Distributed Dynamic Capacity Contracting: An overlay congestion pricing framework for differentiated-services architecture

Transcription

1 Distibuted Dynamic apacity ontacting: An oveay congestion picing famewok fo diffeentiated-sevices achitectue Muat Yukse Shivkuma Kayanaaman Anuj Goe Rensseae Poytechnic Institute oy NY Abstact Sevea congestion picing poposas have been made in the ast decade Usuay howeve those poposas studied optima stategies and did not focus on impementation issues Ou main contibution in this pape is to addess impementation issues fo congestion-sensitive picing ove a singe domain of the diffeentiated-sevices (diff-sev achitectue of the Intenet We popose a new congestion-sensitive picing famewok Distibuted Dynamic apacity ontacting (Distibuted-D which is abe to povide a ange of fainess (eg max-min popotiona in ate aocation by using picing as a too Within the Distibuted-D famewok we deveop two picing schemes based on the manne of using picing to conto congestion: Picing fo ongestion onto (PF and Picing ove ongestion onto (PO PF uses picing diecty fo contoing congestion whist PO uses an undeying edge-to-edge congestion conto mechanism by oveaying picing on top of it Keywods Netwok Picing ongestion Picing uaity-of-sevice Fainess ongestion onto Diffeentiated-Sevices I INRODUION Impementation of congestion picing sti emains a chaenge athough sevea poposas have been made eg [] [] [] Among many othes two majo impementation obstaces can be defined: need fo timey feedback to uses about the pice detemination of congestion infomation in an efficient ow-ovehead manne he fist pobem timey feedback is eativey vey had to achieve in a wide aea netwok such as the Intenet In [] the authos showed that uses do need feedback about chaging of the netwok sevice (such as cuent pice and pediction of sevice quaity in nea futue Howeve in ou ecent wok [] we iustated that congestion conto though picing cannot be achieved if pice changes ae pefomed at a time-scae age than oughy ound-tip-times (Rs his means that in ode to achieve congestion conto though picing sevice pices must be updated vey fequenty (ie - seconds since R is expessed in tems of miiseconds fo most cases in the Intenet We beieve that the pobem of timey feedback can be soved by pacing inteigent intemediaies (ie softwae o hadwae agents between uses and sevice povides In this pape we do not focus on this paticua issue and eave deveopment of such inteigent agents fo futue eseach he second pobem congestion infomation is aso vey had to do in a way that does not need a majo upgade at netwok outes Howeve in diff-sev [] it is possibe to detemine congestion infomation via a good ingess-egess coodination So this fexibe envionment of diff-sev motivated us to his wok is sponsoed by NSF unde contact numbe ANI99 and cosponsoed by Inte opoation deveop a picing scheme on it In ou pevious wok [] we pesented a simpe congestionsensitive picing famewok Dynamic apacity ontacting (D fo a singe diff-sev domain (see Section III D teats each edge oute as a station of a sevice povide o a station of coodinating set of sevice povides Uses (ie individuas o othe sevice povides make shot-tem contacts with the stations fo netwok sevice Duing the contacts the station eceives congestion infomation about the netwok coe at a time-scae smae than contacts he station then uses that congestion infomation to update the sevice pice at the beginning of each contact Sevea picing schemes can be impemented in that famewok D assumed that a the povide stations advetise the same pice vaue fo the contacts which is vey costy to impement ove a wide aea netwok his is simpy because the pice vaue cannot be communicated to a stations at the beginning of each contact In this pape we eax this assumption by etting the stations to cacuate the pices ocay and advetise diffeent pices than the othe stations We ca this new vesion of D as Distibuted-D We intoduce ways of managing the ovea coodination of the stations fo the common puposes of fainess and stabiity We then deveop two picing schemes based on the way of appoaching congestion conto pobem: Picing fo ongestion onto (PF Picing ove ongestion onto (PO Whie PF ties to conto congestion diecty by picing PO oveays picing on top of an existing edge-to-edge congestion conto mechanism We iustate stabiity of the schemes by simuation expeiments We addess fainess pobems eated to picing and show that PF can achieve max-min and popotiona fainess by tuning a paamete caed as fainess coefficient he est of the pape is oganized as foows: In the next section we position ou wok and biefy suvey eevant wok in the aea In Section III we evise ovea chaacteistics of D In Section IV we deveop a simpe mode fo use behavio and make optimization anaysis that is basis to ou famewok Distibuted-D hen in Section V we descibe popeties of Distibuted-D famewok and investigate vaious issues (such as pice cacuation fainess scaabiity egading it Next in Section VI we deveop two picing schemes (PF and PO based on method of using picing to conto congestion In Section VII we make expeimenta compaative evauation of PF and PO We finaize with summay and discussions

2 II RELAED WORK hee has been sevea picing poposas which can be cassified in many ways: static vs dynamic pe-packet chaging vs pe-contact chaging and chaging pio to sevice vs posteio to sevice Athough thee ae opponents to dynamic picing in the aea (eg [] [9] [] most of the poposas have been fo dynamic picing (specificay congestion picing of netwoks Exampes of dynamic picing poposas ae MacKie-Mason and Vaian s Smat Maket [] Gupta et a s Pioity Picing [] Key et a s Popotiona Fai Picing (PFP [] Semet et a s Maket Picing [] [] and Wang and Schuzinne s Resouce Negotiation and Picing (RNAP [] [] Odyzko s Pais Meto Picing (PMP [] is an exampe of static picing poposa ak s Expected apacity [] and occhi et a s Edge Picing [] aow both static and dynamic picing In tems of chaging ganuaity Smat Maket Pioity Picing PFP and Edge Picing empoy pe-packet chaging whist RNAP and Expected apacity do not empoy pe-packet chaging Smat Maket is based pimaiy on imposing pe-packet congestion pices Since Smat Maket pefoms picing on pepacket basis it opeates on the finest possibe picing ganuaity his makes Smat Maket capabe of making idea congestion picing Howeve Smat Maket is not depoyabe because of its pe-packet ganuaity (ie excessive ovehead and its many equiements fom outes (eg equies a outes to be updated In [] we studied Smat Maket and difficuties of its impementation in moe detai Whie Smat Maket hods one exteme in tems of ganuaity Expected apacity hods the othe exteme Expected apacity poposes to use ong-tem contacts