Decoupling QoS Control from Core Routers: A Novel Bandwidth Broker Architecture for Scalable Support of Guaranteed Services*

Transcription

1 Decouplng QoS Control from Core Routers: A Novel Bandwdth Broker Archtecture for Scalable Support of Guaranteed Servces* Zh-L Zhang y, Zhenha Duan y, Lxn Gao z, and Ywe Thomas Hou x y Unversty of Mnnesota z Smth College x Fujtsu Labs of Amerca Mnneapols, MN Northampton, MA 0060 Sunnyvale, CA fzhzhang,duang@csumnedu gao@cssmthedu thou@flafujtsucom ABSTRACT We present anovel bandwdth broker archtecture for scalable support of guaranteed servces that decouples the QoS control plane from the packet forwardng plane More specfcally, under ths archtecture, core routers do not mantan any QoS reservaton states, whether per-flow or aggregate Instead, QoS reservaton states are stored at and managed by bandwdth broker(s) There are several advantages of such a bandwdth broker archtecture Among others, t releves core routers of QoS control functons such as admsson control and QoS state management, and thus enables a network servce provder to ntroduce new (guaranteed) servces wthout necessarly requrng software/hardware upgrades at core routers Furthermore, t allows us to desgn effcent admsson control algorthms wthout ncurrng any overhead at core routers The proposed bandwdth broker archtecture s desgned based on a core stateless vrtual tme reference system developed n [20] In ths paper we focus on the desgn of effcent admsson control algorthms under the proposed bandwdth broker archtecture We consder both per-flow guaranteed delay servces and class-based guaranteed delay servces wth flow aggregaton We demonstrate how admsson control can be done on an entre path bass, nstead of on a hop-byhop" bass Such an approach may sgnfcantly reduce the complexty of the admsson control algorthms We also study the mpact of dynamc flow aggregaton on the desgn of class-based admsson control algorthms Based on the proposed bandwdth broker archtecture, we devse effectve mechansms to crcumvent the problem caused by dynamc flow aggregaton Λ Ths work was supported n part by NSF under the CA- REER Award NCR Any opnons, fndngs, and conclusons or recommendatons expressed n ths paper are those of the authors and do not necessarly reflect the vews of NSF Permsson to make dgtal or hard copes of all or part of ths work for personal or classroom use s granted wthout fee provded that copes are not made or dstrbuted for proft or commercal advantage and that copes bear ths notce and the full ctaton on the frst page To copy otherwse, or republsh, to post on servers or to redstrbute to lsts, requres pror specfc permsson and/or a fee SIGCOMM '00, Stockholm, Sweden Copyrght 2000 ACM /00/0008 $500 INTRODUCTION The ablty to provde end-to-end guaranteed servces (eg, guaranteed rate or delay) for networked applcatons s a desrable feature of the future Internet To enable such servces, Qualty-of-Servce (QoS) support from both the network data plane (eg packet schedulng) and the control plane (eg, admsson control and resource reservaton) s needed For example, under the Internet IETF Integrated Servces (IntServ) archtecture, schedulng algorthms such as Weghted Far Queueng (WFQ), Vrtual Clock (VC) and Rate-Controlled Earlest Deadlne Frst (RC-EDF) [5, 8] were developed to support the Guaranteed Servce [] Furthermore, a sgnalng protocol, RSVP, for settng up end-toend QoS reservaton along a flow's path was also proposed and standardzed [4, 9] However, due to ts need for performng per-flow management at core routers, the scalablty of the IntServ archtecture has been questoned To address the ssue of scalablty, several alternatve archtectures have been proposed n recent years, among others, the IETF Dff- Serv model [2] and the more recent core stateless approach usng dynamc packet state [2, 3] In addressng the ssue of scalablty n QoS provsonng, the majorty of the recent works have focused on elmnatng per-flow router state management n the data plane For example, under the DffServ archtecture no per-flow QoS state s mantaned at core routers, and user flows are aggregated and processed based on a number of servce bts carred n the packet headers Consequently, only coarse-gran QoS support s provded to users In contrast, the core stateless approach amsatprovdng end-to-end per-flow guarantees wthout the complextyof per-flow QoS management To accomplsh ths goal, a novel schedulng mechansm the Core Jtter Vrtual Clock (CJVC) s developed n [2] to support end-to-end per-flow delay guarantees wthout requrng per-flow states n core routers Attempts at reducng the complexty of QoS control plane have mostly followed the conventonal hop-by-hop reservaton set-up approach adopted by RSVP through QoS control state aggregaton In the hop-by-hop reservaton set-up approach, each router mantans ts own QoS state database and admnsters a local admsson control test to determne whether a flow reservaton set-up request can be honored or not To ensure consstency among the QoS state databases mantaned by ndvdual routers, RSVP uses soft QoS states, whch requres perodc state exchange among routers, thus 7

2 ncurrng addtonal communcaton and processng overheads These overheads can be reduced through a number of control state reducton technques [6, 6, 7] Other hop-by-hop reservaton set-up protocols have also been proposed [8, 5] In general, the conventonal hop-by-hop reservaton set-up approach tes such QoS control functons as admsson control, resource reservaton and QoS state managementtocore routers, whether per-flow or aggregate QoS states are mantaned at core routers Therefore t requres admsson control and QoS state management modules to be nstalled at every router to support QoS provsonng In the context of the DffServ archtecture, an alternatve, and perhaps more attractve, approach the bandwdth broker approach s proposed n [7] to support the so-called Premum Servce In ths approach, admsson control, resource provsonng and other polcy decsons are performed by a centralzed bandwdth broker (BB) n each network doman Although several mplementaton efforts n buldng bandwdth brokers are under way (see, eg, [4]), so far many ssues regardng the desgn of bandwdth brokers, such as admsson control and QoS provsonng, have not been addressed adequately n the lterature For example, under the proposed BB archtecture n [7], t appears that only coarse-gran QoS provsonng can be supported and that explct confguraton of core routers s stll needed to provde QoS guarantees [4] Clearly, the delverable QoS performance wll hnge on how frequently such confguraton s performed In addton, t s not clear how admsson control should be performed under such a BB archtecture, n