Virtual Queuing: An Efficient Algorithm for Bandwidth Management in Resilient Packet Rings

Transcription

1 Virtual Queuig: A Efficiet Algorithm for Badwidth Maagemet i Resiliet Packet Rigs Arash Shokrai, Siavash Khorsadi, Ioais Lambadaris, ad Lutful Kha Broadbad Network Laboratory Departmet of Systems ad Computer Egieerig, Carleto Uiversity, Ottawa, Caada {shokrai, khorsad, ioais}@sce.carleto.ca, lkha@radialik.com Abstract- Resiliet Packet Rig (RPR) is beig devised as part of IEEE stadard, where fairess i badwidth allocatio amog rig odes, efficiecy i resource utilizatio, ad a low computatioal complexity are the mai requiremets. Although recet efforts have improved the performace of the RPR fairess algorithms to have acceptable steady-state behavior, we demostrate that curret algorithms suffer from extreme ufairess ad throughput loss i some dyamic traffic scearios. I this paper 1, we address the badwidth maagemet i RPR. First, we propose a geeral fairess model for packet rigs. The, a ew algorithm for badwidth maagemet i RPR called Virtual Queuig () is itroduced. We study the fairess properties of algorithm both aalytically ad with simulatio results. Compared to the RPR stadard fairess algorithms that suffer from a throughput loss of up to 28% i some cases, the throughput loss with is less tha 2%. Comparig to aother algorithm, called Distributed Virtual-time Schedulig i Rigs (DVSR), has a lower computatioal complexity ad a better performace i a dyamic traffic eviromet. We show that the average throttled rate of the head ode i a cogestio spa ca be up to 8% for DVSR. With, it is less tha 4% i all cases. I. INTRODUCTION Resiliet Packet Rig (RPR) IEEE techology is a ew MAC layer for metro-rig etworks [1], [2]. It is aimed to provide high throughput, fault tolerace, ad spatial reuse i a rig etwork. Spatial reuse, which is multiple cocurret trasmissios over differet parts of the rig, is provided i RPR by packet removal at the destiatios. However, spatial reuse ca result i cogestio, ad cosequetly ufairess amog differet odes i accessig the rig badwidth. Hece, a badwidth allocatio mechaism is required to esure fairess amog RPR odes. Fairess i rig etworks has bee of particular attetio [3]-[5]. It is also the mai challege i RPR [6]. The Badwidth maagemet i RPR is based o the cocept of explicit rate feedback. Whe a RPR ode (statio) becomes cogested, it calculates a fair rate ad advertises it through a cotrol message to its upstream odes cotributig to the cogestio. Whe the upstream odes receive the fair rate, they adjust the rate of their local traffic accordigly. As a result, the cogested ode will be able to add more of its local traffic to the rig. 1 This research was supported by a grat from Commuicatios ad Iformatio Techology Otario (CITO). The mai proposed RPR fairess algorithms are the RPR draft stadard algorithm, which operates i Aggressive Mode (RPR-AM) or Coservative Mode (RPR-CM), ad Distributed Virtual-time Schedulig i Rigs (DVSR) [1], [6], [7]. RPR- AM ad RPR-CM algorithms suffer from extreme ufairess ad throughput loss i some dyamic traffic scearios. I particular, RPR-AM algorithm suffers from permaet oscillatios ad RPR-CM has a low covergece speed, which results i throughput loss i some ubalaced traffic scearios [6]. DVSR is aother fairess algorithm that performs the badwidth allocatio based o the cocept of virtual-time. Compared to RPR-AM ad RPR-CM algorithms, DVSR coverges much faster. However, i a dyamic traffic eviromet, it ca result i overestimatio of the local fair rate ad extreme starvatio ad ufairess at the local ode. I this paper, first we itroduce a ew fairess model for packet rigs that is a geeralizatio of Rig Igress Aggregated with Spatial reuse (RIAS) fairess model i [6]. The, we propose a ew algorithm called Virtual Queuig () for fair rate calculatio i RPR with a lower computatioal complexity, better fairess properties, ad the same covergece scale as DVSR. The rest of this paper is orgaized as follows. I Sectio