NTT Access Network Service Systems Laboratories, NTT Corporation. 1-1 Hikarinooka ... Email: {nakayama.yu, oota.noriyuki}@lab.ntt.co.jp. AbstractâA ...
IEEE ICC 2013 - Communication QoS, Reliability and Modeling Symposium
Weighted Fairness in Cascade Aggregation for Access Networks Yu Nakayama and Noriyuki Oota NTT Access Network Service Systems Laboratories, NTT Corporation 1-1 Hikarinooka, Yokosuka-shi, Kanagawa, 239-0847 Japan Email: {nakayama.yu, oota.noriyuki}@lab.ntt.co.jp Abstract—A cascade aggregation can enable access networks to be deployed efficiently in areas with a low subscriber density. To achieve fairness for best effort (BE) traffic from subscribers, we proposed N rate N+1 color marking (NRN+1CM). However, it is important to realize weighted fairness. Network operators often provide different services that limit the maximum bandwidth or ensure that bandwidth is allocated with appropriate weights. This paper proposes weighted NRN+1CM which can set the maximum bandwidth and the weight for each subscriber and to allocate bandwidth based on the weights. The proposed algorithm modifies the color generation probability with the weight. If the input rate exceeds the maximum rate, frames are discarded to limit the output rate. We confirmed the effect of the proposed algorithm from computer simulations. The throughput ratio matched the weights and the throughput was limited to the maximum rate regardless of changes in traffic.
I. I NTRODUCTION Fiber to the home (FTTH) has been widely deployed to provide broadband access services. In Japan, FTTH accounts for over 50 % of the market [1]. FTTH is expected to be deployed in rural areas with a low subscriber density [2]. However, it has been costly in such areas because of its inefficiency. The populations of industrialized countries will decline over the coming decades, and it is estimated that the Japanese population will fall by 20 % over the next 30 years [3]. As subscriber density decreases along with the decrease in population, inefficiency will increase in many areas. It is important to deploy the FTTH access network efficiently in areas with a low subscriber density. Generally, an access network consists of passive optical network (PON) systems and layer-2 switches (SWs). A PON system consists of one optical line terminal (OLT) installed in a central office and multiple optical network units (ONUs) installed on subscriber premises. An SW is installed in the central office for the aggregation of subscriber lines from multiple PON systems. The SW is linked to an edge router (ER), which is connected to a next generation network (NGN) and the Internet. The current aggregation is the single aggregation shown in Fig. 1 (a) where large SWs are linked to the ER. This configuration is optimized for urban areas. We have proposed the cascade aggregation shown in Fig. 1 (b) [4] [5]. The cascade aggregation consists of small SWs that are linked together and connected to an ER. A cascade aggregation is as efficient as a network with a WDM ring topology [6] [7], which can link subscribers from multiple
978-1-4673-3122-7/13/$31.00 ©2013 IEEE
offices in rural areas. However, theoretically they can only link a maximum of several hundred subscribers because of constraints such as optical power. To improve the efficiency of access networks in rural areas, it is important to improve the efficiency of the layer-2 network with a cascade aggregation. To achieve fairness for best effort (BE) traffic in a cascade aggregation, we proposed N rate N+1 color marking (NRN+1CM) [4] [5]. The idea behind NRN+1CM is to mark BE frames with a color and discard BE frames based on queue length and frame color. NRN+1CM can achieve approximately fair bandwidth sharing with a simple queue configuration. The proposed marker can select a color from N+1 colors according to the traffic rate independent of burstiness. However, it is important to realize both fair bandwidth sharing and a different configuration for different subscribers. Network operators often provide services that limit the maximum bandwidth or ensure that bandwidth is allocated with appropriate weights. For example, it is assumed that a larger bandwidth will be guaranteed for subscribers with higher weights who use more expensive services, or that plural services differentiated by the maximum bandwidth will be provided. It is important to realize different configurations for different subscribers with NRN+1CM, which has only been able to realize simple bandwidth sharing. In this paper, we propose weighted NRN+1CM (WNRN+1CM). WNRN+1CM enables us to set a maximum bandwidth and weight for each subscriber. The bandwidth is allocated to subscribers based on their weights. The rest of the paper is organized as follows. Section II describes the system configuration and problems with existing algorithms. Section III proposes WNRN+1CM. In Section IV, we evaluate the algorithm with computer simulations. We provide our conclusion in Section V. II. S UBJECT The system configuration for WNRN+1CM is shown in Fig. 2. The SW connected to the other side of the ER is called the upstream SW. The traffic from the upstream SW is called upstream traffic, and that from subscribers linked to the SW through PON systems is called confluent traffic. Although the physical topology of the cascade aggregation can be a ring network, the traffic is transmitted through a logical daisy chain network. Although the priority of the traffic can be identified using a number of classes, for simplicity we
