A far buffer allocaton scheme Juha Henanen and Kalev Klkk Telecom Fnland P.O. Box 228, SF-330 Tampere, Fnland E-mal: juha.henanen@tele.f Abstract An approprate servce for data traffc n ATM networks requres large buffers n network nodes. However, large buffers wthout a proper allocaton scheme may lead to an unsatsfactory qualty of servce. Most present allocaton schemes ether necesstate a complcated queueng system or they do not offer a suffcent farness. Ths paper descrbes a rather smple buffer management scheme that results n far allocaton of bandwdth among competng connectons by usng only a FIFO buffer. The performance and farness of the allocaton scheme has been analysed by means of a smulaton program.. Introducton Asynchronous Transfer Mode (ATM) s the bass for future hgh-speed telecommuncaton networks. The strength of ATM les n ts superor flexblty whch enables a wde varety of servces and applcatons to be effcently ntegrated n one network. One of the man dffcultes of ATM s related to management of the network. Especally the control of multple types of traffc wth dfferent servce requrements has proved to be very dffcult. There are dfferent strateges for controllng an ATM network. The smplest one s to use the peak-rate allocaton method wth an approprate Usage/etwork Parameter Control (UPC/PC) scheme (see e.g., []). However, ths approach s somewhat nconsstent wth the orgnal dea of ATM, whch mples the possblty to explot the statstcal behavour of traffc streams. Especally n case of data traffc, peak-rate allocaton may lead to very low utlsaton. Another approach, called rate envelope multplexng [2], the operator endeavours to ensure that the combned nput rate of multplexed connectons s wthn the envelope, at least wth a very hgh probablty. Rate envelope multplexng s usually based on small FIFO buffers whch allows a relatvely smple mplementaton of network nodes. Ths approach has several drawbacks: the statstcal propertes of connectons could be very dffcult to predct, the achevable utlsaton remans low f the peak rate of sources ncreases beyond a small fracton of the lnk rate, and durng an overload stuaton, the QoS of all connectons s deterorated ndependent of source type and behavour. In data networks a dfferent scheme, rate sharng, s usually adopted. The am of rate sharng s to use avalable bandwdth to the maxmum whle ensurng at least some degree of far sharng between contendng users [2]. Rate sharng requres very large buffers at every network node, f the traffc process s smlar to that of local area networks. Because the queue length dstrbuton depends sgnfcantly on several traffc parameters (e.g., burst and slence length dstrbuton) t s
very dffcult to make any guarantees about the mean delays and delay varaton. In addton, a far share of bandwdth remans a problem f FIFO buffers are used. The farness problem can be allevated by usng dfferent schemes, e.g., vrtual spacng [2], round robn/prorty schedulng [3], weghted round-robn schedulng [4], dynamc tme-slce [5], asynchronous tme sharng [6], and per vrtual crcut buffer lmt [7]. Although these schemes make possble to protect the well-behaved connectons from the msbehavng ones, the complexty of mplementaton may restrct ther applcablty, see e.g. [2], [8], and [9]. An approach whch makes possble a smpler mplementaton s to offer Avalable Bt Rate (ABR) or Unspecfed Bt Rate (UBR) servce. In both servces the accessble bandwdth for a connecton depends on the traffc condton n the bottleneck node. In ABR servce each traffc source s nformed about the maxmum momentary rate possble to offer by the network, whereas the UBR servce counts more on the proper functon of hgher layer protocols f frames are lost due to overload stuaton n the ATM network. In order to provde bandwdth farness among competng ABR or UBR connectons, the buffer capacty at each swtch needs to be allocated farly among the competng connectons. Otherwse a connecton that gets more than ts far share of the buffer space, also gets more than ts far share of the bandwdth. Ths s true n case of both FIFO and per VC buffer management, snce the buffer space s always lmted and cannot be statcally allocated for each connecton. In ths paper we propose an allocaton scheme that allows a far share of lnk capacty usng only a pure FIFO buffer. The farness of the allocaton scheme has been studed n some smple cases. The results are very promsng although more extensve studes are needed to assess the real performance of the scheme. 