On Fair Rate Allocation Policies with Minimum Cell Rate Guarantee for. Anovel concept in available bit rate (ABR) service model as dened by the ATM

Transcription

1 1 On Fair Rate Allocation Policie with Minimum Cell Rate Guarantee for ABR Service in ATM Network Yiwei Thoma Hou, a Henry H.-Y. Tzeng, b and Vijay P. Kumar c a Dept. of Electrical Engineering, Polytechnic Univerity, Brooklyn, NY 11201, USA. b Bell Laboratorie, Lucent Technologie, Room 4G-526, 101 Crawford Corner Road, Holmdel, NJ 07733, USA. c Bell Laboratorie, Lucent Technologie, Room 4G-533, 101 Crawford Corner Road, Holmdel, NJ 07733, USA. Anovel concept in available bit rate (ABR) ervice model a dened by the ATM Forum i the minimum cell rate (MCR) upport for each ABR virtual connection. In thi paper, we preent a fundamental tudy of rate allocation policie with MCR guarantee. In particular, we dene three network bandwidth allocation policie that guarantee MCR requirement. For each policy, we preent a centralized algorithm to compute rate allocation. The practical ignicance of our policie are ubtantiated with our further development of ditributed algorithm for ABR ervice. The performance of our ABR algorithm are demontrated with imulation reult. 1. INTRODUCTION A key performance iue aociated with ABR ervice i fair allocation of network bandwidth for each virtual connection (VC). The ATM Forum ha adopted the max-min fairne criterion for ABR ervice [2]. Prior eort on max-min fair rate allocation for ABR ervice uch a [3,5,6] did not addre the fairne iue in the context of MCR requirement. For connection with MCR requirement, a et of new policie need to be dened. Our paper focue on thi fundamental problem for ABR ervice. We conider three policie, namely MCRadd, MCRprop, and MCRmin to upport MCR contraint. Thee three policie were informally decribed in [4,9] for the imple ingle node cae. Each policy trive to achieve a dierent fairne objective with MCR guarantee for each connection. In particular, the MCRadd policy allocate each VC eion with it MCR plu a max-min fair hare from the remaining network capacity; the MCRprop policy allocate network bandwidth in proportional to each VC' MCR; 2 MCRmin policy guarantee each VC eion with either it MCR or a max-min fair hare, whichever Part of thi work wa completed while the rt author pent the ummer of 1996 at Bell Lab, Lucent Technologie, Holmdel, NJ. Mr. Hou i upported by a National Science Foundation (NSF) Graduate Reearch Traineehip at the New York State Center for Advanced Technology in Telecommunication (CATT), Polytechnic Univerity, Brooklyn, NY, USA. 2 We aume nonzero MCR requirement for the MCRprop policy throughout the paper.

2 2 i greater. In thi paper, we formally dene thee three policie. We alo preent a centralized bandwidth aignment algorithm to achieve each policy. Even though centralized algorithm are eential for our undertanding on how each policy allocate network bandwidth for eachvc, the practical ignicance of thee policie would be limited if we can not develop ditributed algorithm to achieve each policy in the context of ABR trac management. Therefore, we propoe a et of heuritic algorithm conitent with the ABR trac management pecication in [1]. We demontrate the eectivene of our ABR algorithm with imulation reult baed on benchmark network conguration uggeted by the ATM Forum. The remainder of thi paper i organized a follow. Section 2 rt ummarize key reult on max-min fairne, and then dene three rate allocation policie with MCR guarantee. We alo preent a centralized algorithm for each policy. Section 3 how the ditributed ABR implementation for each policy. In Section 4, we preent imulation reult. Section 5 conclude thi paper. 2. FAIR RATE ALLOCATION POLICIES WITH MCR GUARANTEE Before we dene our rate allocation policie, we hall briey ummarize key reult on max-min fairne for the pecial cae when there i no MCR requirement [2] Preliminarie In our model, a network N i characterized by a et of link L and eion S. 3 Each eion 2Stravere one or more link in L and i allocated a pecic rate r. The (aggregate) allocated rate F on link 2Lof the network i F = X 2S travering link r : Let C be the capacity of link. A link i aturated or fully utilized if F = C. A rate vector r =(;r ; )ifeaible if the following two contraint are atied: r 0 for all 2S, F C for all 2L. Denition 1 A rate vector r i max-min fair if it i feaible, and for each 2Sand every feaible rate vector ^r in which ^r >r, there exit ome eion t 2Such that r r t and r t > ^r t. 2 Denition 2 Given a feaible rate vector r, a link 2 Li a bottleneck link with repect to r for a eion travering if F = C and r r t for all eion t travering link. 2 Theorem 1 A feaible rate vector r i max-min fair if and only if each eion ha a bottleneck link with repect to r From now on, we hall ue the term \eion", \virtual connection", and \connection" interchangeably throughout the paper. 4 For a proof of Theorem 1, ee [2].