partcular, whether core routers are stll requred to perform local admsson control and QoS state management In ths paper we present a novel bandwdth broker archtecture for support of QoS provsonng that decouples the QoS control plane from the data forwardng plane Ths BB archtecture s desgned under the core stateless framework, usng the technque of dynamc packet state [3] Under our proposed BB archtecture, the QoS reservaton states are stored at and managed solely by the BB(s) n a network doman, and no or mnmal confguraton of core routers s requred In other words, core routers are completely releved of QoS control functons such as admsson control and state management (whether per-flow or aggregate), makng them potentally more effcent Ths decouplng of data plane and QoS control plane s appealng n several aspects Among others, t allows anetwork servce provder to ntroduce new QoS servces wthout necessarly requrng software/hardware upgrades at core routers Furthermore, as we wll demonstrate, t also enables the deployment of sophstcated QoS provsonng and admsson control algorthms to optmze network utlzaton n a network-wde fashon Such network-wde optmzaton s dffcult, f not mpossble, under the conventonal hop-by-hop reservaton set-up approach The objectve of ths paper s to demonstrate how guaranteed servces (both per-flow and class-based) can be supported usng the proposed BB archtecture, despte the fact that no QoS states are mantaned at core routers We focus on guaranteed servces partly because these servces are well-defned and understood, and partly because a unfyng core stateless framework the vrtual tme reference system [20] has been developed that provdes a QoS abstracton of the data plane for supportng guaranteed delay and rate servces Usng guaranteed servces as examples, we llustrate how admsson control can be performed usng the proposed BB archtecture wthout the assstance of core routers In partcular, we develop a path-orented approach to the desgn of effcent admsson control algorthms under the proposed BB archtecture We establsh that the proposed bandwdth broker archtecture s capable of supportng guaranteed servces wth the same granularty and expressve power (f not more) as the IntServ/Guaranteed Servce model, despte the fact that all QoS reservaton states are removed from core routers and mantaned solely at the bandwdth broker Ths s acheved wthout the potental complexty and scalablty problems of the IntServ model However, the bandwdth broker approach to QoS provsonng ntroduces a set of new ssues In partcular, the scalablty of the BB archtecture ts ablty to manage a large number of QoS control states and process a large volume of user flow QoS requests s an mportant ssue that must be nvestgated To partally address ths ssue, n ths paper we also consder the support of coarse-gran class-based guaranteed servces usng the proposed BB archtecture Va flow aggregaton, the number of QoS states mantaned by the BB can be reduced, and the complexty of admsson control operatons can be lowered, thereby enhancng the processng capacty of the BB However, n the context of guaranteed servces, (dynamc) flow aggregaton can havean undesrable transent effect that may result n delay bound volaton, f proper care s not taken We llustrate how ths problem can be solved usng relatvely smple mechansms under the proposed BB archtecture Our work s only a frst step towards addressng many problems that stll reman n the desgn and mplementaton of the proposed BB archtecture For example, to further mprove scalablty, a dstrbuted (or herarchcal) archtecture consstng of multple BBs may be necessary to support QoS provsonng n a large network doman Such an archtecture ntroduces many new desgn and mplementaton ssues The problem of nter-doman QoS reservaton and servcelevel agreement [2, 7] s another mportant ssue that must be addressed In addton, supportng statstcal or other forms of QoS guarantees usng the proposed BB archtecture s also a challengng problem Clearly, all these ssues must be satsfactorly resolved before the proposed BB archtecture can be deployed n practce The remander of ths paper s structured as follows Secton 2 outlnes the proposed bandwdth broker archtecture, where we also brefly revew the vrtual tme reference system developed n [20], and present a hgh-level overvew of the admsson control operatons under the proposed BB archtecture In Secton 3, we desgn effcent path-orented admsson control algorthms for per-flow guaranteed servces These admsson control algorthms are extended n Secton 4 to support class-based guaranteed servces wth dynamc flow aggregaton Smulaton nvestgaton s conducted n Secton 5, and the paper s concluded n Secton 6 Ths phenomenon s not unque to the core stateless framework, and may occur n any guaranteed servces wth dynamc flow aggregaton 72

3 Step : new flow servce request new flow arrval Edge condtoner Step 2: admsson control process Control plane BB S S 2 S S h Core router A network doman Data plane Step 3: decson (accept/reject) Management nformaton bases (MIBs) - topology nformaton base - polcy nformaton base - flow nformaton base - path QoS state nformaton base - node QoS state nformaton base Servce modules - admsson control module - QoS routng module - polcy control module Fgure : Illustraton of a bandwdth broker (BB) and ts operaton n a VTRS network doman 2 OVERVIEW OF THE PROPOSED BAND- WIDTH BROKER ARCHITECTURE In ths secton we outlne the proposed bandwdth broker archtecture for support of guaranteed servces wthn a sngle network doman Ths bandwdth broker archtecture s bult upon the vrtual tme reference system (VTRS) developed n [20], a core stateless framework that provdes a QoS abstracton of the data plane Under the proposed BB archtecture, core routers perform only data plane functons such aspacket schedulng and forwardng, usng the dynamc packet state carred n packet headers No QoS states, whether per-flow or aggregate, are mantaned at any core routers Instead, all QoS states are solely mantaned at and managed by the BB(s), no or mnmal confguraton of core routers s needed Furthermore, all QoS control plane functons such as admsson control and resource reservaton are performed by the BB(s), wthout nvolvement of core routers Fgure llustrates the basc components and operatons of the proposed BB archtecture as well as ts relatonshp to the data plane As shown n Fgure, a bandwdth broker 2 (BB) conssts of several servce modules (e, servers) such as admsson control, routng and polcy control The routng module peers wth routers to obtan the topology nformaton of the network doman [] and s responsble for path selecton and set-up (usng, eg, MPLS [0]) The polcy control module mantans a polcy nformaton