2. The Buffer Allocaton Scheme The basc dea of the proposed allocaton scheme s that the buffer mplementaton should be as smple as possble, whereas t s possble to allow a relatvely complex algorthm to decde whether an ncomng cell should be accepted or rejected. If ths acceptance algorthm s suffcently far, there s no need to use more complex queue dscplnes than FIFO for ABR or UBR class of servce. Let us suppose that ncomng cells to an ATM node are generated by several sources, all of whch send AAL5 frames. Frstly, t s mportant to know whether the arrvng cell s the frst cell of a frame, and whether some cells of the same frame have already been delvered forward. If there s an mpendng danger of buffer overflow, whole frames should be dropped nstead of ndvdual cells. The random early drop (RED) scheme has shown to have much better performance than a smpler scheme n whch the remander of a frame s dscarded after one cell s dropped [8]. Therefore, f the buffer occupancy exceeds a certan lmt, the frst cell and all the followng cells of a frame should be dropped. Consequently, f the frst cell of a frame s accepted nto the buffer, all the followng cells of the frame should also be accepted, provded that the buffer s not fully occuped. ow the frst algorthm (A) can be defned as follows: 2
The frst cell of an AAL5-frame s dropped f X > R, where X s the number of cells n the buffer and R s a lmt for buffer occupancy. Unfortunately, ths buffer allocaton scheme does not guarantee a far share between dfferent type of connectons f some connectons have exploted more resources than the other ones. If a network operator s ntenton n an overload stuaton s to share the lnk capacty evenly among all actve connectons durng an overload stuaton, then the operator should drop cells from those connectons that have exploted the largest part of the lnk and buffer capacty. One way to do ths s to consder the number of cells n the buffer. If a connecton gets more than ts far share of the buffer space, t also gets more than ts far share of the bandwdth. Therefore, by restrctng the number of cells each connecton can have n the buffer one can also share the lnk capacty farly. Ths type of approach has been presented by Huang and Wu [0]. However, the applcaton of the scheme dffers essentally from our approach. Ther system conssts of two traffc classes (delay-senstve and loss-senstve classes) and an output-buffered ATM swtch. In arrval rate based state-dependent prorty scheme both the number of cells that a class of traffc has n the buffer and the correspondng arrval rate are used to decde whch class s selected for servce n the next tme slot. Ramamurthy and Dghe have proposed that buffer threshold for hgh runnng VC's should be modfed f cells have to be dscarded because of full buffers [4]. However, they do not present any explct method to dstngush hgh runnng connectons from the other ones. Let us denote the number of cells connecton has n the buffer by Y and the total number of actve connectons by a. More precsely, a s the number of connectons whch have at least one cell n the buffer. If durng an overload stuaton a connecton has more cells n the buffer than the average value (.e., Y >X/ a ), we may conclude that the connecton s to some extent responsble for the overload stuaton. Let us denote W Y a =. X Parameter W can be used as a measure of the explotaton of network resources provded that the buffer capacty s suffcently large n comparson wth the typcal burst sze. In contrast, f the buffer sze s small as compared of burst sze, the algorthm may not offer an approprate level of performance (see table 6 n Secton 5). ow we can defne an advanced algorthm by applyng parameter W : In the second algorthm (A2) the frst cell of an AAL5-frame s dropped f (X > R) and (W > ). Although ths smple scheme levels down n some degree the dfferences n lnk capacty used by connectons, the result s not qute satsfactory. When X exceeds R all connectons whch have more cells n the buffer than average (.e., W > ) experence roughly the same cell (or frame) loss rato, ndependent of the nstantaneous rate of the connecton. In order to amend the performance of the algorthm we can replace the on/off type of rejecton functon by a smoother one. In the thrd algorthm (A3) the frst cell of an AAL5-frame wll be dropped f: 3