which can give moe cea pefomance expectation fo statistica capacity aocation and picing Pices ae updated at the beginning of each ongtem contact which incopoates itte dynamism to pices Ou wok Distibuted-D is a midde-gound between Smat Maket and Expected apacity in tems of ganuaity Distibuted-D pefoms congestion picing at shot-tem contacts which aows moe dynamism in pices whie keeping picing ovehead sma Anothe cose wok to ous is RNAP which aso mainy focused on impementation issues of congestion picing on diffsev Athough RNAP povides a compete pictue fo incopoation of admission conto and congestion picing it has excessive impementation ovehead since it equies a netwok outes to paticipate in detemination of congestion pices his equies upgades to a outes simia to the case of Smat Maket We beieve that picing schemes that equie upgades to a outes wi eventuay fai in impementation phase his is because of the fact that the Intenet outes ae owned by diffeent entities who may o may not be wiing to coopeate in the pocess of oute upgades Ou wok soves this pobem by equiing upgades ony at edge outes athe than at a outes III DYNAMI APAIY ONRAING (D D modes a shot-tem contact fo a given taffic cass as a function of pice pe unit taffic voume maximum voume (maximum numbe of bytes that can be sent duing the Fig D famewok on diff-sev achitectue contact and the tem of the contact (ength of the contact:! "! $ ( Figue iustates the big pictue of D famewok ustomes can ony access netwok coe by making contacts with the povide stations paced at the edge outes Access to avaiabe contacts can be done in diffeent ways what we ca edge stategy wo basic edge stategies ae bidding (many uses bids fo an avaiabe contact o contacting (uses negotiate with the povide fo an avaiabe contact So edge stategy is the decision-making mechanism to identify which custome gets an avaiabe contact at the povide station Stations can pefecty advetise congestion-based pices if they have actua infomation about the congestion eve in the netwok coe his congestion infomation can come fom the inteio outes o fom the egess edge outes depending on the congestion-detection mechanism being used D assumes that the congestion detection mechanism is abe to give congestion infomation in time scaes (ie obsevation intevas smae than contacts In summay D famewok has been designed to use picing and dynamic capacity contacting as a new dimension in managing congestion as we as to achieve simpe economic goas he key benefits of D ae: % a congestion-sensitive picing famewok empoyabe on diffsev achitectue % does not equie pe-packet accounting (woks at ganuaity of contacts % does not equie upgades o softwae suppot anywhee in the netwok except the edges IV USER ADAPAION In this section we pesent a simpe optimization anaysis that is basis to Distibuted-D One impotant chaacteistic of congestion-sensitive picing is that the pice must be osciating aound an optimum pice &(' to guaantee both congestion conto and high utiization of netwok esouces We now deive a fomua fo & ' by expicity modeing custome utiities We mode custome s utiity with the we-known function *( - / [] [9] [] [] whee is the aocated bandwidth to the custome and is custome s sensitivity to bandwidth hen suppose& is the pice advetised to Wang and Schuzinne intoduced a moe compex vesion of this function in []

3 K a U d U K G a paticua use he use wi maximize his/he supus by making sue that he/she contacts fo & ie : 9;:< >=? 9;:< =A@ *B - D& FE G H& Assuming that the customes obey this above pocedue the povide of the netwok sevice can now figue out what pice to advetise to each use by maximizing the socia- wefae RS K be a MLON whee N is the povide evenue Let P inea function and be the cost of poviding amount of capacity to a use whee is a positive constant hen the socia wefae K wi be: WV Y *( - & D& L JI D& ZP \ U *( S DV We maximize K with the condition that ] whee is the tota avaiabe capacity Notice that to maximize K a the avaiabe capacity must be aocated to the uses because we assume sticty inceasing utiity functions (ie (- fo them By appying Lagange-Mutipie Method [] we fist convet K to the foowing: K`_ba *( - DVc (Led f U WV - g [ ^ We can get the foowing system of equations by equating patia deivative of K to zeo fo each unknown vaiabe: ah \ U WV kj m n? iji Lod I qp sutwt Afte soving system of equations we get the soution as foows: ] WV Sv wp ixtdt ] WV his esut shows that wefae maximization of the descibed system can be done ony by aocating capacity to the uses popotiona to thei bandwidth sensitivity eative to tota sensitivity to bandwidth So any use shoud be given a capacity of ] DVc ( ( Since we showed that the use wi contact fo & when advetised a pice of & then the optimum pice fo povide to advetise (ie &(' can be cacuated as foows: & ' & ] WV &B ] DVc his means that the povide shoud advetise the same pice to a uses Howeve notice that this above study assumed two majo things: % the cost fo povisioning capacity pe unit bandwidth to each use is the same % a uses have the same type of utiity function ie * - Since optimaity is not ou singe goa in picing we do not focus on addessing the above assumptions Study of how much optimaity can be achieved by Distibuted-D is eft fo futue wok We can aso intepet use s budget y as his/he sensitivity to bandwidth since a use who is moe sensitive to bandwidth is expected to spae moe budget fo the netwok sevice So we wi use budget instead of sensitivity to bandwidth fo the est of the pape Assuming that the customes has a tota budget of z ] y fo netwok sevice pe unit time and the netwok has a capacity of pe unit time we can ewite the optimum pice as foows: & ' z ( V DISRIBUED-D: HE FRAMEWORK Distibuted-D is specificay designed fo diff-sev achitectue because the edge outes can pefom compex opeations which is essentia to sevea equiements fo impementation of congestion picing In Distibuted-D famewok each edge oute is teated as a station of the povide Each station advetises ocay computed pices with infomation eceived fom othe stations he main famewok basicay descibes how to peseve coodination among the stations such that stabiity and fainess of the ovea netwok is peseved A Logica Picing Seve (LPS pays a cucia oe in tems of functioning of the Distibuted-D famewok Figue iustates basic functions (which wi be bette undestood in the foowing sub-sections of LPS in the famewok he contacting takes pace between the customes and the ingess stations So each ingess station keeps a cuent pice vaue fo each edge-to-edge fow and advetises that pice vaue & to customes of the fow fom ingess to egess p? So how do we cacuate the pice-pe-fow &? he ingesses make estimation of budget fo each edge-to-edge fow passing though themseves Let { be the cuenty estimated A How to acuate & y budget fom ingess p to egess he ingesses send thei estimated budgets to the coesponding egesses (ie y { is sent fom ingess p to egess at a deteministic time-scae At the othe side the egesses eceive budget estimations fom a the

