lke as they do, n Poceedngs of the 4th Beln Intenet Economc Wokshop, L. Anana and R. J. Solomon, Flat The mnmalst pce, Lee W. McKnght and Joseph P. Baley, ed., Intenet Economcs, MIT Pess, 997, pp A. M. Odlyzko, The cuent state and lkely evoluton of the ntenet, n Poceedngs of Globecom 99, 999, pp Z. Fan, Pcng and povsonng fo guaanteed ntenet sevces, P. Loenz, ed., Intenatonal Confeence on Netwokng 200, LNCS, Spnge-Velag, Vol. 2093, 200, pp R. J. Gbbens and F. P. Kelly, Measuement-based connecton admsson contol, n Poceedngs of the 5th Intenatonal Teletaffc Congess, 997, pp R. J. Gbbens and F. P. Kelly, Dstbuted connecton acceptance contol fo a connectonless netwok, n Poceedngs of the 6th Intenatonal Teletaffc Congess, 999, pp F. P. Kelly, P. B. Key, and S. Zachay, Dstbuted acceptance contol, IEEE Jounal on Selected Aeas n Communcatons, Vol. 8, 2000, pp D. Songhust, ed., Chagng Communcaton Netwoks: Fom Theoy to Pactce, Elseve, Amstedam, F. P. Kelly, Note on effectve bandwdths, F. P. Kelly, S. Zachay, and I. B. Zedns, ed., Stochastc Netwoks: Theoy and Applcatons, Royal Statstcal Socety Lectue Notes Sees, Oxfod Unvesty Pess, 996, Vol. 4, pp L. S. Zhang, D. Estn, S. Shenke, and D. Zappala, RSVP: a esouce ReSeVaton potocol, IEEE Netwok Magazne, 993, pp Q. Wang, J. M. Peha, and M. A. Sbu, Optmal pcng fo ntegated sevces netwoks, Lee W. McKnght and Joseph P. Baley, ed., Intenet Economcs, MIT Pess, 997, pp R. J. Gbbens, S. K. Sagood, F. P. Kelly, H. Azmoodeh, R. Macfadyen, and N. Macfadyen, An Appoach to Sevce Level Ageements fo IP netwoks wth Dffeental Sevces. 2. I. Ch. Paschalds and J. N. Tstskls, Congeston-dependent pcng of netwok sevces, IEEE/ACM Tansactons on Netwokng, Vol. 8, 2000, pp X. Ln and N. B. Shoff, Pcng-based contol of lage netwoks, S. Palazzo, ed., Evolutonay Tends of the Intenet, 200 Tyhenan Intenatonal Wokshop on Dgtal Communcatons (IWDC), LNCS, Spnge-Velag, Vol. 270, 200, pp D. Mta, K. G. Ramakshnan, and Q. Wang, Combned economc modelng and taffc engneeng: jont optmzaton of pcng and outng n mult-sevce netwoks, n Poceedngs of the 7th Intenatonal Teletaffc Congess, 200, pp A. Odlyzko, Pas meto pcng fo the ntenet, n ACM Confeence on Electonc Commece (EC 99), 999, pp

19 CHARGING THE INTERNET P. Rechl, P. Fluy, J. Geke, and B. Stlle, How to ovecome the feasblty poblem fo taffng ntenet sevces: the cumulus pcng scheme, n Poceedngs of IEEE Intenatonal Confeence on Communcatons 200, Vol. 7, 200, pp P. Rechl and B. Stlle, Edge pcng n space and tme: theoetcal and pactcal aspects of the cumulus pcng scheme, n Poceedngs of the 7th Intenatonal Teletaffc Congess, R. Bohn, H. W. Baun, K. C. Claffy, and S. Wolff, Mtgatng the comng ntenet cunch: multple sevce levels va pecedence, Jounal of Hgh Speed Netwoks, Vol. 3, 994, pp R. Cocch, D. Estn, S. Shenke, and L. Zhang, A study of poty pcng n multple sevce class netwoks, n Poceedngs of SIGCOMM 9, 99, pp R. Cocch, D. Estn, S. Shenke, and L. Zhang, Pcng n compute netwoks: motvaton, fomulaton and example, IEEE/ACM Tansactons on Netwokng, Vol., 993, pp A. Gupta, D. O. Stahl, and A. B. Whnston, Poty pcng of ntegated sevces netwoks, L. W. McKnght and J. P. Baley, ed., Intenet Economcs, MIT Pess, 997, pp M. L. Hong and K. Stegltz, Usage-based pcng of packet data geneated by a heteogeneous use populaton, n Poceedngs of IEEE INFOCOM 95, 995, pp H. Mendelson and S. Whang, Optmal ncentve-compatble poty pcng fo the M/M/ queue, Opeatons Reseach, Vol. 38, 990, pp P. Mabach, Pcng dffeentated sevces netwoks: busty taffc, n Poceedngs of IEEE INFOCOM 200, 200, pp P. Mabach, The ole of pcng n dffeentated sevces netwoks, Techncal Repot CSRG-42, Dept. of Compute Scence, Unvesty of Toonto, P. Mabach, Dffeentated sevces netwoks: pcng and softwae agents, Techncal Repot CSRG-422, Dept. of Compute Scence, Unvesty of Toonto, F. P. Kelly, Chagng and ate contol fo elastc taffc, Euopean Tansactons on Telecommuncatons, 997, Vol. 8, pp A. Y. Ha, Optmal pcng that coodnates queues wth custome-chosen sevce equements, Management Scence, Vol. 47, 200, pp J. K. McKe-Mason and H. R. Vaan, Some economcs of the ntenet, Techncal epot, No. 940, Unvesty of Mchgan, Novembe 993; /eps/comp/papes:940/94000.pdf. 39. J. K. McKe-Mason and H. R. Vaan, Pcng congestble netwok esouces, IEEE Jounal on Selected Aeas n Communcatons, Vol. 3, 995, pp A. A. Laza and N. Semet, Desgn and analyss of the pogessve second pce aucton fo netwok bandwdth shang, to appea n Telecommuncaton Systems, Vol. 3, 200; 4. N. Semet, Maket mechansms fo netwok esouce shang, PhD thess, Dept. of Compute Scence, Columba Unvesty, N. Semet, R. R.-F. Lao, A. T. Campbell, and A. A. Laza, Maket pcng of dffeentated ntenet sevces, n Poceedngs of the 7th Intenatonal Wokshop on Qualty of Sevce, 999, pp

20 D. D. Clak, Intenet cost allocaton and pcng, n L. W. McKnght and J. P. Baley, ed., Intenet Economcs, MIT Pess, 977, pp H. Yaïche, R. R. Mazumda, and C. Rosenbeg, A game theoetc famewok fo bandwdth allocaton and pcng n boadband netwoks, IEEE/ACM Tansactons on Netwokng, Vol. 8, 2000, pp F. P. Kelly, A. K. Mauloo, and D. K. H. Tan, Rate contol n communcaton netwoks: shadow pces, popotonal faness and stablty, Jounal of the Opeatonal Reseach Socety, Vol. 49, 998, pp S. Athualya and S. H. Low, Optmzaton flow contol wth Newton-lke algothm, Telecommuncaton Systems, Vol. 3, 2000, pp S. Athualya and S. H. Low, Optmzaton flow contol, II: mplementaton, Techncal Repot, Net Lab., Calfona Insttute of Technology, S. H. Low and D. E. Lapsley, Optmzaton flow contol, I: basc algothm and convegence, IEEE/ACM Tansactons on Netwokng, Vol. 7, 999, pp S. H. Low, F. Pagann, and J. C. Doyle, Intenet congeston contol, IEEE Contol Systems Magazne, Vol. 22, 2002, pp R. J. La and V. Ananthaam, Chage-senstve TCP and ate contol n the ntenet, n Poceedngs of IEEE INFOCOM 2000, 2000, pp R. J. La and V. Ananthaam, Wndow-based contol wth heteogeneous uses, n Poceedngs of IEEE INFOCOM 200, 200, pp R. J. Gbbens and F. P. Kelly, Resouce pcng and the evoluton of congeston contol, Automatca, Vol. 35, 999, pp D. Hazlett, An ntem economc soluton to ntenet congeston, Socal Scence Compute Revew, Vol. 5, 997, pp F. P. Kelly, Models fo a self-managed ntenet, Phlosophcal Tansactons of the Royal Socety, Vol. A358, 2000, pp S. Shenke, Sevce models and pcng polces fo an ntegated sevces ntenet, n Pefomance of Publc Access to the Intenet, 993, pp T. Bonald and L. Massoulé, Impact of faness on ntenet pefomance, n Poceedngs of ACM Sgmetcs 200, 200, pp L. Massoulé and J. Robets, Aguments n favou of admsson contol fo TCP flows, n Poceedngs of the 6th Intenatonal Teletaffc Congess, 999, pp L. Massoulé and J. Robets, Bandwdth shang: objectves and algothms, n Poceedngs of IEEE INFOCOM 99, 999, pp J. Mo and J. Waland, Fa end-to-end wndow-based congeston contol, n Poceedngs of SPIE 98, 998, pp J. W. Robets and L. Massoulé, Bandwdth shang and admsson contol fo elastc taffc, Telecommuncaton Systems, Vol. 5, 2000, pp R. Gbbens, R. Mason, and R. Stenbeg, Intenet sevce classes unde competton, IEEE Jounal on Selected Aeas n Communcatons, Vol. 8, 2000, pp A. Gupta, D. O. Stahl, and A. B. Whnston, A stochastc equlbum model of ntenet pcng, Jounal of Economc Dynamcs and Contol, Vol. 2, 997, pp N. Semet, R. R.-F. Lao, A. T. Campbell, and A. A. Laza, Pcng, povsonng