K X (X > R) and W > Z + X R where K s the buffer capacty n cells and Z s a free parameter (typcally from 0.5 to ). Ths formula can also be presented n a smpler form: Y a ( X R) > Z( K R)X Because the term Z(K-R) does not depend on the traffc condton, the mplementaton of Algorthm 3 actually requres 3 multplcatons, one subtracton and one comparson. The forms of the rejecton functons of dfferent algorthms are presented n Fgure. If we apply Algorthm 3 and the buffer occupancy exceeds R, cells are rejected from a connecton only f t has a consderably amount of cells n the buffer. For nstance, f K = 2000, R = 500, Z = 0.5, X = 525, and a = 50, each connecton s allowed to have 305 cells n the buffer. When X approaches K, the allowed number of cells decreases eventually below (f Z < ). As a consequence, fnally most of the cells (= frst cells of AAL5-frames) wll be dropped, because the schedulng algorthm tends to level down the dfferences n the number of cells whle X s ncreasng. Ths property s desrable snce some of the buffer capacty should be left for the remanng cells of accepted frames. An approprate behavour of algorthm can be obtaned by a proper selecton of parameters R and Z. 0 W 8 6 A3,Z= A3,Z=0.5 A2 A 4 2 0 400 500 600 700 800 900 2000 X Fgure. Rejecton functons of Algorthms, 2 and 3 3. Farness In order to assess the farness of the proposed schedulng schemes we should have a reference model. The reference model n ths paper s based on the assumpton that traffc varatons are very slow. In ths case a far schedulng scheme rejects cells n a way that there s a maxmum cell rate whch satsfes the followng condton when the offered load exceeds the lnk capacty: w max w ( B ) = C = 4
where w s the nstantaneous cell rate of connecton, C s the lnk rate and: B = 0 f w w w w = max f w w In other words, w s the maxmum bandwdth whch the connecton can employ durng the max overload stuaton. Parameter w, and consequently B s, can be resolved qute easly. In addton, max we should take nto account that the buffer capacty reduces the actual cell loss rato. Therefore the fnal reference value for cell loss rato of connecton s defned as: > w max max B m B j j j= = B m j B j j= where m s the mean bt rate of the connecton and s the number of connectons. On the bass of the above reference model the followng farness ndex can be ntroduced: where propertes: F m = = = = m m B ( B B ) s the smulated cell loss rato of connecton. Ths farness ndex has the followng F= f = B for all connectons. If m = m 0, B = B 0 for every, and s are exponentally dstrbuted random varables, F s typcally about 0. F does not change f every B and B s multpled by the same constant. F s weghted by the mean bandwdth of each connecton n order to avod the overweghtng of connectons wth very small cell rate. 4. Smulaton results In ths secton we present some prelmnary results concernng the farness of algorthms A, A2 and A3. The results are based on smulatons wth only one ATM-node. Although ths lmtaton restrcts the applcablty of the results, the man propertes of the allocaton scheme can presumably be obtaned. The am of the algorthms s to share the lnk capacty farly durng an overload stuaton. Therefore the smulatons have been performed n a way that the average offered load s nearly, and because of traffc varatons the load exceeds the lnk capacty almost half of the smulaton tme. As a consequence, the average cell loss ratos observed n the smulatons represent the cell 2 5