II, the RPR ode architecture is explaied ad a ew mathematical model for fairess i RPR is proposed. The the performace of the curret RPR algorithms is evaluated. I Sectio III, we preset Virtual Queuig algorithm ad characterize its properties. Sectio IV cotais our simulatio results, ad coclusios are draw i Sectio V. II. AN OVERVIEW OF RESILIENT PACKET RING A. RPR Node Architecture The rig i RPR is bidirectioal ad cosists of two uidirectioal couter-rotatig riglets. Fig. 1 illustrates the geeral RPR ode architecture, where oly the traffic of oe of the riglets is show. At each ode, the arrivig traffic from the rig is dropped if destied to that ode. Otherwise, it is forwarded to the trasit buffer. The trasit buffer may be implemeted i two modes: sigle queue or dual queue. I sigle queue mode, the Low Priority (LP) ad High Priority (HP) trasit packets are forwarded ito a sigle queue. I this mode, the scheduler gives the service priority to the trasit traffic over the local traffic, which guaratees a lossless rig /5/$2. (C) 25 IEEE 982

2 Iput Lik Traffic from Rig Cotrol Messages Drop Traffic Trasit Buffer Rate Cotroller Fairess Module LP Local Buffer Add I Traffic Scheduler HP Local Buffer Fig. 1. The RPR ode architecture Output Lik Traffic to Rig I dual queue mode, there are two trasit queues for HP ad LP trasit traffic to improve the delay performace of the HP traffic [8]. I this mode, the scheduler gives the highest priority to the HP trasit traffic. The, packets from local buffers are forwarded prior to packets from the LP trasit queue. Whe the LP trasit queue is almost full, the scheduler gives the service priority to the trasit queues over the local buffers. A RPR ode with a sigle trasit queue is cogested, whe the utilizatio at the output lik of its scheduler exceeds a certai threshold (e.g. 95% of the available badwidth of the lik) or if its local traffic experieces a log delay to access oto the rig. I dual queue mode, cogestio is triggered whe the LP trasit queue depth exceeds a threshold. Note that i RPR, HP traffic has a reserved badwidth throughout the rig. Hece, we do ot cosider HP traffic i our discussios i this paper. LP traffic is called fairess eligible (FE) as its rate is cotrolled by the fairess algorithm. B. Fairess Model I this sectio, we propose a fairess model for packet rigs that is a geeralizatio of RIAS fairess model i [6]. The stated objective of the badwidth maagemet mechaism i RPR is to provide per-statio fairess i utilizig the rig badwidth. Give the same per-statio weights (or priority) ad the same badwidth demads, the rig badwidth should be equally divided amog the competig statios. Let us deote a source-destiatio flow from ode i to ode j by f(i,j) ad a Igress Aggregated (IA) super-flow trasitig ode ad origiated at ode i by sf(i,). The rig badwidth maagemet cosists of two compoets: 1) Rig behavior: It deals with calculatig a fair rate at each ode i order to maitai iter-statio fairess. From a fairess poit of view, IA super-flows are visible ad ot the idividual source-destiatio flows. The advertised fair rates regulate the rate of IA super-flows so that oe of the statios suffers from starvatio. 2) Source behavior: It deals with itra-statio fairess ad allocatig the badwidth to the idividual flows at each ode based o the received fair rates from dowstream odes. Source behavior should be optimized to maximize spatial reuse i the rig. That is, if some of log-haul flows face cogestio, other flows destied to the odes before the cogestio poit must be able to claim the uused badwidth. However, fairess i the rig should ot deped o ay particular assumptio o the source behavior. RIAS fairess assumes a maximal spatial reuse source behavior. I the followig, we provide a alterative fairess defiitio that does ot have this costrait. Let C be the available badwidth o a lik, also called ureserved_rate, r i be the rate of sf(i,), ad F be the local fair rate at ode. Note that r i is a o-icreasig fuctio of, that is, r i r +1 i. I the