4 { { { & { Aso the ingess can " use the tota estimated netwok capacity in cacuating the contact paamete defined in Equation Admission " conto techniques can be used to identify the best vaue fo We " use a simpe method which does not put any estiction on ie whee is the contact ength One can caim: Why not use fo cacuating "? his wi pevent fows to send moe than avaiabe capacity Howeve it wi not aow fows to compete fo the capacity which wi not give oppotunity to the fows with highe budget than the othes By aowing fows to contact fo moe than the aowed we can eave the shaing of the tota avaiabe capacity to the fows themseves In this way the fows wi shae the capacity based on thei budgets ie wiingness to pay Fig Majo functions of LPS ingesses and aso they make estimation of capacity fo each paticua fow { p In othe wods egess cacuates { and is infomed about { by ingess p he egess then pe- y naizes o favos fow p to by updating its budget vaue ie y y k} x~a >F Mƒ } whee & ~A F > Mƒ ae the othe paametes that ae used fo deciding whethe to penaize o favo the fow Fo exampe if the fow p to is passing though moe congested aeas than the othe fows then the p egess can penaize this fow by educing its budget estimation y At anothe time-scae the egesses keep sending infomation to LPS (which can be paced to one of the egesses o can be impemented in a fuy distibuted p manne see Section V-E Moe specificay the egess sends the foowing infomation to LPS: the updated budget estimations of a fows passing though utwt itsef ie y fo and f whee is the numbe of edge outes the estimated capacities (pease efe to Section V- fo moe about capacity estimation of a fows passing though itsef ie sutwt p fo and " whee is the numbe of edge outes LPS eceives infomation fom egesses and cacuates aowed capacity fo each edge-to-edge fow acuation of vaues is a compicated task which depends on updated budget estimation of each fow (ie y In genea the fows shoud get capacity of the same botteneck in popotion to thei budgets We wi ate define a geneic agoithm to do capacity aocation task LPS then sends the foowing infomation to ingess : the tota estimated netwok capacity (ie ] ] the aowed capacities to each edge-to-edge fow stating fom ingess p xtdt p ie fo and whee is the numbe of edge outes Now the ingess can cacuate pice fo each fow as foows: p & ˆ y { B Budget Estimation at Ingesses he ingess stations pefom vey tivia opeation to estimate budgets of each fow y { he ingess basicay knows its cuent pice fo each fow &B When it eceives a packet it just needs to detemine which egess station the packet is going to Given that the ingess station has the addesses of a the egess stations (this is a eaistic assumption of the same diff-sev domain it can find out which egess the packet is going to So by monitoing the packets tansmitted fo each fow the ingess can be the tota numbe of estimate the budget of each fow Let packets tansmitted fo fow p to in unit time then the budget estimate fo the fow p to is y { ˆ & apacity Estimation at Egesses he cucia popety of capacity estimation in Distibuted- D is that it can be made congestion-based With a simpe mechanism (such as making of packets at inteio outes when congested it is possibe to detect congestion at the egess station So fo a paticua edge-to-edge taffic fow one can make the capacity estimation congestion-sensitive by deceasing the estimation when congestion is detected and by inceasing when congestion is not detected fo that fow In this sense sevea capacity estimation agoithms can be used eg Additive Incease Additive Decease (AIAD Additive Incease Mutipicative Decease (AIMD We wi povide a fu desciption of such an agoithm ate in Section VI-A D Fainess Fainess of a picing scheme is indiecty equivaent to fainess of ate aocation schemes A picing scheme detemines and advetises the pices to the uses then the uses contact fo netwok capacity accoding to thei budgets So a picing scheme aocates netwok capacity indiecty Assuming that uses have a utiity function of fom * - in Section IV we povided a simpe poof that the povide shoud advetise a pice of & z whee z is the tota budget of the uses and is the netwok capacity in ode to maximize socia wefae his wi cause uses to shae the netwok capacity in popotion to thei budgets Howeve fainess issues ae not that simpe We examine the issues egading fainess in two main cases We now fist detemine these two cases and then povide soutions within Distibuted-D famewok

5 K L L L L L L D ases Singe-botteneck case: he picing potoco shoud chage the same pice to the uses of the same botteneck In this way among the customes using the same botteneck the ones who have moe wiingness to pay wi be given moe ate than the othes he intuition behind this easoning is that the cost of poviding capacity to each custome is the same he simpe poof in Section IV aso shows that chaging a uses equay is optima in such a case Muti-botteneck case: he picing potoco shoud chage moe to the customes who cause moe costs (eg congestion to the povide his wi make sue that the evenue wi be highe whie being faie to the customes So othe than popotionaity to custome budgets we aso want to aocate ess ate to the customes whose fows ae passing though moe bottenecks than the othe customes Fo muti-botteneck netwoks two main types of fainess have been defined: max-min fainess [9] popotiona fainess [] We now study popotiona fainess and max-min fainess in tems of socia wefae maximization with a canonica exampe onside a muti-botteneck netwok in which thee is a ong fow that is cossed by paae fows An exampe of such a netwok is shown in Figue -b Suppose a the bottenecks ae equivaent in capacity Intuitivey whateve the ong fow gets!š a the paae fows wi get the est of the capacity Let be the capacity given to the ong fow and be the capacity given to one of the paae fows Suppose that the utiity of the ong fow is * Š Š Š Š and the utiity of one of the paae fows is *? - > k Š Notice that and ae the sensitivity of the fows to capacity (aso intepeted as fow s budget see Section IV Since the ong fow is passing though bottenecks cost of poviding capacity to the ong fow is times moe than cost of poviding capacity to one of the paae fows So et cost of poviding to one of the paae fows be PH - > / Š Š Š g andš et the cost of poviding to the ong fow be P Within this context the socia wefae K and its Lagangian wi be: KŒ_ a J Š (- Š L Š (- Š ŽL (- c gs Š g g Š g Ld - Š Afte soving!