loss ratos durng overload stuaton rather than the average cell loss ratos durng long perods. The source types used n smulatons are presented n Table. Source onprobablty* peak rate/ lnk rate frame sze n cells mean rate/ lnk rate S 0.0 0 0.0 S2 0.5 0.08 4 0.04 S3 0.5 0.2 6 0.06 S4 0.5 0.6 8 0.08 S5 0.5 0.20 0 0.0 S6 0.2 0.50 0 0.0 * n the smulaton program the actvty of a source s determned randomly at every 8000 tme slots Table. Source types In all cases the followng algorthms have been compared: Pure FIFO queue Algorthm, R=500 Algorthm 2, R=500 Algorthm 3, R=500, Z=0.5, 0.9 and In the frst smulaton seres (Table 2) we have tred to apprase the ablty of dfferent algorthms to dscern connectons wth moderately dfferent rates. Frstly, we can see that Algorthm has a notable mpact on the perceved cell loss rato due to ts prncple that only whole frames are dropped (note that all cells belongng to a frame are supposed to be lost f at least one of the cells s dropped). However, the farness of algorthm s poor, snce all connectons encounter almost the same cell loss probablty even a FIFO queue s better n ths respect. Algorthm 2 offers much better farness although t cannot dstngush very well small dfferences n mean rates. In contrast, the results of algorthm 3 are qute satsfactory: farness ndex s as hgh as 0.96 and the dfference of cell loss ratos between the reference model and smulaton result s small especally wth source types S3, S4 and S5. Wth S2 there s a larger relatve error, but because of the form of farness ndex these errors have an nsgnfcant effect on the overall farness. sources 5*S2 4*S3 3*S4 3*S5 B ave farness Algorthm smul. refer. smul. refer. smul. refer. smul. refer. ndex Pure FIFO 0.0443 2.38E-4 0.0734 0.0270 0.0860 0.039 0.307 0.829 0.088 0.5 A 0.0647 2.28E-4 0.0667 0.0209 0.0639 0.0763 0.0640 0.336 0.0648 0.7 A2 5.28E-4 2.30E-4 0.0362 0.099 0.0827 0.074 0.2 0.33 0.0632 0.77 A3, Z=0.5 4.00E-4 2.2E-4 0.0233 0.093 0.073 0.076 0.2 0.257 0.0608 0.95 A3, Z=0.9 2.80E-4.78E-4 0.025 0.085 0.0689 0.0679 0.57 0.9 0.0576 0.96 A3, Z= 8.57E-4.8E-4 0.027 0.09 0.0724 0.074 0.27 0.250 0.0605 0.96 Table 2. Smulaton results wth sources S2, S3, S4 and S5 6
In the next smulaton cases (Table 3) there are sources wth essentally smaller mean rate n addton to the sources wth hgh bandwdth demand. The low rate sources could be ether CBR sources or, more lkely, sources that have both a hgh actvty level and a low actvty level (e.g., fle transfer wth user responses). The effect of the sources wth low nstantaneous traffc demand s presumably rather small on the offered load, but they may ncrease consderably the number of actve sources (.e., parameter a ). The effect of these sources s dscernble wth Algorthm 2, whch yelds almost the same cell loss rato for sources S3, S4 and S5, although the reference model gves clearly dfferent cell loss probabltes. Agan, the results are much better wth Algorthm 3. An especally mportant property of Algorthm 3 s that low bt rate sources (S) dd not experence any cell losses durng any smulaton. sources: 20*S 4*S3 3*S4 3*S5 B ave farness Algorthm smul. refer. smul. refer. smul. refer. smul. refer. ndex Pure FIFO 0.0895 0 0.0630 0.024 0.0784 0.0989 0.024 0.767 0.0842 0.27 A 0.0483 0 0.069 0.056 0.069 0.0683 0.062 0.254 0.0589 0.20 A2 0 0 0.0627 0.038 0.0730 0.0640 0.070 0.73 0.0548 0.34 A3, Z=0.5 0 0 0.0223 0.060 0.0703 0.0683 0.80 0.247 0.0589 0.92 A3, Z=0.9 0 0 0.095 0.053 0.0672 0.0658 0.53 0.97 0.0565 0.94 A3, Z= 0 0 0.09 0.049 0.0657 0.0645 0.33 0.76 0.0556 0.94 Table 3. Smulaton results wth sources S, S3, S4 and S5 In the last cases we examne the effect of connectons wth very hgh cell rates. Two sources of type 6 generate cells wth half of the lnk rate durng actve perods. As regards the farness of allocaton scheme, t s mportant that these sources experence essentally hgher cell loss rato than the other connectons. Algorthms 2 and 3 satsfy ths requrement whereas the performance of A s defcent. sources: 2*S6 4*S3 3*S4 3*S5 B ave farness Algorthm smul. refer. smul. refer. smul. refer. smul. refer. ndex Pure FIFO 0.276 0.508 0.0884 5.67E-3 0.086 0.0437 0.523 0.09 0.503 0.9 A 0.439 0.352 0.0846 3.60E-3 0.0956 0.030 0.099 0.0768 0.039-0.04 A2 0.3502 0.378 5.68E-3 3.53E-3 0.0433 0.0329 0.0842 0.0803 0.094 0.90 A3, Z=0.5 0.3574 0.3509 4.67E-3 3.47E-3 0.0322 0.034 0.0702 0.0762 0.035 0.96 A3, Z=0.9 0.356 0.3433 4.7E-3 3.5E-3 0.0293 0.0288 0.066 0.0729 0.002 0.95 A3, Z= 0.3509 0.3487 6.84E-3 3.39E-3 