particular case whe =i, r represets the total rate of local fairess eligible traffic measured after the local rate cotrollers (shapers). Defiitio 1: The set of rates F={F, } ad alteratively the matrix of super-flow rates R={r i, i,} are defied to be fair if they meet the followig criteria simultaeously: r i F, i,, F = max_mi * (C, { r i, i}) = max_mi(c, {r i, i})+α [C i r i ] +, (1) where [x] + =max{x,} ad <α 1. The distictio betwee max_mi * ad max_mi is essetial. Whe the badwidth is ot utilized, max_mi * results i a value that is larger tha the rate of ay of the curret super-flows. This is cotrolled by parameter α. For α >, the uused badwidth ca be claimed by the backlogged flows. As a result, ay backlogged superflow will have a bottleeck ode m, where i r m i = C. Let us assume that the local traffic is buffered o a perdestiatio basis at each statio ad r i,j be the service rate of queue j at ode i. We have r i = j > r i,j ad the set of rates {r i,j, j} is called feasible if j > r i,j F, i,. A example of a feasible source behavior is r i,j mi i<<j {F /N (i)}, where N (i) is the umber of flows at ode origiated at statio i. More details about this fairess model ca be foud i [1]. Example 1: Let us cosider the sceario i Fig. 2 ad assume a fair behavior at the rig level ad that all flows are backlogged. Flow f(1,3) is facig cogestio i the dowstream ad ca sed oly at 4% of the lik capacity. Let F 2 =F 3 =.5. With a maximal feasible source behavior, we have r 1,3 =.4, r 1,4 =.46, ad r 2,4 =.5. With the source behavior, which is give above as a example of a feasible behavior, we have r 1,3 =.4, r 1,4 =.25, r 2,4 =.5. This is ot a fair solutio sice (1) is ot satisfied for =2 ad =3, that requires F 2 >.5 ad F 3 >.5. The solutio that satisfies (1) is F 2 =F 3 =.64, r 1,3 =.4, r 1,4 =.32, ad r 2,4 =.64. From a rig poit of view, this is also a fair solutio. C. Curret RPR Fairess Algorithms 1) RPR-AM: Let add-rate be the isertio rate of FE traffic at the local ode ad forward_rate be the service rate of its trasit traffic, which are measured by each ode over a fixed time-iterval legth of T secods called agig_iterval (or Co- f (1,3) f (1,4) f (2,4) r 1,3=.4 Fig. 2. A sceario to compare feasible ad maximally feasible source behaviors 983

3 trol Iterval). At the ed of each agig_iterval, a RPR ode checks its cogestio status. I RPR-AM, a cogested ode advertises the low-pass-filtered of its add_rate as the fair rate to its upstream odes. The low-pass-filterig is a expoetial averagig with parameter lpcoef as explaied i [7]. Whe cogestio clears the fair rate is set to uesereved_rate, C. The odes i the cogestio spa directly apply the received fair rates to their local FE traffic, if it is less tha C. Otherwise, their allowed isertio rate for FE traffic is ramped up. 2) RPR-CM: I Coservative Mode, whe cogestio is detected for the first time, the local fair rate is set to a iitial value of C divided by the umber of active statios. A active statio is the oe that has trasmitted at least oe packet over the past agig_iterval. This fair rate is advertised to the upstream odes. If the cogested ode remais cogested ad add_rate+forward_rate is greater tha a high threshold (e.g..95 C), the fair rate is ramped dow. If add_rate+forward_rate is less tha a low threshold (e.g..8 C), the fair rate is ramped up. This process is iterated oly oce i every fairess roud trip time (FRTT) to allow the etwork to settle with the ew rates. 