š the above Lagangian we get the foowing soutions fo and to maximize K : Š$ Š Š Š Fom the above esut we make two obsevations: % Fist if both the ong fow and a paae fow have equa bandwidth sensitivity Š Š ie then the optima aocation wi be and his is the popotiona fai case So popotiona fainess is optima ony when a the fows have equa bandwidth sensitivity As anothe intepetation it is optima ony if a the fows have equa budget % Second if the ong fow is sensitive to bandwidth times moe than a paae!š R Š fow ie then the optima aocation wi be his is the max-min fai case So max-min fainess is optima ony when the ong fow s utiity is sensitive to bandwidth in popotion to the cost of poviding capacity to it In othe wods by intepeting bandwidth sensitivity as the fow s budget max-min fainess is optima ony when the ong fow has budget in popotion to the cost of poviding capacity to it Obsevations simia to above have been made in the aea eg [] [] D Soutions within Distibuted-D In ode to achieve the objectives mentioned in the pevious section the picing potoco shoud chage the customes equay in a singe-botteneck topoogy whie it shoud chage them diffeenty in a muti-botteneck topoogy his means that the picing famewok must give the abiity to chage some customes equay whie the abiity to chage some othe customes diffeenty o achieve the fainess objectives in Distibuted-D we intoduce new paametes fo tuning ate aocation to fows In ode to penaize fow p p to the egess can educe y { whie updating the fow s estimated budget It uses the foowing fomua to do so: y $ y { S m - y { whee is the congestion cost caused by the fow p to is the minimum possibe congestion cost fo the fow and is fainess coefficient Instead of y { p the egess now sends y to LPS can be at minimum When it is geate than it means that Distibuted-D is empoying popotiona fainess in its ate aocation When it is Distibuted-D is empoying max-min fainess So using age vaues yied to moe popotiona fainess in the ate aocation of Distibuted-D Assuming that each botteneck has the same amount of congestion and aso assume that they have the same capacity hen in ode to cacuate and we can diecty use the numbe of bottenecks the fow p to is passing though In such a case wi be and shoud be numbe of bottenecks the fow is passing though If the inteio nodes incement a heade fied of the packets at the time of congestion then at the egess station we can estimate the numbe of bottenecks the fow is passing though o do that estimation the egess station does the foowing at time inteva fo fow p to : - { š ž! { ( œ whee { is the highest numbe of bottenecks that fow passed though in time inteva is a pe-defined vaue Reaize that the heade fied of the packets ae being incemented ony if they ae passing though a congested botteneck It is possibe that some of the bottenecks ae not congested when a paticua packet is passing though them Fo exampe the heade fied of the packet may be incemented ony thee times athough it actuay passed though six bottenecks So it is necessay to bias the estimation to the agest numbe of bottenecks

6 ƒ { p { { the packets of that fow have passed ecenty Aso as anothe issue IP outing causes oute of the fows to change dynamicay o conside the dynamic behavio of the outes it is aso necessay to decease when - - So if the oute of the fow has changed then afte some time (depending on how age the is the vaue of wi decease to the actua numbe of bottenecks the fow is passing though E Scaabiity Distibuted-D opeates on pe edge-to-edge fow basis hee ae mainy two issues egading scaabiity: LPS the numbe of fows Fist of a the fows ae not pe-connection basis ie a the taffic going fom edge oute to p is counted as ony one fow his actuay eieves the scaabiity pobem fo opeations that happen on pe-fow basis he numbe of fows in the system wi be Ÿ- whee is the numbe of edge outes in the diff-sev domain So indeed scaabiity of the fows is not a pobem fo the cuent Intenet since numbe of edge outes fo a singe diff-sev domain is vey sma If it becomes so age in futue then aggegation techniques can be used to ovecome this scaabiity issue of couse by sacificing some optimaity Scaabiity of LPS can be done two ways Fist idea is to impement LPS in a fuy distibuted manne he edge stations exchange infomation with each othe (simia to ink-state outing Basicay each station wi send tota of messages each of which headed to othe stations So this wi incease the ovehead on the netwok because of the exta messages ie the compexity wi incease fom? to in tems of numbe of messages Atenativey LPS can be divided into mutipe oca LPSs which synchonize among themseves to maintain consistency his way the compexity of numbe of messages wi educe Howeve this wi be at a cost of some optimaity again Since these above-defined scaing techniques ae vey weknown we do not focus on detaied desciption of them VI DISRIBUED-D: PRIING SHEMES One of the main puposes fo congestion picing is to conto congestion by making the pices congestion-sensitive Sevea studies (eg [] [] showed that congestion-sensitive picing eads to stabiity Within Distibuted-D famewok we now descibe two picing schemes which ae mainy inspied of diffeent appoaches to the pobem of congestion conto Picing fo ongestion onto (PF uses picing diecty fo the pupose of congestion conto whie Picing ove ongestion onto (PO uses an undeying edge-to-edge congestion conto mechanism to impose tighte conto on congestion Figue iustates the big pictue of the two appoaches In the foowing sub-sections we wi descibe and investigate these two appoaches within Distibuted-D famewok A PF A apacity Estimation and ongestion Detection In ode to make congestion detection at the egess station we assume that the inteio outes mak the packets when thei queue passes a theshod When an egess station eceives a maked packet it teats it as a congestion indication Given the above congestion detection mechanism egess stations make a congestion-based estimation of the capacity fo the fows passing though themseves Remembe that estimated capacity { fo each fow is sent to LPS in Distibuted-D famewok Egess stations divide time into deteministic obsevation intevas and identify each obsevation inteva as congested o non-congested Basicay an obsevation inteva is congested if a congestion indication was eceived duing that obsevation inteva At the end of each obsevation inteva p the egesses update the estimated capacity hen egess cacuates the estimated capacity fo fow p to at the end of obsevation inteva as foows: m ( >F G { -?LO? { (S >F G - whee is in ( x- is the measued