0.032 0.030 0.0698 0.0749 0.023 0.97 Table 4. Smulaton results wth sources S3, S4, S5 and S6 Accordng to the above tables factor Z does not have any sgnfcant effect on the farness ndex and, n consequence, t s perhaps not a necessary parameter. However, because t does not complcate the mplementaton of the algorthm, t can be appled to regulate the behavour of the allocaton process. In partcular, f the cell rate of most of the connectons s roughly the same and Z=, the probablty that the buffer wll be fully occuped s relatvely large. In ths case some frames mght be lost partally, whch leads to an neffcent use of network resources. The actual 7
selecton of parameters R (n relaton to buffer capacty) and Z depends on the propertes of real traffc n ATM networks. 5. Implementaton aspects Although the formula used n the proposed algorthm s relatvely smple, Algorthm 3 requres 3 multplcatons. Because the constrant for calculaton tme s very strngent at hgh cell rates, an mplementaton, n whch multplcatons are avoded by usng beforehand calculated tables, could be more expedent. A prme ssue as regards the applcablty of ths approach s the requred amount of memory. The table could be realsed n a way that t contans the allowed value for Y (the number of cells of the connecton n the buffer) for each value of X (the number of cells n the buffer) and a (the number of actve connectons). If no compresson s used the sze of the table s (K-R)*K*2 bytes (note that the maxmum number of actve connectons s K because of the defnton appled). Ths s presumably too large a table for practcal mplementatons. Fortunately, t s possble to reduce the actual sze of both terms, K-R and K. In practcal cases t s very unlkely that all cells n the buffer belong to dfferent connectons. Consequently, a maxmum value for the number of actve sources used n the table could be essentally smaller than K, and f the actual number of actve sources exceeds the lmt, the largest value n the table s used. Moreover, as the results presented n the tables 2, 3 and 4 have shown, the actual form of rejecton functon may vary consderably wthout any sgnfcant effect on the performance of the algorthm (the change of farness ndex s qute small between cases Z = 0.5 and Z=). Therefore, t s not necessary to have every value of X n the table. We have performed some smulatons wth dfferent granulartes (G) by replacng X n the decson formula by a rounded one: X = G X G+05., where denotes the nteger part. The results presented n table 5 show that we can use rather coarse granularty: even 5 dfferent levels for the allowed W s n some cases suffcent. By applyng conservatve approxmatons: 000 for the number of actve connectons and 50 for the number of W levels, we need a table of sze 00 kbytes (note that the granularty depends on the buffer sze). Ths sze s most lkely acceptable n real mplementatons. Granularty (G): 0 25 50 00 umber of levels: 500 50 20 0 5 Sources 5*S2 + 4*S3 + 3*S4 + 3*S5 0.95 0.95 0.94 0.92 0.88 20*S + 4*S3 + 3*S4 + 3*S5 0.92 0.88 0.83 0.79 0.70 2*S6 + 4*S3 + 3*S4 + 3*S5 0.96 0.96 0.96 0.97 0.92 Table 5. The effect of granularty on farness ndex (K=2000, R=500, Z=0.5) Another problem of mplementaton s that n order to guarantee a suffcent farness the buffer sze should be qute large compared wth the frame sze. It s qute easy to notce that f the dle tme between successve frames of a connecton s longer than the emptyng tme of the buffer, a new frame wll always be accepted. Thus, t s advantageous for the customer to send large frames wth as hgh rate as possble. The prmary soluton to ths problem s to use large buffers. In our 8