3 Rate Allocation Policie with MCR Guarantee We are now ready to dene our rate allocation policie to upport MCR requirement. We alo preent a centralized algorithm for each policy. For the ake of feaibility, we aume that the um of VC' MCR requirement travering any link doe not exceed that link' capacity, i.e. Pall 2S travering MCR C for every 2L. Thi aumption i enforced by admiion control at call etup time for each connection. Furthermore, we ay that a rate vector r =(;r ; )imcr-feaible if the following two contraint are atied: r MCR for all 2S, F C for all 2L Policy 1: MCRadd The MCRadd fairne policy rt allocate each eion 2Swith it MCR and then applie max-min fairne algorithm for all eion on the remaining network capacity. The rate allocation of each eion i it MCR plu a max-min fair hare from the network with the remaining capacity. Formally, thi policy i dened a follow. Denition 3 A rate vector r i MCRadd fair if it i MCR-feaible, and for each 2S and every MCR-feaible rate vector ^r in which ^r >r, there exit ome eion t 2S uch that r, MCR r t, MCR t and r t > ^r t. 2 We dene a new notion of bottleneck link a follow. Denition 4 Given an MCR-feaible rate vector r, a link 2 L i an MCRaddbottleneck link with repect to r for a eion travering if F = C and r, MCR r t, MCR t for all eion t travering link. 2 It can be hown that the following theorem i true. Theorem 2 An MCR-feaible rate vector r i MCRadd fair if and only if each eion ha an MCRadd bottleneck link with repect to r. 2 The following centralized algorithm compute the rate allocation for each eion in any network N uch that the MCRadd fairne policy i atied. Algorithm 1 Initial condition: k =1,S 1 = S, L 1 = L, r 0 = MCR, for every 2S, F 0 = X all 2S travering MCR, for every 2L. 1. n k := number of eion 2S k travering link, for every 2L k. 2. a k := min 2L k k,1 (C, F n k ).

4 4 3. r k := 4. F k := ( r k,1 + a k if 2S k, otherwie. r k,1 X all 2S travering r k ; for every 2Lk : 5. L k+1 := f j C, F k > 0;2Lk g. 6. S k+1 := f j doe not travere any link in (L,L k+1 )g. 7. k := k If S k i empty, then r k,1 =(;r k,1 ; ) i the rate vector atifying the MCRadd fairne policy and thi algorithm terminate; otherwie, go back to Step Policy 2: MCRprop The MCRprop fairne policy allocate a rate for each eion proportional to it MCR and achieve max-min fairne on the normalized rate (with repect to it MCR) for each eion. Formally, thi policy i dened a follow. Denition 5 A rate vector r i MCRprop fair if it i MCR-feaible, and for each 2S and every MCR-feaible rate vector ^r in which ^r >r, there exit ome eion t 2S r uch that MCR rt MCR and r t > ^r t. t 2 We dene a new notion of bottleneck link a follow. Denition 6 Given an MCR-feaible rate vector r, a link 2 L i an MCRpropbottleneck link with repect to r for a eion travering if F = C and r MCR rt MCR t for all eion t travering. 2 It can be hown that the following theorem i true. Theorem 3 An MCR-feaible rate vector r i MCRprop fair if and only if each eion ha an MCRprop-bottleneck link with repect to r. 2 Since the centralized algorithm for MCRprop fairne policy i very imilar to Algorithm 1, we omit to how it here due to pace limitation Policy 3: MCRmin A rate vector r i MCRmin fair if it i MCR-feaible and for each eion, one cannot generate a new MCR-feaible rate vector by increaing the allocated rate r without decreaing the allocated rate of ome other eion t with a rate r t already le than or equal to r in the rate vector r. Formally, thi policy i dened a follow. Denition 7 A rate vector r i MCRmin fair if it i MCR-feaible, and for every 2S and every MCR-feaible rate vector ^r in which ^r >r, there exit ome eion t 2S uch that r r t, and r t > ^r t. 2