base and s responsble for network polcy admnstraton The admsson control module mantans the QoS states of the network doman, whch are stored n several management nformaton bases (see Secton 22), and s responsble for admsson control and resource reservaton In ths paper we wll focus prmarly on the operatons of the admsson control module for support of guaranteed ser- 2 In ths paper we assume that there s a sngle centralzed BB for a network doman In practce, a dstrbuted or herarchcal archtecture consstng of multple BBs can be employed to mprove relablty and scalablty We wll explore these ssues n future research Note that an mportant advantage of the BB approach s that the relablty and scalablty ssues of the QoS control plane (e, the bandwdth broker archtecture) can be addressed separately from, and wthout ncurrng addtonal complexty to, the data plane vces In partcular, we wll demonstrate how effcent admsson control can be performed under the proposed BB archtecture Before we embark on the problem of admsson control usng the proposed BB archtecture, we need to understand the basc operatons of the vrtual tme reference system and ts mplcaton on QoS provsonng In the followng, we frst brefly revew the vrtual tme reference system, and then present a hgh-level descrpton of the admsson control module and the QoS state nformaton bases t mantans 2 The Vrtual Tme Reference System The vrtual tme reference system s desgned as a unfyng schedulng framework based on whch both the per-hop behavors of core routers (n terms of ther abltes to provde delay and bandwdth guarantees) and the end-to-end propertes of ther concatenaton can be characterzed Ths unfyng schedulng framework enables core routers to focus on packet schedulng and forwardng functons based on the packet state carred n packet headers wthout drect nvolvement n QoS control The key construct n the vrtual tme reference system s the noton of packet vrtual tme stamps, whch, as part of the packet state, are referenced and updated as packets traverse each core router Packet vrtual tme stamps are computed usng only the packet state carred by packets (plus a couple of fxed parameters assocated wth core routers), and thus the vrtual tme reference system s core stateless Conceptually, the vrtual tme reference system conssts of three logcal components: packet state carred by packets, edge traffc condtonng at the network edge, and per-hop vrtual tme reference/update mechansm at core routers (see Fgures 2 and 3) These three components are brefly descrbed below A more detaled descrpton can be found n [20] Edge Traffc Condtonng Edge traffc condtonng playsakey role n the VTRS, as t ensures that the packets of a flow 3 wll never be njected nto the network core at a rate exceedng ts reserved rate Formally, foraflow j wth a reserved rate r j,thenter-arrval tme of two consecutve packets of the flow at the frst hop core router s such that ^a j;k+ ^a j;k Lj;k+ r j, where ^a j;k denotes the arrval tme of the kth packet p j;k of flow j at the network core, L j;k the sze of packet p j;k, and r j the reserved rate of flow j Packet State After gong through the edge condtoner at the network edge, packets enterng the network core carry n ther packet headers certan packet state nformaton that s ntalzed and nserted at the network edge The packet state carred bypacket p j;k of a flow j contans three types of nformaton: ) a rate-delay parameter par hr j ;d j of the flow, determned by the bandwdth broker based on flow j's QoS requrement; 2) the vrtual tme stamp ~! j;k of the packet that s assocated wth the router currently beng traversed (t s ntalzed to ^a j;k, the actual tme t leaves the edge condtoner and enters the frst core router along the flow's path); and 3) the vrtual tme adjustment term 3 Here a flow can be ether an ndvdual user flow, or an aggregate traffc flow of multple user flows, defned n any approprate fashon 73

4 Core router Core Stateless Vrtual Tme Plane ~ j,k ~ j,k ~ j,k w v w + Edge condtoner Packet state Vrtual Fnsh Tme Computaton + ~ d j,k Core Stateless Vrtual Tme Update + Ψ + π,+ Schedulng Blackbox Real Tme Plane Network core a ^ j,k ^j,k f Fgure 2: A conceptual network model n the vrtual tme reference system Fgure 3: Vrtual tme reference system: per-hop behavor and operatons ff j;k of the packet, a parameter that s computed at the edge and used to ensure that the vrtual spacng property (see below) of vrtual tme stamps s satsfed [20] Vrtual Tme Reference/Update Mechansm and Per- Hop Router Behavor Characterzaton In the conceptual framework of the vrtual tme reference system, each core router s equpped wth a per-hop vrtual tme reference/update mechansm to mantan the contnual progresson of the vrtual tme emboded by the packet vrtual tme stamps Ths vrtual tme stamp ~! j;k represents the arrval tme of packet p j;k of flow j at the th core router n the vrtual tme, and thus t s also referred to as the vrtual arrval tme of the packet at the core router The vrtual tme stamps ~! j;k 's assocated wth packets of flow j satsfy the followng two mportant propertes: ) vrtual spacng property: ~! j;k+ ~! j;k Lj;k+ r j, and 2) the realty check property: ^a j;k» ~! j;k, where ^a j;k denotes the actual arrval tme of packet p j;k at router In order to ensure that these two propertes are satsfed, the vrtual tme stamps must be approprately referenced or updated as packets enter or leave a core router The referencng/updatng rule depends on the schedulng algorthm (or scheduler) employed by a core router We dstngush two types of schedulers: rate-based and delay-based, dependng on how thevrtual deadlne and vrtual fnsh tme are computed for packets traversng t For example, f the scheduler S at the th router s rate-based, packet p j;k s assocated wth the vrtual deadlne ~ d j;k fnsh tme s defned as ~ν j;k delay-based, ~ d j;k = d j and ~ν j;k = L j;k =r j +ff j;k and ts vrtual + d ~ j;k Whereas, f S s + d ~ j;k =~! j;k =~! j;k The per-hop behavor of a core router (or rather, ts scheduler) s characterzed by an error term, whch s defned wth respect to the vrtual fnsh tme and actual fnsh tme j;k of packets at the router Let ^f denote the actual tme packet p j;k departs the scheduler S We say that S can guarantee flow j ts reserved rate r j (f S s rate-based) or ts delay parameter d j (f S s delay-based) wth an error j;k term Ψ, f for any k, ^f» ~ν j;k +Ψ In other words, each packet of flow j s guaranteed to depart S by the tme ~ν j;k +Ψ =~! j;k + d ~ j;k +Ψ Gven the error term Ψ of the scheduler S, the vrtual tme stamp of packet p j;k after t has traversed S s updated usng the followng concatenaton rule: ~! j;k + = ~ν j;k +Ψ + ß =~! j;k + d ~ j;k +Ψ + ß () where ß denotes the propagaton delay