smulaton cases the buffer sze s only 2000 cells because of restrctons n smulaton program but n practcal mplementatons the buffer sze could be much larger. The essental factor s the rato of buffer sze to frame sze. We have performed some smulatons wth varyng frame szes. The traffc stuatons are smlar to those used n the above table expect that the sources S5 have dfferent frame szes (mean and peak rates of the sources reman unchangeable). By ncreasng the frame sze sources could reduce ther frame loss ratons, and n consequence, the frame loss rato of other sources wll be ncreased. On the bass of smulaton (see Table 6) the rato of buffer sze to maxmum frame sze should be about 50, whch means that the buffer sze should be about 0000 cells f the maxmum frame sze s about 200 cells. The frame sze of sources S5: 0 20 32 50 00 Rato of buffer sze to 200 00 62.5 40 20 maxmum frame sze: 5*S2 + 4*S3 + 3*S4 + 3*S5 0.95 0.92 0.89 0.87 0.78 20*S + 4*S3 + 3*S4 + 3*S5 0.92 0.88 0.84 0.77 0.66 2*S6 + 4*S3 + 3*S4 + 3*S5 0.96 0.96 0.95 0.95 0.90 6. Modfcatons Table 6. The effect of frame sze on farness ndex (K=2000, R=500, Z=0.5) As notced the prevous secton, f the buffer sze s not suffcently large n comparson wth frame sze, farness could be deterorated. One possble soluton s to perform the checkng procedure when the last cell of a frame arrves at the buffer. The algorthm 3 can be preserved unchanged. If the result of Algorthm 3 s rejecton and the buffer occupancy exceeds the lmt R when frst cell of next frame comes, the frame wll be dropped. After ths modfcaton the frame loss rato s the hgher the larger s the frame sze (as opposed to the orgnal algorthm). On the network performance pont of vew ths property could be desrable. Algorthm 3 s a sutable scheme provded that all connectons are supposed to have the same bandwdth requrements. However, n practcal mplementatons there may arse a need for allocatng dfferent bandwdth for dfferent connectons. Ths type of allocaton scheme can be realsed by usng weghtng coeffcents n algorthm 3. Let us suppose that every connecton has a weghtng coeffcent (q ), whch determnes the share provded for the connecton durng an overload stuaton. By usng these coeffcents the parameter W can be modfed n the followng way: W YQ = Xq where Q s the sum of weghtng coeffcents of actve connectons: Q= a q j j= The decson formula s smlar to that of Algorthm 3: n Algorthm 4 the frst cell of an AAL5- frame wll be dropped f: 9
Y Q ( X R) > Z( K R) q X It should be noted that Algorthm 4 can be reduced to Algorthm 3 by usng equal weghtng coeffcents. 7. Conclusons Ths paper shows that t s possble to attan a hgh farness by usng FIFO buffers and a smple allocaton scheme. The proposed allocaton algorthms are especally sutable for the allocaton of UBR connectons, because t reacts accurately and quckly durng overload stuaton and reduces the bandwdth only by those connectons that use an excessve amount of the lnk bandwdth. At the same tme, connectons wth small cell rate do not experence any cell losses. By usng weghtng coeffcents t s possble to allocate lnk capacty accordng to pre-defned values. However, further smulatons wth several nodes and upper protocol levels are needed to assess the real performance of the buffer allocaton schemes. REFERECES [] Internatonal Telecommuncaton Unon, Telecommuncaton Standardzaton Sector (ITU-T), Recommendaton I.37, Traffc Control and Congeston Control n B-ISD, Geneva 993. [2] Roberts, J Rate envelope multplexng and rate sharng n B-ISD, To be appeared n IEICE Transactons on Communcatons (Japan), 995. [3] Chen, W-T and Lu, U-J A feasble framework of traffc control on an ATM wde-area network, Computer etworks and ISD Systems, Vol 27 (994) pp 67-84 [4] Ramamurthy, G and Dghe, R S A multdmensonal framework for congeston control n B- ISD, IEEE J Selected Areas n Commun., Vol 9 o 9 (December 99) pp 440-45 [5] Srram, K Methodologes for Bandwdth Allocaton, Transmsson Schedulng, and Congeston Avodance n Broadband ATM etworks, Computer etworks and ISD Systems, Vol 26 (993) pp 43-69 [6] Hyman, J M, Lazar, A A and Pacfc, G A Separaton Prncple Between Schedulng and Admsson Control for Broadband Swtchng, IEEE J. Selected Areas Commun., Vol o 4 (993) pp 605-66 [7] Dosh, B T and Johr, P K Communcaton protocols for hgh speed packet networks, Computer etworks and ISD Systems, Vol 24 (992) pp 243-273 [8] ewman, P Traffc Management for Local Arena etworks, IEEE Communcatons Mag., Vol 32 (August 994) pp 44-50 [9] Saunders, S ATM forum ponders congeston control optons, Data Communcatons, (March 994) pp 55-60 [0] Huang, T-Y and Wu, J-L Performance analyss of prortzed state-dependent buffermanagement schemes n ATM networks, Computer etworks and ISD Systems, Vol 27 (994) pp 45-66 0