5 5 Remark 1 Note that the MCRmin fairne denition above i imilar to the maxmin fairne denition (Denition 1) except the additional requirement that r mut be MCR-feaible. 2 We dene a new notion of bottleneck link a follow. Denition 8 Given an MCR-feaible rate vector r, a link 2 L i an MCRminbottleneck link with repect to r for a eion travering if F = C and r r t for every eion t travering link for which r t > MCR t. 2 It can be hown that the following theorem i true. Theorem 4 An MCR-feaible rate vector r i MCRmin fair if and only if each eion ha an MCRmin-bottleneck link with repect to r. 2 The following centralized algorithm compute rate allocation for each eion in any network N uch that the MCRmin fairne policy i atied. Algorithm 2 Initial condition: k =1,S 1 = S, L 1 = L, r 0 = MCR, for every 2S, F 0 = X all 2S travering MCR, for every 2L. 1. Sort all the eion in S k in n et (1 n js k j): u 1 ;u 2 ; ;u n uch that (1) every eion in the ame et ha the ame rate; and (2) rate value in thee et are in increaing order, i.e. r 1 2u1 <r 22u2 < <r n2u n 2. n k := number of eion 2 u 1 travering link, for every 2L k. 3. a k := 4. r k := 5. F k := 8>< >: ( minf min travered by 2 u1 (C, F k,1 n k l ) (C, F k,1 min travered by 2 u1 r k,1 + a k if 2 u 1, otherwie. r k,1 X all 2S travering n k l ) r k ; for every 2Lk. ; (r t2u2, r 2u1 )g if n>1, if n =1.

6 6 6. L k+1 := f j C, F k > 0;2Lk g. 7. S k+1 := f j doe not travere any link 2 (L,L k+1 )g. 8. k := k If S k i empty, then r k,1 =(;r k,1 ; ) i the rate vector atifying the MCRmin fairne policy and thi algorithm terminate; otherwie, go back to Step Example We ue the following example to illutrate how our centralized algorithm allocate network bandwidth for each policy. In thi network conguration (Fig. 1), the output port link of SW1 (Link 12) and SW2 (Link 23) are bottleneck node for eion. Specically, VC eion 1, 2 and 3 hare Link 12 while 1 and 4 hare Link 23. Again, the link capacity i aumed to equal to 1 unit. The MCR requirement for each eion i lited in Table 1. Uing centralized algorithm for each policy, we obtain the rate allocation for each eion under each policy in Table 1. Link 12 Link SW 1 4 SW 2 2 SW Figure 1. The three-node network conguration. Table 1 Rate allocation for each eion under each policy for the three-node network conguration. Seion MCR Requirement Policy MCRadd MCRprop MCRmin Although the centralized algorithm preented in thi ection are helpful for our undertanding on how each policy work to perform network-wide bandwidth aignment, they cannot be directly applied to a ditributed trac managementenvironment for ABR