output ate of fow to duing obsevation inteva and { is a pe-defined incease paamete his agoithm is a vaiant of we-known AIMD and is intoduced in [] Aso notice that the above capacity estimation agoithm is congestion-based as it is necessay fo the congestion-sensitivity of Distibuted-D famewok (see Section V- So egesses make capacity estimation fo each fow accoding to the above agoithm and send { cuent estimated capacity fo fow p to As a efinement to the scheme the vaue of the { as the shoud decease when the numbe of active fows inceases he eason is that at LPS the tota estimated netwok capacity is the accumuation of { s sent fom egesses fo each fow So fo exampe et thee be fows that ae outputting some taffic Each of the coesponding egesses wi basicay incease thei s by { when thee was no congestion fo that fow at the ast inteva Howeve when those individua { s ae accumuated at LPS the ovea netwok capacity estimation wi incease by { his basicay shows that the fideity of conto wi be dependent on the tota numbe of active fows Hence in ode to achieve the same eve of conto fideity the { paamete that is being used ocay at each egess must be educed when moe fows get active Let be the best vaue fo { paamete when thee is ony one fow that is outputting taffic hen the genea fomua wi be " { whee is the numbe of cuenty active fows In Distibuted- D famewok ƒ I we can cacuate he egesses count a fow hey then convey the numbe of active as active if fows to LPS which ate on infoms them back with the tota numbe of active fows in the netwok his is an optiona efinement to the capacity estimation capabiity of PF We wi use this efinement in ou simuation expeiments ate in Section VII Notice that this is ony one paticua way of detecting congestion Distibuted-D does not necessaiy need the inteio outes to mak packets as ong as othe ways of detecting congestion ae avaiabe

7 { (a (b Fig (a PF: Picing with no undeying edge-to-edge congestion conto (b PO: Picing ove edge-to-edge congestion conto A apacity Aocation to Edge-to-Edge Fows LPS is supposed to aocate the tota estimated netwok capacity to edge-to-edge fows in such a way that the fows passing though the same botteneck shoud shae the botteneck capacity in popotion to thei budgets and aso the fows that ae not competing with othe fows shoud get a the avaiabe capacity on thei oute he compicated issue is to do this without knowedge of the topoogy fo netwok coe We now popose a simpe and geneic agoithm to pefom this centaized ate aocation within Distibuted-D famewok Fist at LPS we intoduce a new infomation about each edge-to-edge fow A fow p is congested if egess has been eceiving congestion indications fom that fow ecenty (we wi ate p define what ecent is Egess knows whethe each fow was congested in the ast obsevation inteva o is cu- not (pease see the pevious section o detemine if enty congested o not define p at egess as foows: - was I? k( >F (S kf G in obsevation G was - in obsevation o detemine whethe is p congested o not at LPS egess sends the cuent vaue of aong with the othe infomation (ie y and { to LPS Of couse this is done fo a fows simutaneousy At LPS et P be the maintained paamete in ode to detemine whethe is congested o not If P ƒªi LPS detemines as congested If not it detemines as noncongested LPS eguay eceives messages fom egesses Let s ca the time inteva between these messages as LPS in- as foows: teva At evey LPS inteva LPS updates P«P - { s P I ( whee { is a positive intege Notice that { paamete defines ong a fow can stay in congested state afte the ast congestion indication So in othe wods { defines the time-ine to detemine if a congestion indication is ecent o not Note to { at evey congestion indication that instead of setting P sevea diffeent methods can be used fo this pupose but we poceed with the method in ( Given the above method to detemine whethe a fow is congested o not we now descibe the agoithm to aocate capacity to the fows Let be the set of a edge-to-edge fows in the diff-sev domain and be the set of congested edge-to-edge fows Let be the accumuation of { s whee f Futhe et z be the accumuation of y s whee c hen as foows: LPS cacuates the aowed capacity fo =±j $ ²?³ P ƒoi ž > So a congested fow competes with othe congested fows and is aowed a capacity in popotion to its budget eative to budgets of a congested fows If a fow is not congested then it is aowed to use its own estimated capacity which wi give enough feedom to utiize capacity avaiabe to that paticua fow he agoithm wi be undestood moe ceay afte the simuation expeiments in Section VII B PO he essence of PO is to oveay picing on top of congestion conto which is a nove appoach Assuming that thee is an undeying edge-to-edge congestion conto scheme we can set the paametes of that undeying scheme such that it eads to fainess and bette conto of congestion he picing scheme on top can detemine use incentives and set the paametes of the undeying edge-to-edge congestion conto scheme accodingy his way it wi be possibe to favo some taffic fows with highe wiingness-to-pay than the othes Futhemoe the picing scheme wi aso bing benefits such as an indiect conto on use demand by pice which wi in tun hep the undeying edge-to-edge congestion conto scheme to opeate moe smoothy Howeve the ovea system pefomance (eg fainess utiization thoughput wi be dependent on the fexibiity of the undeying congestion conto mechanism We now descibe a possibe PO scheme by oveaying PF (which is a puey picing scheme on top of an edgeto-edge congestion conto scheme Riviea [] We wi fist

8 ~ ~ º { povide a genea desciption of Riviea then outine pobems eveaed by oveaying PF ove Riviea We wi compete the desciption of PO by poviding soutions to the outined pobems he simuation expeiments in Section VII wi use this desciption of PO B Edge-to-Edge ongestion onto: Riviea Riviea takes advantage of two-way communication between ingess and egess edge outes in a diff-sev netwok Ingess sends a fowad feedback to egess in esponse to feedback fom egess and egess sends backwad feedback to ingess in esponse to feedback fom ingess So ingess and egess of a taffic fow keep bouncing feedback to each othe Ignoing oss of data packets the egess of a taffic fow measues the accumuation caused by the fow by using the bounced feedbacks and R estimations he egess node keeps two theshod paametes to detect ~A ž! ~ congestion: and ž! Fo each fow the egess keeps a vaiabe that says whethe the ~ fow is ž n congested o not When fo a paticua fow exceeds the egess updates ~ the vaiabe to congested Simiay when is ess than ž! it updates the vaiabe to not-congested It does ~ ~A ž! not update the vaiabe if is in between and ž! he ingess