from the th router to the next-hop router along the flow's path In [20] t s shown that usng the concatenaton rule () the vrtual spacng and realty check propertes of vrtual tme stamps are satsfed at every router End-to-End Delay Bound and QoS Abstracton of Data Plane Usng the vrtual tme reference system outlned above, the delay experenced by packets of a flow across the network core can be upper bounded n terms of the ratedelay parameter par of a flow and the error terms of the routers along the flow's path Suppose there are total h hops along the path of flow j, of whch q routers employ ratebased schedulers, and h q delay-based schedulers Then for each packet p j;k of flow j, wehave ^f h j;k ^aj;k» d j core = q Lj;max r j +(h q)d j + X (Ψ + ß); (2) where L j;max s the maxmum packet sze of flow j Suppose the traffc profle of flow j s specfed usng the standard dual-token bucket regulator (ff j ;ρ j ;P j ;L j;max ) where ff j L j;max s the maxmum burst sze of flow j, ρ j s the sustaned rate of flow j, P j s the peak rate of flow j Then the maxmum delay packets of flow j experenced at the edge shaper s bounded by d j edge = Ton j P j r j r j + Lj;max r j ; (3) where T j on =(ff j L j;max )=(P j ρ j ) Hence the end-to-end delay bound for flow j s gven by d j e2e = dj edge + dj core = Ton j P j r j r j X +(q+) Lj;max r j +(h q)d j + (Ψ + ß):(4) Observe that the end-to-end delay formula s qute smlar to that specfed n the IETF Guaranteed Servce usng the WFQ as the reference system In ths sense, the vrtual tme reference system provdes a conceptual core stateless 74

5 framework based on whch per-hop behavor (e, ts ablty to support delay guarantees) of a core router can be characterzed usng the noton of error term Ths smple abstracton enables us to derve end-to-end delay bounds for flows traversng an arbtrary concatenaton of core routers wthn a network doman Furthermore, the vrtual tme reference system does not mandate any specfc schedulng mechansms to be mplemented n a network doman as long as ther abltes to provde delay guarantees can be characterzed usng the noton of error term In fact, n [20] t s shown that almost all known schedulng algorthms can thus be characterzed, be they core stateless or stateful In addton, the vrtual tme reference system leads to the desgn of a set of new core stateless schedulng algorthms (both rate-based and delay-based) Two representatve examples of such core stateless schedulng algorthms are: the ratebased core stateless vrtual clock (C 6S VC) and delay-based vrtual tme earlest deadlne frst (VT-EDF) schedulng algorthms The core stateless vrtual clock(c 6S VC) s a work-conservng counterpart of the CJVC schedulng algorthm developed n [2] It servces packets n the order of ther vrtual fnsh tmes It s shown n [20] that as long as the total reserved rate of flows traversng P a C 6S VCscheduler does not exceed ts capacty (e, j rj» C), then the C 6S VC scheduler can guarantee each flow ts reserved rate r j wth the mnmum error term Ψ = L Λ;max =C, where L Λ;max s the largest packet sze among all flows traversng the C 6S VCscheduler Unlke the conventonal rate-controlled EDF, VT-EDF supports delay guarantees wthout per-flow rate control, and thus s core stateless Lke C 6S VC, VT-EDF also servces packets n the order of ther vrtual fnsh tmes The VT- EDF scheduler can guarantee each flow ts delay parameter d j wth the mnmum error term Ψ = L Λ;max =C, f the followng schedulablty condton s satsfed [20]: NX j= [r j (t d j )+L j;max ] ft d j g» Ct; for any t 0 (5) where we assume that there are N flows traversng the VT- EDF scheduler wth 0» d» d 2»»d N The ndcator functon ft d j g =ft d j, 0 otherwse 22 The Admsson Control Module: QoS State Informaton Bases and Basc Operatons In order to support guaranteed servces under the proposed bandwdth broker archtecture, the admsson control module mantans several QoS state nformaton bases They nclude: ) a flow nformaton base, where nformaton regardng ndvdual flows, such asflow d, traffc profle (eg, (ff j ;ρ j ;P j ;L j;max )), servce profle (eg, end-to-end delay requrement D j ), and QoS reservaton (eg, the rate-delay parameter par hr j ;d j ), s mantaned; 2) a node QoS state nformaton base, where nformaton regardng each router n the network doman, such as the bandwdth, buffer capacty, type of scheduler used (e, rate- or delay-based) and ts error term, and current QoS reservaton on each outgong lnk of the router, s mantaned ; and 3) a path QoS state nformaton base, where nformaton regardng the characterstcs of paths between ngress and egress routers s mantaned Examples of path characterstcs are the hop number of a path, the sum of the router error terms and propagaton delay along the path, and the mnmal resdual bandwdth along the path As we shall see n the next secton, mantanng separate path-level QoS state nformaton allows us to perform effcent admssblty test on an entre path bass We now brefly dscrbe the basc operatons of the BB, focusng, n partcular, on those of the admsson control module (see Fgure ) When a new flow wth a traffc profle (ff j ;ρ j ;P j ;L j;max ) and an end-to-end delay requrement D j;req arrves at an ngress router, the ngress router sends a new flow servce request message to the BB Upon recevng the servce request, the BB frst checks for polcy nformaton base to determne whether the new flow s admssble If not, the request s mmedately rejected Otherwse, the BB selects a path (from the ngress router to an approprate egress router n the network doman) for the new flow, and decde whether the flow can be admtted Generally speakng, the admsson control procedure conssts of two phases: ) admssblty test phase durng whch tsdeter- mned whether the new flow servce request can be accommodated and how much network resources must be reserved f t can be accommodated; and 2) bookkeepng phase durng whch the relevant management nformaton bases wll be updated, f the flow s admtted If the flow s admtted, the BB wll also pass (usng, eg, COPS [3]) the QoS reservaton nformaton such ashr j ;d j to the ngress router, so that t can set up a new or re-confgure an exstng edge condtoner (whch s assumed to be co-located at the ngress router) for the new flow As the packets of the flow arrve at the ngress router, the edge condtoner wll approprately ntalze and nsert these packet states, before njectng them nto the core of the network doman In the remander of ths paper we demonstrate how effcent admsson control can be performed under the proposed BB archtecture In Secton 3 we present a path-orented approach to perform effcent admsson control operatons for support of per-flow guaranteed servces Unlke the conventonal hop-by-hop approach whch performs admsson control