3) DVSR: I DVSR, rates of idividual IA flows are measured. The fair rate is calculated as a fuctio of these measured rates. Hece, a better decisio i terms of the fair rate calculatio is made at the expese of further complexity of measurig per-flow rates. Assume a arbitrary ode, ad let r i be the arrival rate of traffic to ode origiatig at ode i icludig ode. It ca be show that the DVSR fair rate, F, satisfies the followig coditios [6]: F max{ ri } + ( C r if r < C i i ), i i, (2) = ( C r I otherwise r < F i ) / i, where I is the umber of flows with rates more tha or equal to F, that is, I = {i: r i F }. This is i fact a max-mi* operatio o the observed traffic rates of the statios. It is implicitly assumed that r i represets the badwidth demad of statio i. Note that F caot simply be calculated from (2) as it has a recursive form. The algorithm for calculatio of the fair rate i DVSR requires a sort ad a loop operatio with complexity O(Nlog 2 N), where N is the umber of IA flows at ode [6]. The complexity of RPR-AM ad RPR-CM algorithms is ivariat of N. D. Evaluatio of the Curret RPR Fairess Algorithms i Dyamic Traffic Scearios To evaluate these schemes, we cosider the parkig lot sceario of Fig. 3, which is widely studied as a bechmark sceario [6]. I a -ode parkig lot, odes 1,2,, sed traffic to ode +1, where ode is the head ode ad ode 1 is the tail ode i the cogestio spa. We cosider a simple 2-state source model called o-off source. It fluctuates betwee a high rate, S h, ad a low rate, S l. Let T h ad T l be the sojour times of the high (o) ad the low (off) states, respectively. I the followig, we discuss the potetial performace problems i RPR-AM, RPR-CM, ad DVSR algorithms. 1) To evaluate CM-RPR algorithm, a 2-ode parkig lot sceario was cosidered. A o-off source is itroduced to the head ode (ode 2) ad ode 1 ca sed at C. The simulatio parameters are as follows: C=1Mbps, T=1msec, lpcoef=16, rampupcoef=rampdcoef=32, S h =C/2, S l =.5Mbps, T h =2T, ad T l =T. Fig. 4 shows the output lik utilizatio at ode 2. Due to slow covergece, CM-RPR caot adapt to traffic chages quickly eough. I this case, a throughput loss of 27% is observed 2) For RPR-AM algorithm, we take the same sceario as for RPR-CM except that T l = 1T to see the impact of traffic imbalace o the throughput. Fig. 5 presets the advertised fair rate of the head ode. This rate is ot applied at the head ode accordig to the RPR stadard. Due to the oscillatios of the fair rate, a total throughput loss of 16% is observed. 3) DVSR is more vulerable to traffic variatios towards the tail. A 4-ode parkig lot sceario was cosidered. The o-off source is itroduced at the tail (ode 1), while other odes ca sed at C. We have T=1msec, S h =C/4, S l =C/1, ad T h =T l =T. Fig. 6 depicts the advertised fair rate ad also throughput of the head ode. Due to overestimatio of the fair rate, the head ode faces periodic starvatios ad has received substatially a lower share of the badwidth tha its upstream odes. The average throttled rate of the head ode is 38%. This will be further discussed i Sectio III-C. Lik Utilizatio (%C) Fair Rate (%C) 1 f (1,5) f (2,5) f (3,5) f (4,5) Fig. 3. Parkig lot sceario Time (Cotrol Iterval) Fig. 4. Lik utilizatio of the head ode i CM-RPR Time (Cotrol Iterval) Fig. 5. Oscillatios of the RPR-AM fair rate 984

4 III. Rate (Mbps) Fair Rate Rate of the Head Node Time (Cotrol Iterval) Fig. 6. The DVSR fair rate ad the rate of ode 4 VIRTUAL QUEUEING: A DISTRINUTED FAIR BANDWIDTH MANAGEMENT ALGORITHM FOR RPR A. Algorithm Descriptio I RPR, we are dealig with a distributed rate cotrol system (See Fig. 7). To achieve fairess, a global fair rate should be calculated so that if all of the rate cotrollers are set accordigly, cogestio does ot occur. The fair rate calculatio algorithm should be desiged i such a way that a distributed implemetatio with a limited complexity, speedily coverges (i a average sese) to a solutio that is close to the fair solutio. The observed traffic at a ode (r i (k)) is ot a accurate idicatio of the badwidth demad of a statio, as it is subject to costraits imposed by the advertised fair rate ad also by the limitatio of the available badwidth. Therefore, applyig max_mi * to the observed rates does ot ecessarily result i the global fairess. Several iteratios may be eeded to adjust the errors i demad estimatios. A more accurate estimatio of the demads results i a faster covergece. The average rate of the arrival process to a arbitrary ode durig cotrol iterval k is equal to r (k)= i r i (k) = i r i (k) + r (k). (3) The first term i (3) is the average rate of the trasit traffic at ode ad the secod term is the average rate of the local traffic at ode to the virtual queue, i cotrol iterval k. We have i r i (k) C ad r (k) F (k). Note that r (k) is the amout of the local traffic coformig to the curret fair rate, whether it is serviced or buffered. Therefore, r (k) C+F (k). Whe r (k) > C, the local ode does ot receive its fair share. The eligible traffic i the excess of the available badwidth is buffered at the local ode. Therefore, each ode ca be modeled as a virtual queue with a service rate of C ad the average arrival rate of r (k). Rate Cotroller D A Cogestio Spa Local Traffic Fig. 7. A distributed rate cotrol Model D Fair Rate Feedback A Virtual Queue Propositio 1: Ay rig fairess algorithm that maitais i r i (k) C,, results i a fair solutio. Proof: Assume a arbitrary ode ad let r max =max i {r i (k)}. If i r i (k)<c, we have F (k)>r max, r max =max_mi(c,{r i, i}) ad we ca fid <α 1 so that (1) is satisfied. Hece, it is a fair solutio. If i r i (k)=c, the we have F (k)=r max. I this case, we ca write r max =(C i V r i (k)) / {i: r i (k)=r max } = max_mi(c,{r i, i}), where V={i: r i (k)<r max }. As i r i (k)=c, F (k)=r max =max_mi * (C,{r i (k), i} ), which is a fair solutio based o Defiitio 1. The ramificatio of this propositio is sigificat. It idicates that ay rate cotrol mechaism that stabilizes the virtual queue at every ode will result i a fair solutio. However, a speedy covergece is the mai requiremet. We have already demostrated that performig max_mi* operatio o the observed rates may overestimate the fair rate i a dyamic traffic eviromet. I desigig algorithm, istead of takig the observed rates as the badwidth demads, all of the flows sedig at or above the curret fair rate are assumed to be backlogged. Hece, their badwidth demads over the ext cotrol period are assumed to be equal to C. The goal is to match the total arrival rate of the virtual queue at ode to the available badwidth, that is, r (k) C. is a algorithm that performs this i a simple maer. Let F (k) be the fair rate advertised by cogested ode for cotrol iterval k. We eed the followig measured parameters at ode i cotrol iterval k to calculate the fair rate for cotrol iterval k+1: - N i (k): Traffic received at cogested ode from ode i. - N (k): The maximum of local queue size ad local traffic eterig the virtual queue at ode. - E i : Total amout of arrivig traffic from ode i to cogested ode, coformig to the last advertised fair rate, F (k). - E S : Total amout of arrivig traffic from rate-limited odes. - E U : Total amout of arrivig traffic from iput-limited odes. The rate of iput-limited odes is below the advertised fair rate ad a flow is cosidered to be rate-limited if it fully utilizes its available fair share. Table 1 shows the fair rate calculatio procedure i algorithm. Table 1: fair rate calculatio algorithm N i (k) = r i (k) T N (k) = max{r (k) T, local_queue_size} E i = mi{n i, T F (k)}, i S = {i: E i T F (k)} U = {i: E i < T F (k)} E S = i S E i E U = i U E i if (E S && E U < C T) f = (C T E U )/E S (7) if (E U C T) f = (C T)/(E U +E S ) if (E S = && E U < C T) f = 1 F (k+1) = mi{f F (k), C} 985

5 This algorithm is robust with respect to the size of the cotrol iterval, T. Oly the eligible part of traffic is used i the fair rate calculatio. At the steady state, E i is equal to N i but i the trasiet period, N i ca exceed E i before the cogestio feedback takes effect. However, for the purpose of the fair rate adjustmet, the latest fair rate is applied. E S is the total amout of arrivig traffic from rate-limited odes ad E U is the total amout of arrivig traffic from iputlimited odes. Whe E S = ad E U < C T, oe of the flows is throttled. Therefore, the ode does ot eed to chage the fair rate ad the rate icrease/decrease factor, f, is equal to 1. Whe E U >C T, the fair rate is very large ad should be rapidly decreased to match the total rate of icomig traffic to the