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ER
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as follows. Each ER maintains its state for each active flow. The estimated flow rate i is calculated as:
(a)
k
rinew = (1 − e−Ti /K ) Subscriber
Small SW
k lik + e(−Ti /K) riold k Ti
(1)
where tki and lik denote the arrival time and length of the k packet of i, and Tik = tki − tk−1 and K are constants. The i number of colors to be used is decided based on the estimated rate ri . Each packet is assigned a color with the constraint of the average rate of each color. Therefore, the distribution of the colors depends on the burstiness of the traffic. This results from the oscillation of the estimated rate of the burst traffic. Such a marker is unsuitable for an access network where SWs receive different types of burst. Various bursts are transmitted to the access network because it is connected directly to subscribers. We proposed NRN+1CM to reduce the effect of burstiness [4] [5]. SWs have a dropper and per subscriber markers for BE confluent traffic. The color is assigned according to the input rate with a single token bucket per subscriber. The proposed marker can select a color from N+1 colors according to the traffic rate and independent of burstiness. However, it is important to realize both fair bandwidth sharing and different configurations for different subscribers. For example, it is assumed that plural services differentiated by the maximum bandwidth will be provided, or that a larger bandwidth for subscribers who use more expensive services. Weighted fairness algorithms , such as weighted fair queueing (WFQ) [12] and weighted RFQ (WRFQ), have been proposed for the allocation of different bandwidths. It is important to realize weighted fairness with NRN+1CM, which has only been able to realize simple bandwidth sharing. In this paper, we propose WNRN+1CM, which can set a maximum bandwidth and weight for each subscriber. th
(b)
Fig. 1. Aggregation for access network. (a) current single aggregation. (b) proposed cascade aggregation. Upstream SW
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Fig. 2.
System configuration of WNRN+1CM.
assume that there is a BE class and one priority traffic class. We assume that priority traffic is managed so that it does not become congested. Priority frames line up in a first-in-first-out (FIFO) queue and are transmitted first. The QoS for priority traffic is maintained. All BE traffic forms one FIFO queue. This configuration is simple. If we assume that the BE traffic is divided by the subscribers and separated into per subscriber queues, the queue configuration would become large in scale and complicated and therefore costly. This BE queue configuration requires traffic control to achieve fairness between subscribers, because upstream traffic is always aggregated with confluent traffic when it is transmitted to another SW. The unfairness caused by the network topology is inappropriate for access services. Fairness algorithms with multicolor marking have been proposed. Multicolor marking algorithms do not need per subscriber BE queues. They are called core-stateless fair queuing (CSFQ) [8], rainbow fair queuing (RFQ) [9], and multi-rate multi color marker(mrMCM) [10]. To mark a color means to write a specific sequence on a frame header. Each sequence indicates the dropping priority. Multicolor marking is capable of controlling the traffic rate more accurately than a typical two-rate three-color marker (trTCM) [11]. The constraint is that the color is marked on the frame header, and so the number of colors is limited. Any increase in the number of colors makes implementation more difficult. As regards mrMCM, it uses multiple token buckets for each subscriber to mark a color on frames. Therefore, SWs need to have a number of token buckets. Too many token buckets cause complications and are hard to implement. The outline of the marking algorithm of CSFQ and RFQ is
III. W EIGHTED NRN+1CM A. Requirements We describe the requirements for the bandwidth allocation for each subscriber. Let s denote the identifier of a subscriber. For each s, we set the maximum bandwidth Rs and the weight ks . If the input rate exceeds Rs , frames are discarded to limit the rate to Rs . When the link is congested, the bandwidth is allocated based on ks . The throughput ratio should be equal to the ratio of the weight. This means that the throughput ratio between subscribers whose weights are k and 1 is k. B. Algorithm of NRN+1CM NRN+1CM [4] [5] is outlined in Fig. 3. Each BE frame is marked with a color indicating the dropping priority. The color is assigned according to the input rate. More colors are used for high rate traffic. There are a maximum of N+1 colors. The marking algorithm of NRN+1CM is as follows. When a frame arrives, a marking threshold integer d is updated with a single token bucket for each subscriber. d converges at (2) where is denotes the input rate and w denotes the token accumulation rate.