ndvdually based on the local QoS state at each router along a path, ths path-orented approach examnes the resource constrants along the entre path smultaneously, and makes admsson control decson accordngly Clearly, such a path-orented approach s only possble because the avalablty of QoS state nformaton of the entre path at the BB Note that although any bandwdth broker archtecture can adopt a smlar path-orented approach toresource allocaton, under our BB archtecture no local admsson control test or explct resource (re-)confguraton s needed at any core router, thanks to the use of dynamc packet state n the data path As a result, we can sgnfcantly reduce the tme of conductng admsson control and resource reservaton Furthermore, we can also perform path-wde optmzaton when determnng resource allocaton for a new flow In Secton 4, we study the problem of admsson control for class-based guaranteed delay servces, where a fxed number of guaranteed delay servce classes are offered n a network doman As n the DffServ, there are two mportant benefts n provdng class-based servces under our framework Frst, aggregatng flows n a small number of servce classes greatly smplfes the mplementaton of the data plane (n partcular, the edge condtoners) Second, t also enhances 75

6 the scalablty of the QoS control plane (e, the BB archtecture) For example, the number of QoS states that need to be mantaned by a BB can be sgnfcantly reduced Ths leads to faster admsson control operatons, thereby ncreasng the number of flow servce requests a BB can handle However, as ponted out n the ntroducton, n class-based guaranteed servces certan transent behavor of dynamc flow aggregaton must be taken care of to avod potental delay bound volaton In Secton 4, we nvestgate the problem of dynamc flow aggregaton and devce smple mechansms to effectvely crcumvent ths problem 3 ADMISSION CONTROL FOR PER-FLOW GUARANTEED SERVICES In ths secton, we study the problem of admsson control for support of per-flow guaranteed servces under the proposed bandwdth broker archtecture In partcular, we present a path-orented approach to perform effcent admsson control operatons We llustrate how ths approach works by frst consderng a smple case, where only rate-based schedulers are employed along the path of a new flow We then look at the general case where the path of a new flow conssts of both rate-based and delay-based schedulers We present an effcent admsson control algorthm that ) determnes whether a new flow s admssble by examnng the resource constrants along the entre path smultaneously, and 2) mnmzes the bandwdth allocaton along the path for the new flow, f t s admssble 3 Path wth Only Rate-based Schedulers We frst consder the smple case where we assume that the path P for a new flow ν conssts of only rate-based schedulers Hence n ths case, we only need to determne whether a reserved rate r ν can be found for the new flow for t to be admtted The delay parameter d ν wll not be used For smplcty of exposton, we assume that a scheduler suchascore-stateless vrtual clock (C 6S VC) or corejtter vrtual clock (CJVC) s employed at the routers S along P Let F be the set of flows currently traversng S, and C be the total bandwdth at S Then as long as Pj2F rj» C, S can guarantee each flow j ts reserved rate r j We usec S res to denote the resdual bandwdth at P S,e,C S res = C j2f rj Let (ff ν ;ρ ν ;P ν ;L ν;max ) be the traffc profle of a new flow ν, and D ν;req be ts end-to-end delay requrement Let h be the number of hops n P, the path for the new flow From (4), n order to meet ts end-to-end delay requrement D ν;req, the reserved rate r ν for the new flow ν must satsfy: and ρ ν» r ν» P ν D ν;req Ton ν P ν r ν r ν +(h+) Lν;max r ν +Dtot; P (6) where T ν on =(ff ν L ν;max )=(P ν ρ ν ) and D P tot = P 2P (Ψ+ ß ) Furthermore, r ν must not exceed the mnmal resdual bandwdth Cres P along path P, where Cres P =mn 2P C S res s mantaned, as a path QoS parameter assocated wth P, n the path QoS state MIB Let r ν mn be the smallest r ν that satsfes (6), e, r ν mn = [T ν onp ν +(h +)L ν;max ]=[D ν;req D P tot + T ν on] Defne r low fea =maxfρ ν ;r ν mng and r up fea = mnfp ν ;C P resg: Then R Λ fea = [r low ] s the feasble rate range, from whch a feasble reserved rate r ν can be selected Clearly, f R Λ fea s empty, the servce request of the new flow ν must fea;rfea up be rejected Otherwse, t s admssble, and r ν = r low fea s the mnmal feasble reserved rate for the new flow ν Gven that the path QoS parameters D P tot and C P res assocated wth P are mantaned n the path QoS state MIB, the above admssblty test can be done n O() 32 Path wth Mxed Rate- and Delay-based Schedulers We now consder the general case where the path P for a new flow ν conssts of both rate-based and delay-based schedulers In ths case, we need to determne whether a rate-delay parameter par hr ν ;d ν can be found for the new flow ν for t to be admtted Because of the nter-dependence of the reserved rate r ν and the delay parameter d ν n the end-to-end delay bound (4) as well as the more complex schedulablty condton (5) for the delay-based schedulers, the admssblty test for ths case s less straghtforward In ths secton, we present an effcent admsson control algorthm usng the path-orented approach that mnmzes the bandwdth allocaton along the path of the new flow: f the new flow ν s admssble, ths admsson control algorthm fnds a feasble rate-delay parameter par hr ν ;d ν such that r ν s the mnmal feasble rate In other words, no other rate-delay parameter par hr ν0 ;d ν0 such that r ν0 < r ν s feasble Let q be the number of rate-based schedulers and h q the number of delay-based schedulers along path P For smplcty of exposton, we assume that the rate-based schedulers S along path P employ C 6S VC (or any smlar) schedulng algorthm whose schedulablty condton s P j2f rj» C, whereas the delay-based schedulers S employ the VT- EDF schedulng algorthm, whose schedulablty condton s gven n (5) As before, let (ff ν ;ρ ν ;P ν ;L ν;max ) be the traffc profle of the new flow ν, and D ν;req ts end-to-end delay requrement In order for the new flow ν to be admtted along the path P wth a rate-delay parameter par hr ν ;d ν, ts end-to-end delay requrement D ν;req must be satsfed, namely, and ρ ν» r ν» P ν D ν;req Ton ν P ν r ν r ν +(q+) Lν;max r ν +(h q)d ν +Dtot: P (7) Furthermore, the schedulablty condton at each scheduler S must not be volated Let Cres P be the mnmal resdual bandwdth along P, e, Cres P = mn 2P C S res Then from the schedulablty condtons for the rate- and delay-based schedulers, we must have r ν» Cres P In addton, for every delay-based scheduler S along P, let hr k ;d k be the ratedelay parameter par of flow k, where k 2F Then for each 76