node gets infomed about the congestion detection by backwad feedbacks and empoys AIMD- ER (ie a vaiant of egua AIMD to adjust the sending ate In a singe-botteneck netwok Riviea can be tuned such that each fow gets weighted shae of the botteneck capacity he ingess nodes maintain an additive incease paamete and a mutipicative decease paamete fo each edge-toedge fow hese paametes ae used in AIMD-ER Among the edge-to-edge fows by setting the incease paametes ( at the ž! ~A ž n ingesses and the theshod paametes ( and at the egesses in atio of desied ate aocation it is possibe to make sue that the fows get the desied ate aocation Fo exampe assume thee ae two fows and competing fo a botteneck (simia to Figue -a If we want fow to get a capacity of times moe than fow then the foowing conditions must be hod: ~ ž n J~ ž n ž! JJ~ ž n B PO: Pobems Oveaying PF ove Riviea aises two majo pobems : Paamete mapping: Since PF wants to aocate netwok capacity accoding to the uses budgets that changes dynamicay ove time it is a equied abiity set coesponding paametes of Riviea such that it aocates the capacity to the use fows accoding to thei budgets So this aises need fo a method of mapping PF paametes to the Riviea paametes Notice that this type of mapping equies Riviea to be abe to povide paametes that tunes the ate being given to the edge-to-edge fows µ Note that these pobems ae not specific to PF ove Riviea hey ae genea pobems fo oveaying a soey picing scheme ove an edge-to-edge congestion conto mechanism Edge queues: he undeying congestion conto scheme Riviea wi not aways aow a the taffic admitted by the picing scheme PF which wi cause queues to buid up at the netwok edges So management of these edge queues is necessay to oveay PF ove Riviea Figues -a and -b compae the situation of the edge queues in the two cases when thee is an undeying congestion conto scheme and when thee is not B PO: Soutions Paamete mapping: Fo each edge-to-edge fow LPS can cacuate the capacity shae of that fow out of the tota netwok capacity Let be the faction of netwok capacity that must be given to the fow p to Aong with s LPS can convey s to the ingess stations and they can mutipy the incease paamete with Aso LPS can send ~ ~A ž! s to the egesses and they can mutipy and ž! with his soves the paamete mapping pobem defined in the pevious section Edge queues: We now popose soutions to the second pobem ie management of edge queues Each ingess station can manage the edge queue with the aeady avaiabe infomation: % aowed capacity of fow p to (in packet/seconds %w cuent size of edge queue fo fow p to (in packets % contact ength (in seconds Notice that ingess stations get the aowed capacities fo fows fom LPS and then cacuate pices accoding to that infomation So one intuitive way of making sue that the use wi not contact fo moe than the amount that the netwok can hande is to subtact necessay capacity to dain the aeady buit edge queue fom and then make contacts accodingy In othe wods the ingess station e-cacuates the aowed capacity fo fow p ¹ to by the foowing fomua ¹ fo cacuating pice ie &B y ¹ and uses Distibuted-D can aso empoy anothe technique to manage the edge queues Remembe that PF makes capacity estimation at egesses accoding to making of packets Specificay maked packet is counted as a congestion indication and capacity estimation is educed which in tun causes pice fo that fow to incease So the ingess station can mak the packets if size of the edge queue exceeds a theshod his wi indiecty educe the capacity estimation and hence dain the edge queue Notice that it is aso possibe to empoy this method simutaneousy with the method descibed in the pevious paagaph In the simuation expeiments of the next section we wi use both techniques simutaneousy We ae woking on moe consevative appoaches by making moe pessimistic capacity estimations in ode to manage the edge queues VII SIMULAION EPERIMENS AND RESULS We now pesent ns [] simuation expeiments of PF and PO on singe-botteneck and muti-botteneck topoogy Ou goas ae to iustate fainess and stabiity popeties of the two schemes with possibe compaisons of two he singe-botteneck topoogy has a botteneck ink which is connected to edge nodes at each side whee is the numbe of uses he muti-botteneck topoogy has botteneck Notice that the edge queue at ingess» is ¼ ½!¾ ]e À Á ½ ¼ ½

9 9 (a (b Fig (a Singe-botteneck (b Muti-botteneck netwok fo Distibuted-D expeiments inks that ae connected to each othe seiay hee ae again ingess and egess edge nodes Each ingess edge node is mutuay connected to the beginning of a botteneck ink and each egess node is mutuay connected to the end of a botteneck ink A botteneck inks have a capacity of Mb/s and a othe inks have Mb/s Popagation deay on each ink is ms and uses send UDP taffic with an aveage packet size of B o ease undestanding the expeiments each use sends its taffic to a sepaate egess Fo the muti-botteneck topoogy one use sends though a the bottenecks (ie ong fow whie the othes coss that use s ong fow he queues at the inteio nodes (ie nodes that stand at the tips of botteneck inks mak the packets when thei oca queue size exceeds packets In the muti-botteneck topoogy they incement a heade fied instead of just J making Figue -a shows a singe-botteneck topoogy with Figue -b shows muti-botteneck topoogy with Z Â he white nodes ae edge nodes and the gay nodes ae inteio nodes hese figues aso show the taffic fow of uses on the topoogy he use fow ties to maximize its tota utiity by contacting fo y & amount of capacity whee y is its budget and & is pice he fows s budgets ae andomized accoding to Noma distibution with a given mean vaue his mean vaue is what we wi efe to as fows s budget in ou simuation expeiments ontacting takes pace at evey s obsevation inteva is s and LPS inteva is s Ingesses send budget estimations to coesponding egesses at evey obsevation inteva LPS sends infomation to ingesses at evey LPS inteva he paamete { is set to which means a fow is detemined to be non-congested at east afte (pease see Section VI-A LPS intevas equivaent to one contacting inteva he paamete is set to packet (ie B the initia vaue of { is set to Mb/s is set to 9 and is set to Aso note that in the expeiments packet dops ae not aowed in any netwok node his is because we woud ike to see pefomance of the schemes in tems of assued sevice fo each fow A Expeiments on Singe-botteneck opoogy We un simuation expeiments fo PF and PO on the singe-botteneck topoogy which is epesented in Figue -a In this expeiment thee ae uses with budgets of espectivey fo uses ota simuation time is s and at the beginning ony the use is active in the system Afte s the use gets active