7 7 ervice. To how the practical merit of our dened rate allocation policie, we will develop ditributed algorithm conforming to the ATM Forum ABR trac management pecication [1] to achieve thee policie in the next ection. 3. DISTRIBUTED HEURISTIC ALGORITHMS Our ABR implementation for MCRadd, MCRprop, and MCRmin are all baed on the Intelligent Marking technique, originally propoed in [6] and further rened in [7,8]. The key idea of thi technique i to let each congeted witch etimate \optimal" cell rate for each VC bottlenecked at the witch with a mall number of computation and without having the witch keeping track of each VC' tate information (o called per-vc accounting). Uing imple feedback mechanim, thi etimated rate will be employed to adjut the cell rate of the ource. It ha been hown in [7,8] that thi algorithm provide max-min fair allocation. Fig. 2 illutrate the behavior of the Intelligent Marking technique. For each queue of a witch, four variable LOAD, MCCR (Mean CCR), UCR (Upper Cell Rate), and EBR (Etimated Bottleneck Rate) are dened. The value of LOAD correpond to the aggregated cell rate entering the queue normalized with repect to link capacity and i meaured by the witch over a period of time. The value of MCCR contain an etimated average cell rate of all VC travering thi queue; the value of UCR contain an etimated upper limit on the cell rate of all VC travering thi queue; and the value of EBR contain an etimated bottleneck rate at thi queue. Furthermore, two parameter TLR and are dened for each queue, where the value of TLR i the target load ratio, and 0 <<1. S O U R C E RM(CCR,ER) fale if CCR>MCCR true UCR:=UCR+a(CCR-UCR) EBR:=UCR*TLR/LOAD RM(CCR,ER) fale if ER > EBR ER:=EBR true MCCR:=MCCR+a(CCR-MCCR) RM(CCR,ER) RM(CCR,ER) D E S T I N A T I O N Figure 2. Switch behavior of Intelligent Marking protocol. The Intelligent Marking algorithm i a heuritic algorithm. We will give anintuitive explanation on how itwork. The RM cell from all VC participate in exponential averaging for MCCR with MCCR := MCCR + (CCR, MCCR) while only ome VC with greater than average rate (potentially VC bottlenecked at thi witch) participate in UCR averaging, which i ued to etimate bottleneck link rate. Since there can be only one bottleneck rate at a link and it i no le than any of the VC' rate at teady tate,

8 8 the nal rate aignment for each VC converge to max-min fair rate (the \if" part of Theorem 1) for the entire network Heuritic Algorithm for MCRadd Since the Intelligent Marking technique allocate max-min fair rate for each VC from network bandwidth when there i no MCR requirement [7,8] and our MCRadd policy allocate each VC with MCR plu a max-min fair hare from the remaining network capacity, we can let the oetted cell rate, CCR, MCR for each VC to participate in Intelligent Marking and etimate the MCRadd-bottleneck link rate from the remaining network bandwidth. Fig. 3 illutrate the witch behavior of our heuritic algorithm. Similar to the Intelligent Marking algorithm, for each queue of a witch, four variable named LOAD, MFSR (Mean Fair Share Rate), Upper Fair Share Rate (Upper Fair Share Rate), and EBR (Etimated Bottleneck Rate) are dened. The LOAD i the ame a before. The value of MFSR contain an etimated MCR-oetted average rate of all VC travering thi queue; the UFSR contain an etimated MCR-oetted upper rate; and the value of EBR contain an etimated MCRadd-bottleneck link rate. The parameter TLR and are dened the ame a before. S O U R C E RM RM if (CCR-MCR)>MFSR true UFSR := UFSR + a [(CCR-MCR) - UFSR] EBR := UFSR * TLR / LOAD fale if (ER-MCR)>EBR ER := MCR + EBR true fale MFSR := MFSR + a [(CCR - MCR) - MFSR] RM(CCR,MCR,ER) RM D E S T I N A T I O N Figure 3. Switch behavior of heuritic implementation for the MCRadd policy Heuritic Algorithm for MCRprop Similar to the heuritic implementation for the MCRadd policy, heuritic algorithm for MCRprop can be implemented by letting normalized cell rate (e.g. CCR/MCR, ER/MCR) of each VC at the witch to participate in Intelligent Marking. Fig. 4 illutrate the witch behavior of our heuritic algorithm. Four variable named LOAD, NMR (Normalized Mean Rate), NUR (Normalized Upper Rate) and NBR (Normalized Bottleneck Rate) are dened for each output port of an ATM witch. The value of LOAD i the ame a before. The value of NMR contain an etimated normalized (with repect to MCR) average rate for all VC travering thi link; the value of NUR