7 0 t ν = h q Dtot P + T on ν ] Let m Λ such that d mλ <t ν» d mλ 2 for m = m Λ ;m Λ ;::: ;2; 3 R m fea ψ [rfea m;l fea ] 4 5 R m del ψ [rdel m;l del ] f (R m fea Rm del == ;) 6 7 f (R m fea == ;jjrm del == ;jjrm;r fea <rm;l del ) break wth d ν = d m 8 else /*R m fea R m del 6= ;*/ 9 f (rfea m;l del ) 0 r ν ψ rdel m;l ψ t ν Ξν rν break wth d ν 2 f (d ν >t ν ) no feasble value found 3 else return d ν nterval shrnkng at each teraton nterval movng towards left at each teraton R [ del ] [ fea ] m,l R m r del r r r d 0 = 0 d 2 dm- dm d dm *- dm* dm m m,r m,l m,r del fea fea d ν t ν (constant) rate d = M+ delay Fgure 4: Path-orented admssblty test for mxed rate/delay-based schedulers Fgure 5: The relatonshp between feasble range R m fea and delay constrant ranger m del X k 2F, S 2P such that d k d ν,wemust have [r j (d k dj )+Lj;max ] fj2f:d j»dk g +[r ν (d k dν )+L ν;max ]» Cd k : (8) Hence, n order for hr ν ;d ν to be a feasble rate-delay parameter par for the new flow ν, we must have that r ν 2 [ρ ν ; mnfp ν ;C P resg] and that r ν and d ν must satsfy (7) and (8) In the followng, we present an effcent algorthm to dentfy the feasble rate-delay parameter par hr ν ;d ν for a new flow ν Frst, we ntroduce some notaton Defne t ν = h q (Dν;req Dtot P +Ton), ν Ξ ν = h q [T onp ν ν +(q +)L ν;max ] From (7) we see that the followng condton holds, d ν» t ν Ξν r ν : (9) For any flow k traversng a delay-based scheduler S such that d k d ν, defne S k = C d k X fj2f:d j»dk g [r j (d k d j )+L j;max ]: Let F del be the unon of the sets of the flows at all the delaybased schedulers along the path P of flow ν, e, F del = [fj 2F : S s delay-basedg Suppose there are a total of M dstnctve delay parameters assocated wth the flows n F del Let these dstnctve M delay parameters be denoted by d ;d 2 ;::: ;d M, where 0» d < d 2 < < d M For m =; 2;::: ;M,defne S m = mnfs k : k 2F and d k = d m ; S s delay-basedg: Note that S k denotes the mnmum resdual servce over any tme nterval of length d k at scheduler S Therefore S m represents the mnmal resdual servce among all the delay-based schedulers at tme d m Hence we refer to S m as the mnmal resdual servce ofpath P at tme d m Defne d 0 = 0 and d M+ = Then f the new flow ν s admssble, there must exst a rate-delay parameter par hr ν ;d ν,whered ν 2 [d m ;d m ) for some m =; 2;::: ;M+ From (9), t s clear that 0» d ν» t ν Let m Λ be such that d mλ <t ν» d mλ Clearly, [d mλ ;d mλ ) s the rghtmost delay nterval that may contan a feasble d ν For m = m Λ ;m Λ ;::: ;2;, defne R m fea = [r m;l where fea ;rm;r fea ], r fea m;l Ξ = ν maxf t ν d m ;ρν g; rfea m;r Ξ = ν mnf t ν d m ;Pν ;Cres P g: (0) Smlarly, defne R m del =[r m;l r m;r del = mn ρ del ;rm;r del mn Ξν +L ν;max m»k<m Λf t ν d k ], where g; mn k m Λ S k Ξ ν L ν;max d k t ν r del m;l = max S k Ξ ν L ν;max m»k<m Λf d k t ν g () R m fea and R m del have the followng mportant monotoncty propertes, as llustrated n Fgure 5 When we movefrom the current delay nterval [d m ;d m ) to the next delay nterval to the left [d m 2 ;d m ), the correspondng feasble rate range R m fea determned by (0) shfts to the left In contrast, the correspondng feasble rate range R m del determned by thedelay constrants () shrnks: the left edge rdel m;l ncreases whle the rght edgerdel m;r decreases (For an explanaton why these propertes hold, see [2]) Based on ths observaton, we obtan the followng theorem, whch states whether a feasble rate-delay par hr ν ;d ν exsts such that d ν 2 [d m ;d m ] Theorem If R m fea R m del s empty, then no feasble rate-delay pars hr ν ;d ν exst such that d ν 2 [d m ;d m ] Furthermore, f R m fea s empty, or R m del s empty, or r m;r rdel m;l fea <, then no ntervals to the left contan a feasble soluton ether More precsely, no feasble rate-delay pars hr ν ;d ν exst such that d ν 2 [0;d m ) If R m fea R m del s not empty, then a feasble rate-delay par hr ν ;d ν exsts such that d ν 2 [d m ;d m ] Furthermore, f rfea m;l <rm;l del, then rν = rdel m;l s the smallest rate such that there exsts some d ν 0 for whch hr ν ;d ν safeasble ratedelay par In other words, any rate-delay par hr ν ;d ν where r ν <rdel m;l s not feasble Based on Theorem, the admsson control algorthm s presented (n pseudo-code) n Fgure 4 Note that the tme complexty of the algorthm s O(M), and n general, we have ff ; 77

8 M»jF del j» P S s delay-based jf j Hence the complexty of the algorthm hnges only on the number of dstnctvedelay parameters supported by the schedulers along the path of the new flow Ths reducton n complexty can be sgnfcant f many flows have the same delay requrements Ths s partcularly the case when we consder class-based admsson control wth flow aggregaton where a number of fxed delay classes are pre-defned Clearly ths reducton n complexty s acheved because our admsson control algorthm consders all the admssblty constrants along a path smultaneously Ths s not possble usng the conventonal hop-by-hop reservaton set-up approach (eg, as employed n the IETF IntServ model wth RSVP) 4 CLASS-BASED GUARANTEED SERVICES AND ADMISSION CONTROL WITH DY- NAMIC FLOW AGGREGATION In ths secton we address the problem of admsson control for class-based guaranteed servces under the proposed BB archtecture The class-based guaranteed delay servce model s schematcally shown n Fgure 6 A new user flow wll be placed n one of the delay servce classes f t can be admtted nto the network All flows n the same delay servce class that traverse the same path wll be aggregated nto a sngle macroflow Ths macroflow s shaped usng an aggregate reserved rate at the edge condtoner, and s guaranteed wth an end-to-end delay bound determned by the servce class We refer to the ndvdual user flows consttutng a macroflow as the mcroflows Akey ssue n the desgn of admsson control for ths classbased servce model s the problem of dynamc flow aggregaton The dynamcs comes from the fact that mcroflows may jon or leave amacroflow at any tme Hence the aggregate traffc profle for the macroflow may change dynamcally, and as a result, the reserved rate for the macroflow may need to be adjusted accordngly Dynamc flow aggregaton can cause certan undesrable effect on the end-to-end delay experenced by the macroflow, whch we wll descrbe shortly n Secton 4 Here we note that the exstng work on traffc aggregaton (n partcular, n the context of guaranteed servces, see, eg [6, 9]) has mplctly assumed statc flow aggregaton: a macroflow s an aggregaton of n fxed mcroflows, wth no new mcroflows jonng or exstng consttuent mcroflows leavng n the duraton of the macroflow As far as we areaware, ths problem of dynamc flow aggregaton has not been dentfed nor addressed before n the lterature 4 Impact of