Again afte s at simuation time the use gets active Fo PO thee is an additiona component in the simuation: edge queues he edge queues mak the packets when queue size exceeds packets So in ode to manage the edge queues in this simuation expeiment we simutaneousy empoy the two techniques defined in Section VI-B In tems of esuts the voume given to each fow is vey impotant Figues -a and -a show the voumes given to each fow in PF and PO espectivey Just to see a moe smooth view Figues -b and -b show the voumes aveaged ove contact peiods We see the fows ae shaing the botteneck capacity amost in popotion to thei budgets he distotion in voume aocation is caused because of the fact that each fow is shaing the botteneck capacity in popotion to thei budgets when they ae congested When they ae not congested howeve they etun back to thei individua capacity estimation We can obseve this dynamic in Figues -a and -a In compaison to PO PF aocates voume moe smoothy but with the same popotionaity to the fows he noisy voume aocation in PO is caused by coodination issues (ie paamete mapping edge queues investigated in Section VI-B Figues -c and -c show the pice being advetised to fows in PF and PO espectivey As the new uses join in the picing schemes incease the pice in ode to baance suppy and demand Aso we can see the same dynamic as in the voume aocation gaphs caused by the capacity aocation agoithm Figues -d and -d shows the botteneck queue size in PF and PO espectivey Notice that queue sizes make peaks tansienty at the times when new uses gets active Othewise the queue size is contoed easonaby and the system is stabe In compaison to PF PO manages the botteneck queue much bette because of the tight conto enfoced by the undeying edge-to-edge congestion conto agoithm Riviea Figues fom -a to -c show the sizes of edge queues in PO We can obseve that uses get active at s of intevas We obseve stabe behavio but with osciations age than the botteneck queue iustated in Figue -d his is because of the tight edge-to-edge congestion conto which pushes backog to the edges Aso obseve that the edge queues ae geneay much owe than the theshod of packets his means that the packets wee maked at the edge queues vey aey So the technique of making the packets at the edges and educing the estimated capacity indiecty was not dominant in this simuation Rathe the technique of educing the estimated capacity diecty at the ingess was dominant in tems of handing of edge queues (pease see Section VI-B fo fu undestanding of these two techniques

10 Ä Ã Å "voume-" "voume-" "voume-" 9 "avg-voume-" "avg-voume-" "avg-voume-" Voume (Mb Aveaged Voume (Mb (a (b "pice-" "pice-" "pice-" Pice ($/Mb Botteneck ueue Size (packets (c (d Fig Resuts of singe-botteneck expeiment fo PF: (a Voumes contacted by each fow (b Aveage of contacted voumes ove contacts (c Pice advetised to the fows (d Botteneck queue ength In PF aveage utiization of the botteneck ink was moe than 9% and no packet dops wee aowed In PO aveage utiization of the botteneck ink was % his is because of the fact that Riviea s paametes ae set such that it povides % utiization of the netwok So as we caimed in Section VI-B the imitations of the undeying congestion conto scheme aso imits the ovea pefomance We specificay set the paametes of Riviea to show this ovea behavio in eaity Riviea can povide highe utiization given that the paametes ae set popey B Expeiments on Muti-botteneck opoogy On a muti-botteneck netwok we woud ike iustate two popeties fo PF: % Popety : povision of vaious fainess in ate aocation by changing the fainess coefficient of Distibuted-D famewok (see Section V-D % Popety : pefomance of the capacity aocation agoithm of PF in tems of adaptiveness (see Section VI-A Since Riviea does not cuenty povide a set of paametes fo weighted aocation on muti-botteneck topoogy we wi not un any expeiment fo PO on muti-botteneck topoogy In ode to iustate Popety we un a seies of expeiments fo PF with diffeent vaues Remembe that is the fainess coefficient of Distibuted-D Highe vaues impy moe penaty to the fows that cause moe congestion costs We use a age vesion of the topoogy epesented in Figue -b In the muti-botteneck topoogy thee ae uses and 9 botteneck inks ota simuation time is s At the beginning the use with the ong fow is active A the othe uses have taffic fows cossing the ong fow Afte each s one of these othe uses gets active So as the time passes the numbe of bottenecks in the system inceases since new uses with cossing fows join in Notice that the numbe of bottenecks in the system is one ess than the numbe of active use fows We ae inteested in the voume given to the ong fow since it is the one that cause moe congestion costs than the othe use fows Figue -a shows the aveage voume given to the ong fow vesus the numbe of bottenecks in the system fo diffeent va- Æ It is sti being studied by its deveopes

11 È Ä Ç É Ã Å É 9 "voume-" "voume-" "voume-" 9 "avg-voume-" "avg-voume-" "avg-voume-" Voume (Mb Aveaged Voume (Mb (a (b 9 "pice-" "pice-" "pice-" Pice ($/Mb Botteneck ueue Size (packets (c (d Fig Resuts of singe-botteneck expeiment fo PO: (a Voumes contacted by each fow (b Aveage of contacted voumes ove contacts (c Pice advetised to the fows (d Botteneck queue ength Edge ueue Size fo fow (packets Edge ueue Size fo fow (packets Edge ueue Size fo fow (packets (a (b (c Fig Sizes of edge queues in the singe-botteneck expeiment fo PO: (a Edge queue fo fow (b Edge queue fo fow (c Edge queue fo fow

12 Ê Ã Ë Voume of the Long Fow (Mbits 9 "voume apha=" "voume apha=" "voume apha=" "voume apha=" "voume apha=" "voume apha=" "voume apha=" "voume apha=" "voume apha=" "voume apha=" "voume apha=" Pice Advetised to the Long Fow ($/Mbits "pice apha=" "pice apha=" "pice apha=" "pice apha=" "pice apha=" "pice apha=" "pice apha=" "pice apha=" "pice apha=" "pice apha=" "pice apha=" Numbe of Bottenecks (a Numbe of Bottenecks (b "voume-" "voume-" "voume-" "voume-" "avg-voume-" "avg-voume-" "avg-voume-" "avg-voume-" Voume (Mb Aveaged Voume (Mb (c (d Fig Resuts of PF expeiments on muti-botteneck topoogy: (a Voume given to the ong fow in a inea netwok (b Pice advetised to the ong fow in a inea netwok (c Voumes given to the fows (d Voumes given to the fows aveaged fo contacts ues of As expected the ong fow gets ess and ess capacity as inceases When is zeo the scheme achieves max-min fainess As it inceases the scheme gets cose to popotiona fainess Aso note that the othe use fows get the est of the botteneck capacity and hence utiize the bottenecks his vaiation in fainess is basicay achieved by advetisement of diffeent pices to the use fows accoding to the costs incued by them