9 9 contain an etimated normalized upper rate; and NBR contain an etimated normalized MCRprop-bottleneck link rate. Here, NMR, NUR and NBR are all dimenionle. TLR and are dened the ame a before. S O U R C E RM RM if (CCR/MCR)>NMR true NUR := NUR + a [(CCR/MCR) - NUR] NBR := NUR * TLR / LOAD fale if (ER/MCR)>NBR ER := MCR * NBR true fale NMR := NMR + a [(CCR/MCR) - NMR] RM(CCR,MCR,ER) RM D E S T I N A T I O N Figure 4. Switch behavior of heuritic implementation for the MCRprop policy Heuritic Algorithm for MCRmin Since 1) Intelligent Marking at a witch compute a max-min fair hare with zero MCR requirement [7,8]; and 2) SES dened in [1] generate cell alway at a rate no le than MCR, we would expect that combined mechanim of witch algorithm (Intelligent Marking) and SES may omehow erve the MCRmin policy. Thi i indeed the cae and will be demontrated by our imulation reult in the next ection. 4. SIMULATION RESULTS Here we preent a imulation tudy demontrating the eectivene of our heuritic ABR algorithm to achieve three rate allocation policie. Table 2 lit the parameter ued in our imulation. The ditance from ource/detination to the witch i 100 m and the link ditance between ATM witche i 10 km. Due to pace limitation, we will only preent imulation reult on the three-node network conguration hown in Fig. 1. Fig. 5, 7, and 9 how the cell rate of each eion under our heuritic ABR algorithm for MCRadd, MCRprop, and MCRmin policie, repectively. The cell rate hown in thee plot are normalized with repect to the link capacity (150 Mbp) for eay comparion with thoe value obtained with our centralized algorithm (Table 1). We nd that after initial tranient period, the rate allocation through heuritic algorithm are quite accurate to achieve each policy. Fig. 6, 8, and 10 how the link utilization (Link12 and Link23) and buer occupancy (SW1 and SW2) from the ame imulation run under each ABR algorithm. We nd that the bottleneck link are eciently utilized with mall buer requirement.

10 10 Table 2 Simulation parameter. End Sytem PCR 150Mbp ICR MCR Nrm 32 AIR 3.39 Mbp Link Speed 150 Mbp Switch Cell Switching Delay 4 ec Output Buer Size 2000 cell 5. CONCLUSION Wehave dened three fair rate allocation policie to upport MCR requirement for ABR ervice in ATM network. Centralized algorithm to compute rate allocation under each policy are alo preented. Furthermore, imple ditributed implementation of three rate allocation policie are developed in the context of ATM Forum ABR trac management pecication and their eectivene are demontrated with imulation reult. REFERENCES 1. ATM Forum Technical Committee, \Trac Management Specication - Verion 4.0," ATM Forum/ R13, February D. Berteka and R. Gallager, Data Network, Prentice Hall, A. Charny, D. Clark, and R. Jain, \Congetion Control with Explicit Rate Indication," Proc. IEEE ICC'95, pp D. Hughe, \Fair Share in the Context of MCR," ATM Forum Contribution , October R. Jain, et al., \ERICA Switch Algorithm: A Complete Decription," ATM Forum Contribution, , Augut K.-Y. Siu and H.-Y. Tzeng, \Intelligent Congetion Control for ABR Service in ATM Network," ACM SIGCOMM Computer Communication Review, 24(5):81{106, October K.-Y. Siu and H.-Y. Tzeng, \Limit of Performance in Rate-baed Control Scheme," ATM Forum Contribution , November H.-Y. Tzeng and K.-Y. Siu, \Comparion of Performance Among Exiting Rate Control Scheme," ATM Forum Contribution , November N. Yin, \Max-Min Fairne v. MCR Guarantee on Bandwidth Allocation for ABR," Proc. IEEE ATM'96 Workhop, San Francico, CA, Augut 25-27, 1996.

11 Cell Rate (%) Time (m) Figure 5. The cell rate of all connection with the MCRadd policy in the three-node conguration. 120 Link12 (%) Link Utilization & Queue Size Link23 (%) SW1 (cell) SW2 (cell) Time (m) Figure 6. The link utilization and the queue ize of the congeted witche with the MCRadd policy in the three-node network conguration Cell Rate (%) Time (m) Figure 7. The cell rate of all connection with the MCRprop policy in the three-node network conguration.

12 Link12 (%) Link Utilization & Queue Size Link23 (%) SW1 (cell) SW2 (cell) Time (m) Figure 8. The link utilization and the queue ize of the congeted witche with the MCRprop policy in the three-node network conguration Cell Rate (%) & Time (m) Figure 9. The cell rate of all connection with the MCRmin policy in the three-node network conguration Link12 (%) Link Utilization & Queue Size Link23 (%) SW1 (cell) SW2 (cell) Time (m) Figure 10. The link utilization and the queue ize of the congeted witche with the MCRmin policy in the three-node network conguration.