Dynamc Flow Aggregaton on End-to-End Delay In ths secton we llustrate the potental negatve mpact of dynamc flow aggregaton on end-to-end delay guarantee provsonng: f proper care s not taken, mcroflow arrvals or departures n an aggregate macroflow can cause potental delay bound volaton We use an example to llustrate ths problem of dynamc flow aggregaton Frst let us ntroduce some notaton and assumptons Consder a macroflow ff whch currently conssts of n mcroflows Let (ff j ;ρ j ;P j ;L j;max ) be the traffc profle of the mcroflow j,» j» n For smplcty, we wll use a dual-token bucket regulator, (ff ff ;ρ ff ;P ff ;L ff;max ), as the aggregate traffc profle for the macroflow ff Hence we have ff ff = P n j= ff j, ρ ff = P n j= ρj, P ff = P n j= P j,andl ff;max = P n j= Lj;max P Note that L ff;max n = j= Lj;max,asapacket of the maxmum sze may arrve from each of the n mcroflow atthe same tme In contrast, snce only one packet from the macroflow ff may leave the edge condtoner at any gven tme, the maxmum burst" the macroflow may carry nto the network core s max n j= L j;max Let P denote the path of the macroflow ff, and L P;max denote the maxmum packet sze permssble n a macroflow along P Then L P;max max n j= L j;max Wthout loss of generalty, we assume that L P;max s fxed Suppose that we treat the macroflow ff as statc, e, wth no mcroflows jonng or leavng at any tme Let hr ff ;d ff be the rate-delay parameter par reserved for the macroflow For smplcty, assume that path P conssts of only ratebased schedulers (h of them n total) Then from the endto-end delay formula (4), the end-to-end delay experenced by packets from the macroflow ff s bounded by d ff e2e = d ff edge +dff core = Ton ff P ff r ff r ff + Lff;max r ff +h LP;max r ff +Dtot P (2) P where Dtot P = 2P (Ψ + ß) Assume that a new mcroflow ν jons the exstng macroflow ff at tme t Λ Let (ff ν ;ρ ν ;P ν ;L ν;max ) be the traffc profle of the new mcroflow Denote the new" macroflow after the mcroflow ν has been aggregated by ff 0, and let (ff ff0 ;ρ ff0 ;P ff0 ;L ff0 ;max ) be ts traffc profle Suppose that the reserved rate for the new" macroflow ncreases from r ff to r ff0 at tme t Λ We frst show that the packets from the new" macroflow may experence a worst-case delay at the edge condtoner that s larger than d ff0 edge = Ton ff0 P ff0 r ff0 + Lff0 ;max Ths r ff0 r can happen, for example, n the scenaro shown n ff0 Fgure 7 In ths scenaro, Ton ff Ton, ν and thus Ton ν» Ton ff0» T ff We assume that all the consttuent mcroflows of the exstng macroflow ff start at the same tme (e, tme 0) and are greedy: they dump the maxmum allowed burst nto the network at any tme t, e, A ff (0;t) = E ff (t) = mnfp ff t + L ff;max ;ρ ff t + ff ff g The new mcroflow ν jons the exstng macroflow ff at tme t Λ = Ton ff Ton, ν and t s also greedy: at any tme t t Λ, A ν (t Λ ;t) = E ν (t t Λ ) = mnfp ν (t t Λ )+L ν;max ;ρ ν (t t Λ )+ff ν g Then t s not dffcult to see that at tme t = Ton, ff the total amount of traffc that s queued at the edge condtoner s gven by Q(t) =(P ff r ff )T ff on+(p ν +r ff r ff0 )T ν on+l ff0 ;max : Hence the delay experenced by a packet arrvng the edge condtoner at tme t = Ton ff wll be at least Q(t)=r ff0, whch can be shown to be larger than d ff0 edge n general Ths larger delay scausedby the fact that at the tme a new mcroflow s aggregated nto an exstng macroflow flow, the buffer at the edge condtoner may not be empty The old" packets queued there can cause the new" packets to experence addtonal delay that s no longer bounded by d ff0 edge We now consder the delay experenced by packets from the new" macroflow ff 0 nsde the network core Despte the 78

9 Arrval process ρ α+ ν mcroflows class macroflows scheduler scheduler α+ ν,max L P α+ ν α P Q statc Q dynamc r α+ ν class K Edge Condtoners Core Router Core Router L α,max r α One dynamc flow arrval pattern Statc flow aggregaton Q dynamc > Q statc 0 α T on ν T on ν Ton α T on Tme Fgure 6: Class-based guaranteed servces: dynamc flow aggregaton along a path Fgure 7: An example llustratng the edge delay bound volaton after rate change n dynamc flow aggregaton fact that packets from the new" macroflow ff 0 are servced wth a hgher reserved rate r ff0 ( r ff ), some of these packets may experence a worst-case delay n the network core that s bounded by d ff core = hl P;max =r ff + Dtot, P not by d ff0 core = hl P;max =r ff0 +Dtot P Intutvely, ths can happen because the packets from the new" macroflow may catch up wth the last packets from the old" macroflow Consderng both the delay at the edge condtoner and that n the network core, we see that packets of the new" macroflow may experence an end-to-end delay that s no longer bounded by the endto-end delay formula (2) A smlar stuaton may occur when a consttuent mcroflow leaves an exstng macroflow, f we mmedately decrease the reserved rate r ff to a new lower reserved rate r ff0 (see [2] for detals) Before we leave ths secton, we would lke to comment that the problem of dynamc flow aggregaton s not unque to the vrtual tme reference system used n ths paper The same problem exsts n a more general context For example, dynamc flow aggregaton wll have the same effect on a network of WFQ schedulers, the reference system used n the IntServ model Ths s because the stuaton happenng at the edge condtoner descrbed above wll also apply to a WFQ scheduler It appears that ths problem mght be more dffcult to address usng the conventonal hop-by-hop reservaton set-up approach In the followng we show how ths problem can be solved usng relatvely smple mechansms under the proposed BB archtecture 42 End-to-End Delay Bounds under Dynamc Flow Aggregaton In ths secton we present new mechansms to effectvely crcumvent the problems caused by dynamc flow aggregaton The basc objectve of our approach s to enable the bandwdth broker to make admsson control decsons at any gven tme, usng only the traffc profle and reserved rate of the macroflow at that tme In other words, we do not want the bandwdth broker to mantan an elaborate hstory record of the mcroflow arrval and departure events of a macroflow 42 Contngency Bandwdth and Edge Delay Bound We ntroduce the noton of contngency bandwdth to elmnate the lngerng delay effect of the backlog queued n the edge condtoner at the tme a mcroflow s aggregated nto or de-aggregated from an exstng macroflow It works as follows: Suppose at tme t Λ a mcroflow ν jons or leaves an exstng macroflow ff Besdes the reserved rate r ff beng adjusted to a new reserved rate r ff0 at t Λ, acontngency bandwdth r ν s also temporarly allocated to the resultng new" macroflow ff 0 for a contngency perod off ν tme unts The contngency bandwdth r ν and contngency perod f ν s