rig capacity. Whe E S > ad E U < C T, the badwidth demad of the iput-limited flows is deducted from the rig capacity ad the remaiig badwidth is divided amog the rate-limited odes. It ca be show that this is equivalet to a max_mi* operatio with a low computatioal complexity. The differece betwee ad DVSR is i settig the parameter α i (1). I DVSR it is set to 1, while i algorithm it is dyamically set to α=1 / S. Whe there are N active statios cotributig to the cogestio at ode, the fair rate will be o less tha C/N, that is, F C/N. For F (k) = C/N, we have f 1. Therefore, F (k+1) C/N. B. Rate Feedback Mechaism is a fairess algorithm desiged to work withi curret RPR framework. Whe a ode is cogested, special cotrol packets are dispatched every T secods (cotrol iterval) to carry advertised fair rates of the statios. Each statio will write its advertised fair rate i a desigated field i the cotrol packet passig through that ode. If a cotrol packet is ot received durig the past T secods, the statio creates a ew cotrol packet ad forwards it to upstream odes. The size of the cotrol iterval has a impact o the amout of cotrol overhead, which should be limited to a reasoable value. C. Characterizig Fairess Properties of From a fairess poit of view, the head ode i a cogestio spa receives the worst performace. We cosider the amout of the local traffic of the head ode throttled below its fair share to characterize the fairess properties of algorithm. The accumulated throttled traffic (ATT) of the head ode over a period of time is expressed i bytes ad is equal to the icrease i the size of the virtual queue at the head ode over that period (Fig. 7). Also, the average amout of throttled traffic of the head ode i the uit of time, < ATT >, is expressed i bps ad measures the uder-allocatio of the head ode. Let r(k) be the service rate of the local traffic of the head ode, ad F(k) be its fair share i cotrol iterval k. ATT ad < ATT > ca be calculated as follows: ATT(L) = k = 1 L (F(k) r(k)) T, (9) < ATT > (L) = k = 1 L (F(k) r(k)) /L. (1) We ca express < ATT > i percetage of the average service rate of the head ode as follows: < ATT > % = 1 < ATT > / ( k = 1 L r(k) /L). (11) The amout of throttled traffic of the head ode depeds o the etwork ad the traffic sceario. However, to draw some geeral properties, we cosider the followig three cases: steady state, where all of the flows keep their curret rates; tur-o, where some of the flows icrease their rates by C u i total; ad tur-off, where some of the flows decrease their rates by C d i total. The followig propositios provide some upper bouds for the accumulated throttled traffic (ATT) of the head ode i ad DVSR algorithms i a dyamic traffic eviromet, where the badwidth demad of the statios may icrease (tur-o) or decrease (tur-off). The proofs of these propositios are ot give i this paper due to the space limitatios. Details are available i [9]. Let N > be the umber of backlogged flows, M be the total umber of active odes, R be the rate of the local traffic of the head ode, ad g(x,y,z) =.5 ε (2+ε)/(1+ε) + x [log(mi{y,1/x}/z)/log(1+x)] +, where ε = [y/max{z,1/x} 1] +. Propositio 2: I a cogestio period, where the total demad exceeds the available badwidth, we have the followig properties for algorithm: 1) For ay cosecutive tur-o cotrol itervals (without a tur-off), where the rate of the statios icreases by C u i total, we have ATT,o < g(c/r, C/max{C/M,(C C u )/N}, N) C T. 2) For ay cosecutive tur-off cotrol itervals (without a tur-o), where the rate of the statios decreases by C d i total, we have ATT,off =. 