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Outline of NRN+1CM.
d=
is w
−1
(2)
If the value of d in (2) is a fraction, d fluctuates around the value. For simplicity, here we assume d converges at (2). After the update of d, the initial value n0 is generated according to d. The generation probability of n0 is written as (3) for integer j (0 ≤ j ≤ d). 1 ∀j (3) d+1 The probability is the same for all integers ranging from 0 to d. n0 is translated to the marking color n with (4). P r(n0 = j) =
n = nα 0
(4)
α is a parameter that decides the distribution of the marking value n. α satisfies 0 < α ≤ 1. α should be decided in advance by network operators. The maximum value of n increases along with d. More colors are used for high rate flows. n ≤ N is satisfied because the number of colors is limited. There is an input rate threshold at which the number of colors increases. Let imax denote the threshold. From (2) and (4), imax is written as (5). 1
imax = (N α + 1)w
(5)
If n > N in (4), N is substituted for n because n ≤ N . All frames that exceed imax are marked with color N . Therefore n is written as (6).
n=
⎧ ⎨nα ⎩N
0
We describe the marking algorithm of WNRN+1CM. The discarding algorithm is the same as NRN+1CM. 1) Weight: To implement the weight ks and make the throughput ratio correspond to it, for flows of ks the colors that are not discarded are generated ks times as frequently as that of weight 1. The generation probability of n0 is modified to (7) for integer j (0 ≤ j ≤ d). ⎧ ks ⎪ ⎨ d+1 ks P r(n0 = j) = 1 − d+1 ks d+1 ⎪ ⎩ 0
Equation (7) is equivalent to (3) when ks = 1. The ratio of the frequency between ks = k to ks = 1 is k for small j (0 ≤ j ≤ d+1 ks − 1). n0 is not generated for range. The marking rate of frames with color the j > d+1 ks n is ks vn for the 0 ≤ j ≤ d+1 ks − 1 range. Therefore the throughput ratio corresponds to the weight. 2) Maximum bandwidth: To limit the maximum rate to Rs when the input rate exceeds Rs , frames are not marked and are discarded. There are two ways to realize this. One is to equip the marker with a policing function. The other is to assign the frames with a specific flag that is available only inside the SW and discard the flagged frames at the dropper. The function can be realized in both ways and the effect is the same, so we do not discuss their merits and demerits here. Rs is assumed to be a multiple of w. We describe n0 = −1 when the frame is discarded. When the input rate is Rs , d converges at Rws − 1 in (2). If d > Rws − 1, the marking rate is limited to Rs by discarding frames with a probability of (8).
(n0 > N
1 α)
(6)
Let vn denote the marking rate of frames with color n from one subscriber. vn is equal to w times the number of integers that satisfy n − 1 < nα 0 ≤ n. The vn distribution depends on w and α. The dropper has a dropping threshold M (0 ≤ M ≤ N ) and a dropping probability P (0 ≤ P < 1). When a frame arrives, the dropper decides whether or not to discard the frame based on M , P , and n. M and P represent the proportion of the current queue length to the maximum queue length. The frame is discarded if n > N − M . If the frame belongs to the confluent traffic and n = N − M , the frame is discarded at probability P . When the congestion becomes heavy, M and P increase, and the number of colors that must be discarded increases. The frames that belong to low rate traffic are not discarded and are transmitted. The throughputs of subscribers are equalized. The bandwidth is fully utilized because when there is no congestion, all frames are transmitted.
Rs −1 w Rs =1− w(d + 1)
P r(n0 = −1) =
1
(n0 ≤ N α )
(0 ≤ j ≤ d+1 ks − 1) (j = d+1 ) ks (j > d+1 ks ) (7)
d−
1 d+1 (8)
Frames are marked with any color with a probability of From (7), integer a (0 ≤ a ≤ d+1 ks − 1) and b (0 ≤ b < ks ) which satisfy (9), are uniquely decided. Rs w(d+1) .
b Rs aks + = d+1 d+1 w(d + 1)
(9)
Therefore, the generation probability of n0 is modified to (10) with a and b.
P r(n0 = j) =
⎧ 1− ⎪ ⎪ ⎪ ks ⎨
d+1
b ⎪ ⎪ ⎪ ⎩ d+1 0
Rs w(d+1)
(j = −1) (0 ≤ j ≤ a − 1) (j = a) (j > a)
(10)
Equation (10) is equivalent to (7) if d ≤ Rws − 1. After generation, n0 is translated to n with (4). The maximum value of n is N and there is a threshold imax . imax is
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written as (11) because the marking rate of frames with color n is vn ks in the 0 ≤ n ≤ N range. 1
imax = (N α + 1)wk
(11)
All frames that exceed imax are marked with N . n is described as (12).