chosen n such a manner that the maxmum delay n the edge condtoner experenced by any packets from the new" macroflow ff 0 after tme t Λ s bounded above by d new edge» maxfd old edge;d ff0 edgeg: (3) where d old edge denotes the maxmum edge delay bound on the old" macroflow (e, before t Λ ) and d ff0 edge = Ton(P ff0 ff0 r ff0 )=r ff0 + L ff0 ;max =r ff0 The followng two theorems state the suffcent condtons on r ν and f ν so that (3) holds (see [2] for ther proofs) Theorem 2 (Mcroflow Jon) Suppose at tme t Λ a new mcroflow ν wth the traffc profle (ff ν ;ρ ν ;P ν ;L ν;max ) jons an exstng macroflow ff Let r ν = r ff0 r ff and Q(t Λ ) be the sze of the backlog ntheedge condtoner at tme t Λ Then (3) holds f r ν P ν r ν and f ν Q(tΛ ) r ν : (4) Theorem 3 (Mcroflow Leave) Suppose at tme t Λ a mcroflow ν wth the traffc profle (ff ν ;ρ ν ;P ν ;L ν;max ) leaves an exstng macroflow ff Let r ν = r ff r ff0 and Q(t Λ ) be the sze of the backlog ntheedge condtoner at tme t Λ Then (3) holds f r ν r ν and f ν Q(tΛ ) r ν : (5) 79

10 To compute the contngency perod f ν precsely, weneedto know the backlog Q(t Λ ) n the edge condtoner at tme t Λ Snce at tme t Λ the maxmum delay at the edge condtoner s bounded by d old edge, wehave Q(t Λ )» d old edger(t Λ ) = d old edge(r ff + r ff (t Λ )) (6) where r(t Λ )stotal bandwdth allocated to the macroflow at tme t Λ,whch ncludes the reserved rate r ff and the total contngency bandwdth r ff (t Λ ) allocated to the macroflow ff at tme t Λ Gven ths upper bound on Q(t Λ ), the BB can determne an upper bound ^f ν on the contngency perod f ν as follows: ^f ν = d old r ff + r ff (t Λ ) edge r ν : (7) Hence after ^f ν, the BB can de-allocate the contngency bandwdth r ν at tme t Λ +^f ν We refer to ths method of determnng contngency perod f ν as the (theoretcal) contngency perod boundng approach In general ths scheme can be qute conservatve A more practcal approach s to have the edge condtoner to feedback the actual contngency perod to the BB based on the current buffer occupancy of the macroflow at the edge condtoner We refer to ths scheme as the contngency feedback method Note also that whenever the buffer n the edge condtoner becomes empty, the lngerng delay effect of the old macroflow has gone away Hence, the maxmum delay experenced by any packets of the macroflow ff s bounded by d ff edge, whch s solely determned by thecurrent aggregate traffc profle of the macroflow ff Therefore, the edge condtoner can send a message to the BB to reset all of the contngency bandwdth allocated to the macroflow ff (e, settng r ff = 0) before a contngency perod expres 422 Extenson to VTRS and Core Delay Bound As dscussed n Secton 4, packets of the new macroflow may catch up wth the packets of the old macroflow nsde the network core and hence experence addtonal queueng delay In ths secton we llustrate how the vrtual tme reference system can be extended to accommodate flow aggregaton wth dynamc rate changes Based on ths extenson, we present a modfed core-delay bound for flow aggregaton Consder an exstng macroflow ff whchtraverses the path P where there are q rate-based schedulers and h q delay-based schedulers In order to smplfy the dervaton of the delay experenced by packets nsde a network core, we mpose an assumpton: the delay parameter d ff assocated wth a macroflow ff s fxed, no matter whether there are mcroflow arrvals or departures n the macroflow Suppose that at tme f Λ, the reserved rate of the macroflow ff s adjusted at the edge shaper from r to r 0 Let p kλ be the last packet that leaves the edge condtoner before the rate change at f Λ, and p kλ + be the frst packet that leaves the edge condtoner after the rate change at f Λ Then the packets are shaped as follows For k < k Λ, ^a k+ ^a k L k+ =r, and for k k Λ,^a k+ ^a k L k+ =r 0 Furthermore, we need to ensure that the vrtual tme adjustment term that s carred nsde packet headers s properly calculated at the network edge Due to space lmtaton, we omt the detals here, and refer the nterested reader to [2] The followng theorem states a modfed delay bound nsde the network core for packets of a macroflow Theorem 4 Let packets of one macroflow shaped at the network edge as follows For k<k Λ, ^a k+ ^a k L k+ =r, and for k k Λ, ^a k+ ^a k L k+ =r 0 Moreover, let the vrtual tme adjustment term be properly defned as n [2] Then the vrtual spacng and realty check propertes hold for the macroflow after the rate change at f Λ Furthermore, the delay experenced by these packets n the network core s bounded by the followng modfed core delay formula: ^f h k ^a k» ρ L P;max q max ; ff+(h q)d LP;max ff +D r r tot: P (8) 0 43 Admsson Control wth Dynamc Flow Aggregaton We now llustrate how to perform admsson control and resource reservaton wth dynamc flow aggregaton, based on the results obtaned n Secton 42 and Secton 422 Consder a macroflow ff Let D ff;req be ts end-to-end delay requrement, whch we assume s fxed throughout the entre duraton of the macroflow Whenever a mcroflow jons or leaves the macroflow ff, we need to ensure that ts end-to-end delay requrement s stll satsfed At a gven tme, let r ff be the reserved rate of macroflow ff excludng the contngency bandwdth allocated Let P be the path of macroflow ff, and let C P res be the mnmal resdual bandwdth along path P We consder the cases of mcroflow jon and leave separately below Mcroflow Jon Consder a new mcroflow ν wantng to jon the exstng macroflow ff at tme t Λ If the new mcroflow can be admtted, we need to determne, for the resultng new" macroflow ff 0, a new reserved rate r ff0 r ff as well as r ν amount of new contngency bandwdth for a contngency perod of f ν From Theorem 2, wthout loss of generalty, wechoose r ν = P ν r ff0 + r ff Hence n order to be able to admt the new mcroflow ν nto the exstng macroflow ff, we must have P ν» Cres P If ths condton s satsfed, then we need to fnd the mnmal new reserved rate r ff0 so that the end-to-end delay requrement D ff;req can be satsfed for the resultng macroflow ff 0 Note that after contngency perod, the edge queueng delay for any packets of the class s determned by the new class traffc profle and the reserved rate, therefore, d ff0 e2e = d ff0 edge +maxfd ff core;d ff0 coreg»d ff;req : (9) Snce r ff0 r ff, L P;max =r ff0» L P;max =r ff Hence d ff core» d ff0 core The constrant (9) s reduced to d ff0 edge» D ff;req d ff core Hence the new mcroflow can be admtted f the new reserved rate r ff0 can be accommodated along path P (e, f ρ ν» r ff0 r ff» P ν» Cres) P If the mcroflow can be admtted, r ff + P ν s allocated to the macroflow durng the contngency perod (e, from t Λ to t Λ + f ν ), and after t Λ + f ν, only r ff0 wll be allocated for macroflow ff 0 80