Figue -b shows the aveage pice that is advetised to the ong fow as the numbe of bottenecks in the system inceases We can see that the pice advetised to the ong fow inceases as the numbe of bottenecks inceases Finay to iustate Popety we an an expeiment on the topoogy in Figue -b with sma changes We inceased capacity of the botteneck at node D fom Mb/s to Mb/s hee ae fou fows and thee bottenecks in the netwok as epesented in Figue -b Initiay a the fows have an equa budget of ota simuation time is s Between times and budget of fow is tempoaiy inceased to he fainess coefficient is set to A the othe paametes (eg making theshods initia vaues ae exacty the same as in the singe-botteneck expeiments of the pevious section Figue -c shows the voumes given to each fow and Figue -d shows the given voumes aveaged ove contacting peiods Unti time s fows and shae the botteneck capacities equay pesenting a max-min fai aocation because was set to Howeve fow is getting moe than the othes because of the exta capacity at botteneck node D his fexibiity is achieved by the feedom given individua fows by the capacity aocation agoithm (see Section VI-A Between times and fow gets a step incease in its aocated voume because of the step incease in its budget In esut of this fow gets a step decease in its voume Aso fows and adapt themseves to the new situation by attempting to utiize the exta capacity eftove fom the eduction in fow s voume So fow and gets a step decease in thei voumes Afte time fows estoe to thei oigina voume aocations iustating the adaptiveness of the scheme VIII SUMMARY AND DISUSSIONS In this pape we pesented a new famewok Distibuted- D fo congestion picing in a singe diff-sev domain Main contibution of the pape is to deveop an easy-to-impement

13 oveay congestion picing achitectue which povides fexibiity in ate aocation We investigated fainess issues within Distibuted-D and iustated ways of achieving a ange of fainess types (ie fom max-min to popotiona though congestion picing unde cetain conditions he fact that it is possibe to achieve vaious fainess types within a singe famewok is vey encouaging Based on the way of appoaching to the congestion conto pobem we deveoped two picing schemes (PF and PO within the Distibuted-D famewok As a nove appoach distinguishing featue of PO is to oveay picing on top of edge-to-edge congestion conto By compaative evauation of PF and PO we showed that PO pefoms bette in tems of managing congestion in netwok coe because of the tight (ow time-scae conto enfoced by the undeying edge-to-edge congestion conto mechanism Howeve we aso showed that ovea pefomance (eg fainess utiization is dependent on the fexibiity of the undeying edge-to-edge congestion conto mechanism Futue wok shoud incude investigation of issues eated to extending Distibuted-D on mutipe diff-sev domains Anothe futue wok item is to impement soft admission conto techniques in the famewok " by tuning the contact paamete uenty is set to tota netwok capacity which aows individua uses to contact fo significanty age than the netwok can hande Sevea othe impovements ae possibe to the famewok such as bette capacity estimation techniques (see Section V- bette budget estimation techniques (see Section V-B bette estimation of the paamete (see ( REFERENES [] J K MacKie-Mason and H R Vaian Picing the Intenet Kahin Bian and Kee James 99 [] Wang and H Schuzinne RNAP: A esouce negotiation and picing potoco in Intenationa Wokshop on Netwok and Opeating Systems Suppot fo Digita Audio and Video (NOSSDAV 999 pp 9 [] N Semet R R-F Liao A ampbe and A A Laza Picing povisioning and peeing: Dynamic makets fo diffeentiated Intenet sevices and impications fo netwok inteconnections IEEE Jouna on Seected Aeas of ommunications to be pubished [] A Bouch and M A Sasse Why vaue is eveything?: A use-centeed appoach to Intenet quaity of sevice and picing in Poceedings of IEEE/IFIP Intenationa Wokshop on uaity of Sevice (IWoS [] M Yukse S Kayanaaman and B Sikda Effect of picing intevas on the congestion-sensitivity of netwok sevice pices in Submitted to IWoS [] S Bake et a An achitectue fo Diffeentiated Sevices IEF RF Decembe 99 [] R Singh M Yukse S Kayanaaman and Ravichandan A compaative evauation of Intenet picing modes: Smat maket and dynamic capacity contacting in Poceedings of Wokshop on Infomation echnoogies and Systems (WIS [] A M Odyzko he economics of the Intenet: Utiity utiization picing and quaity of sevice ech Rep A & Labs 99 [9] A M Odyzko Intenet picing and histoy of communications ech Rep A & Labs [] I h Paschaidis and J N sitsikis ongestion-dependent picing of netwok sevices IEEE/AM ansactions on Netwoking vo no pp [] A Gupta D O Stah and A B Whinston Pioity picing of Integated Sevices netwoks Eds McKnight and Baiey MI Pess 99 [] F P Key A K Mauoo and D K H an Rate conto in communication netwoks: Shadow pices popotiona fainess and stabiity Jouna of Opeations Reseach Society vo 9 pp 99 [] N Semet R R-F Liao A ampbe and A A Laza Maket picing of diffeentiated Intenet sevices in Poceedings of IEEE/IFIP Intenationa Wokshop on uaity of Sevice (IWoS 999 pp 9 [] Wang and H Schuzinne Picing netwok esouces fo adaptive appications in a Diffeentiated Sevices netwok in Poceedings of onfeence on ompute ommunications (INFOOM [] A M Odyzko A modest poposa fo peventing Intenet congestion ech Rep A & Labs 99 [] D ak Intenet cost aocation and picing Eds McKnight and Baiey MI Pess 99 [] R occhi S Shenke D Estin and L Zhang Picing in compute netwoks: Motivation fomuation and exampe IEEE/AM ansactions on Netwoking vo Decembe 99 [] M Yukse and S Kayanaaman Simuating the Smat Maket picing scheme on Diffeentiated Sevices achitectue in Poceedings of ommunication Netwoks and Distibuted Systems Modeing and Simuation onfeence (NDS pat of Westen Muti-onfeence [9] S Kunniyu and R Sikant End-to-end congestion conto: Utiity functions andom osses and ecn maks in Poceedings of onfeence on ompute ommunications (INFOOM [] J Mo and J Waand Fai end-to-end window-based congestion conto IEEE/AM ansactions on Netwoking vo no pp Octobe [] S H Low and D E Lapsey Optimization fow conto I: Basic agoithm and convegence IEEE/AM ansactions on Netwoking vo no pp 999 [] A hiang Fundamenta Methods of Mathematica Economics Mc- Gaw Hi Inc 9 [] D M hiu Some obsevations on fainess of bandwidth shaing ech Rep R-99- Sun Micosystems Labs Septembe 999 [] J K MacKie-Mason and H R Vaian Picing the congestibe netwok esouces IEEE Jouna on Seected Aeas of ommunications vo pp 9 99 [] D Haison S Kayanaaman and S Ramakishnan Oveay bandwidth sevices: Basic famewok and edge-to-edge cosed-oop buiding bock Poste in SIGOMM [] UB/LBLN/VIN netwok simuato - ns (vesion 99