3) Over a period of time with a tur-o ad a tur-off sequece, which is called a cycle, we have ATT,cycle < g(c/r, C/max{C/M,(C C u )/N}, N) C T C d T. Propositio 3: I a cogestio period, we have the followig properties for DVSR algorithm: 1) For ay cosecutive tur-o cotrol itervals (without a tur-off), where the rate of statios icreases by C u i total, we have ATT DVSR,o =ATT,o. 2) For a tur-off cotrol iterval where the rate of statios decreases by C d i total, it ca be show that ATT DVSR,off < g(c/r, N, N/(1+(N 1) C d /C)) C T. 3) Over a period of time with a tur-o ad a tur-off sequece, we have ATT DVSR,cycle =ATT,cycle +ATT DVSR,off ad ATT DVSR,cycle >. From Propositio 3, the accumulated throttled traffic of the head ode over a cycle is always o-zero for DVSR. Hece, we have show that the bouds give i [6] for a sigle ode caot be exteded to a multi-ode rig sceario. I fact, the ATT of the head ode may ot be bouded over a period of cogestio ad a permaet deviatio from the fair rates ca occur. However, ATT ca be zero i over a period of time. I some scearios, it may grow, but with a much slower pace compared to that of DVSR. Fig. 8 illustrates the ATT bouds of a cycle for ad DVSR with N = 3 ad M = 1 for R =.1 ad R = 1 as a fuctio of C u (= C d ). All rates are ormalized to the lik rate. A poit of dimiishig ad o retur is observed at C u =.7 for this particular case. Durig tur-o period, for C u.7 the fial fair rate ad hece ATT,o remais flat but sice C d icreases, it results i decreasig ATT,cycle for. 986

6 ATT Upper boud per cycle (CT) ATT (kbyte) DVSR, R=1, R=1 DVSR, R=.1, R= Amout of Tur o (or Tur of) (C) Fig. 8. ATT Upper boud per tur-o/tur-off cycle Simulatio Aalytical Upperboud DVSR Time (Cotrol Iterval) Fig. 9. Comparig ATT upper boud with simulatio ad aalytical results To show the tightess of the upper bouds, we compare these bouds with the aalytical ad the simulatio results for some worst-case scearios. Fig. 9 shows the results for a 4- ode parkig lot sceario of Fig. 3 with a o-off source at the tail ode. The simulatio parameters are as described i Sectio II-D. A close match betwee the model ad the simulatio results, ad a acceptable margi for the upper boud are observed. It ca be see that whe the tail ode is i the low state, ATT decreases as the head ode is able to sed more traffic tha its fair share. It should be oted that the differece betwee the upper boud ad the actual values is accumulated over time. IV. SIMULATION RESULTS We coducted simulatios i OPNET to compare the performace of, DVSR ad the RPR stadard algorithms. We cosidered 1Mbps liks with 5µsec propagatio delay (i.e., a distace of 1km betwee each pair of odes) ad cotrol iterval (T) of 1msec. Our study is cocetrated o covergece times ad fairess properties of these algorithms i overload coditios, as these coditios pose greater problems ad are more pressig. The simulatios are preformed with a small packet size of 512 bits to miimize the effect of the packet size. We cosidered a homogeeous traffic i a 4-ode parkig lot sceario (Fig. 3), where each ode 1 to 4 geerated 1Mbps of low priority traffic meaig that the etwork was overloaded to 4%. Nodes 4, 3, 2, ad 1 start sedig traffic at,.1,.2 ad.3 secods, respectively. Fig. 1 shows the ormalized service rate of the head ode i. Whe N odes are o, the fair rate is C/N. This figure shows speedy covergece i after each chage i the traffic. Rate of the Head Node (C) Covergece Time (T) Time (Cotrol Iterval) Fig. 1. Covergece of with homogeeous traffic Number of Nodes RPR AM RPR CM Fig. 11. Covergece time i the sychroized parkig lot Throughput Loss (%) RPR AM RPR CM Off time to O time Ratio Fig. 12. Comparig throughput loss of AM, CM ad Fig. 11 compares covergece times of RPR-CM, RPR-AM ad algorithm i a sychroized parkig lot sceario with 3-8 odes, where all odes start sedig traffic at the same time. I this sceario lpcoef = 16, ad rampupcoef= rampdcoef =32. The covergece time of RPR-AM decreases with the umber of odes. The reaso is that the fial fair rate decreases with the umber of odes ad it is achieved faster i low pass filterig process. However, covergece time i CM-RPR icreases with the umber of odes. It ca be see that the covergece time of is much less tha RPR- CM ad RPR-AM. Due to the slow covergece, RPR-CM ad RPR-AM algorithms result i throughput loss with dyamic traffic. Fig. 12 compares the throughput loss of these algorithms i a 2-ode parkig lot sceario, where a o-off source is itroduced at the head ode. The o-off source is geeratig 5Mbps traffic i the high state ad.5 Mbps i the low state. The upstream ode is backlogged. We have T h =5T, while T l varied from.1t h to 1T h. The throughput loss with CM-RPR is up to 28% ad with AM-RPR up to 17%. CM-RPR shows a o-mootoic behavior with off-time to o-time ratio (T l /T h ). Whe the off-time is large, RPR-CM coverges ad throughput loss is reduced. For small off-times, the released bad- 987