21 CHARGING THE INTERNET 2 and peeng: dynamc makets fo dffeentated ntenet sevces and mplcatons fo netwok nteconnectons, IEEE Jounal on Selected Aeas n Communcatons, Vol. 8, 2000, pp B. Tuffn, Revsted pogessve second pce aucton fo chagng telecommuncaton netwoks, Telecommuncaton Systems, Vol. 20, 2002, pp C. Coucoubets, M. P. Damtnos, and G. D. Stamouls, An aucton mechansm fo bandwdth allocaton ove paths, n Poceedngs of the 7 th Intenatonal Teletaffc Confeence, 200, pp P. Rechl, B. Stlle, and S. Lenen, Aucton models fo multpovde ntenet connectons, n Poceedngs of Messung, Modelleung und Bewetung MMB 99, C. Coucoubets, G. D. Stamouls, C. Manolaks, and F. P. Kelly, An ntellgent agent fo optmzng QoS-fo-money n pced ABR connectons, Telecommuncatons Systems, Specal Issue on Intenet Economcs, to appea. 68. A. Ganesh, K. Laevens, and R. Stenbeg, Dynamcs of congeston pcng, Techncal Repot No. 70, Mcosoft Reseach Lmted, Cambdge, U.K., P. Key and D. R. McAuley, Dffeental QoS and pcng n netwoks: whee flow-contol meets game theoy, n IEE Poceedngs, 999, pp P. Key and L. Massoulé, Use polces n a netwok mplementng congeston pcng, Techncal Repot, Mcosoft Reseach Lmted, Cambdge, U.K., K. Laevens, P. Key, and D. McAuley, An ecn-based end-to-end congeston-contol famewok: expements and evaluaton, Techncal Repot 04, Mcosoft Reseach Lmted, Cambdge, UK, D. E. Lapsley and S. H. Low, Random ealy makng: an optmsaton appoach to ntenet congeston contol, n Poceedngs of IEEE Intenatonal Confeence on Netwoks 99, 999, pp F. Pagann, Flow contol va pcng: a feedback pespectve, n Poceedngs of the 2000 Alleton Confeence, A. Basu and S. J. Golestan, Estmaton of eceve ound tp tmes n multcast communcatons, Techncal Repot, Bell Laboatoes; use/golestan/tt.ps. 75. S. J. Golestan and S. Bhattachayya, A class of end-to-end congeston contol algothms fo the ntenet, n Poceedngs of Intenatonal Confeence on Netwok Potocol 98, 998, pp S. J. Golestan and K. K. Sabnan, Fundamental obsevatons on multcast congeston contol n the ntenet, n Poceedngs of IEEE INFOCOM 99, 999, pp E. E. Gaves, R. Skant, and D. Towsley, Decentalzed computaton of weghted max-mn fa bandwdth allocaton n netwoks wth multcast flows, n S. Palazzo, ed., Evolutonay Tends of the Intenet, 200 Tyhena Intenatonal Wokshop on Dgtal Communcatons, LNCS, Spnge-Velag, Vol. 270, 200, pp S. Shenke, D. Clak, D. Estn, and S. Hezog, Pcng n compute netwoks: eshapng the eseach agenda, Compute Communcaton Revew, Vol. 26, 996, pp

22 22 Buno Tuffn (IRISA/INRIA) eceved hs PhD degee n appled mathematcs fom Rennes Unvesty n 997. Snce, he has been wth INRIA-Rennes, Fance. Hs eseach nteests nclude developng Monte Calo and quas-monte Calo smulaton technques fo the pefomance evaluaton of compute and telecommuncaton systems, and moe ecently developng Intenet actve measuement technques and new pcng schemes. On ths last topc, he s the coodnato of the INRIA s coopeatve eseach acton PRIXNET (see Ext/RA/pxnet/ARC.htm).