7 width by the dowstream ode is ot that much ad hece the loss is less. However, RPR-AM does ot coverge ad the throughput loss icreases with the off-time. I, the throughput loss is less tha 2% i all cases. To compare ad DVSR, we cosidered a 4-ode parkig lot topology (Fig. 3), where a o-off source with S h =25Mbps, S l =1Mbps, ad T h =T l is itroduced at the tail. The other odes are backlogged. I this sceario, T h +T l is chaged from 2T to 16T. Fig. 13 shows <ATT> i percetage of the average service rate of the head ode, <ATT>%. It ca be see that as T h +T l is icreased, <ATT>% reduces as DVSR coverges. I the ext sceario we keep T h +T l =2T, ad chage the umber of odes (M) from 2 to 7. The o-off source is always itroduced at the tail with S h =1/M Mbps ad S l =.5Mbps, while the other odes are backlogged. Fig. 14 shows <ATT>% for DVSR ad. It ca be see that <ATT>% i DVSR drastically grows with the umber of odes. This icrease is much less for. As it is show i Figs. 13, ad 14, the average throttled rate of the head ode i is less tha 4% i all cases. V. CONCLUSION I this paper, we first proposed a fairess model for packet rigs ad the a ew algorithm for fair rate calculatio i RPR called Virtual Queuig () was preseted. It is based o a virtual queuig model of the system. The calculated fair rate aims at stabilizig the queuig system ad maximizig the utilizatio. The covergece speed of is much better tha the RPR stadard algorithms ad is same as DVSR, while it is computatioally less complex tha DVSR, as it does ot require a sort operatio. It was also show through simulatios ad aalysis that has better fairess properties i a dyamic traffic eviromet. As such, is a powerful techique for fair ad efficiet badwidth maagemet i packet rigs. REFERENCES [1] F. Davik, M. Yelmaz, S. Gjessig ad N.Uzu, IEEE Resiliet packet rigs tutorial, IEEE Commuicatios Magazie, March 24. [2] M. Karol, ad R. Gitli, High performace optical, local ad metropolita area etworks: Ehacemets of FDDI ad IEEE 82.6 DQDB, IEEE Joural o Selected Areas i Commuicatios, vol. 8, o. 8, pp , October 199. [3] I. Cideo, ad Y. Ofek, MetaRig a full-duplex rig with fairess ad spetial reuse, IEEE Trasactio o Commuicatios, vol. 41, o. 1, pp , Jauary [4] D. Tsiag, ad G. Suwala, The Cisco SRP MAC layer protocol, IETF RFC 2892, August 2. [5] I. Cido, L. Georgiadis, R. Gueri, ad Y.Shavitt, Improved fairess algorithms for rigs with spatial reuse, IEEE/ACM Trasactios o Networkig 5(2), April [6] V. Gambiroza, P. Yua, L. Balzao, Y. Liu, S. Sheafor, ad E. Kightly, Desig, aalysis, ad implemetatio of DVSR: A fair, high performace protocol for packet rigs, IEEE/ACM Trasactios o Networkig 12(1), February 24. [7] IEEE. IEEE Stadard 82.17: Resiliet Packet Rig (D3.), November 23. [8] D. Schupke, A. Riedl, Packet trasfer delay compariso of a store-adforward ad a cut-through resiliet packet rig, Iteratioal Zurich Semiar o Broadbad Commuicatios (IZS), Zurich, Switzerlad, Februray 19-21, 22. [9] S. Khorsadi, A. Shokrai, ad I. Lambadaris, A Novel Fairess Model ad a Efficiet Algorithm for Badwidth Maagemet i Resiliet Packet Rigs, Carleto Uiversity Techical Report, August 24. [1] S. Khorsadi, A. Shokrai, ad I. Lambadaris, A New Fairess Model for Resiliet Packet Rigs, accepted for presetatio i ICC5, Seoul, Korea, May DVSR <ATT>% O/Off Period (Cotrol Iterval) Fig. 13. Comparig <ATT>% of DVSR ad for differet O-Off period 1 8 DVSR <ATT>% Number of Nodes Fig. 14. Comparig <ATT>% of DVSR ad for the differet umber of odes 988