n=
⎧ ⎨nα ⎩N
0
1
(n0 ≤ (N α + 1)k − 1) 1
(n0 > (N α + 1)k − 1)
(12)
Equations (11) and (12) are equivalent to (5) and (6) when ks = 1. D. Comparison Here we describe the comparison of WNRN+1CM and previous NRN+1CM [4] [5]. Previous NRN+1CM assigns the same color distribution to all subscribers with (3) and (6). With the same color distribution, the throughput of subscribers are equalized. WNRN+1CM is an improved version of NRN+1CM. It assigns colors based on ks and Rs with (10) and (12). The color distribution of each subscriber depends on the weight and the maximum bandwidth. If the input rate exceeds Rs , frames are discarded to limit the rate to Rs . When the link is congested, the bandwidth is allocated based on ks . The throughput ratio becomes equal to the ratio of the weight. WNRN+1CM builds upon previous NRN+1CM and provides full backward compatibility. If ks = 1 is satisfied and Rs is sufficiently large for all subscribers, WNRN+1CM can achieve simple bandwidth fairness in the same way as previous NRN+1CM. Furthermore, the burstiness of the traffic has little effect on the color distribution, compared with a marking algorithm that estimates the traffic rate such as CSFQ and RFQ. IV. P ERFORMANCE E VALUATION We evaluated the performance of WNRN+1CM with computer simulations using network simulator ns-2 [13]. A. Verification First, we confirmed the distribution of colors using simple constant bit rate (CBR) UDP flows. We also verified that the throughput matches the weights and that the throughput is limited to Rs , regardless of the changes in traffic. The simulation conditions are shown in Fig. 4a. There were ten SWs in the cascade aggregation. Every link was 1 Gbps. Five subscribers (S1 – S5) were connected to SW1. To allow us to evaluate the accuracy of the weighted marking, the subscribers were given different weights. To cause traffic congestion, twenty subscribers were linked to SW2 – SW8. The frame length was 1.5 KB. imax for ks = 1 was 64 Mbps. We set N + 1 = 16 and α = 0.7, w = 1.31 Mbps. Other 1 parameters [4] [5] were B = 2.5 KB, xd = B(1 − d+1 ), and B yd = d+1 . The maximum queue length was 10 MB. Rs was set at a multiple of w.
In this situation, the theoretical values are as follows. For S1 – S5, d converges to 75.34 with (2). With (10), the discarding probability at the marker is 0.35 for Rs = 65.5 Mbps, and 0.80 for Rs = 19.6 Mbps. This means that if 35 % of the frames of 100 Mbps flows are discarded the throughput is limited to 65 Mbps. With (9), (a, b) is (50, 0), (25, 0), (16, 2), (12, 2), and (3, 3) for S1 – S5, respectively. The maximum n values are 15, 10, 7, 6, and 3 with (12). Fig. 4b shows the simulation result of the color distribution. The extent of n matches the theoretical value. WNRN+1CM realized the weighted marking since the frequency ratio matches the weights. Fig. 4c shows the throughput dynamics of S1 – S5 and the bandwidth utilization of the SW10 – ER link. The fair 1000 share value for ks = 1 is ks Mbps; that is 5.2ks Mbps for 2 - 4 s, and 9.6ks Mbps otherwise. This matches Fig. 4c. The S5 throughput is always limited to Rs . The link bandwidth is always fully utilized. We confirmed that the throughput ratio matches the weights and the throughput is limited to Rs . B. Realistic situation Second, we confirmed that the weighted fairness is realized with WNRN+1CM in more realistic situations. To perform an evaluation under a condition where we assume realistic access networks, we assume that there are thousands of subscribers connected to an ER. Various types of flows are sent to the ER by the subscribers. We assumed there were priority flows, BE heavy user flows, and BE TCP flows. The priority flows were assumed to be real time UDP traffic such as VoIP. The TCP flows were assumed to be Internet traffic. The heavy user flows were assumed to be high rate UDP flows that cause congestion. We evaluated the fairness of the TCP throughput, which is easily affected by the congestion. The simulation conditions are shown in Fig. 5. There were six SWs. Every link was 10 Gbps. 1000 subscribers were linked to each SW, and they were connected to the destination node via the ERs. The subscribers linked to each SW sent the data described in Fig. 5. The frame length was 1.5 KB. The simulation time was 10 s. The parameters were the same as IV-A, except for imax . imax for ks = 1 was set at 16 Mbps because there were many subscribers and the throughput for each subscriber is expected to decrease compared with that for IV-A. Consequently, w = 0.33 Mbps. The maximum queue length was 100 MB. We compared WNRN+1CM with WRFQ [9]. With WRFQ, the packets in a flow are marked such that the average rate for packets labeled with a color is in proportion to the weight. A larger weight allows more packets to be marked with lower color values than a smaller weight. The WRFQ parameters were set at N = 16, a = 4, b = 4, K = 0.1, and P = 16 Mbps. The queue threshold was 50 % of the maximum queue length. Fig. 6a shows the average throughput for each subscriber with WNRN+1CM. The average values of the subscribers with each weight are 0.56, 1.18, 1.73, 2.25, and 2.75 Mbps,
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respectively. Fig. 6b shows the result with WRFQ. The average values are 0.60, 1.03, 1.41, 1.70, and 2.01 Mbps, respectively. Fig. 7 shows the average ratio of the throughput to the fair share rate for each SW. With WNRN+1CM, the throughput ratio almost matches the weight. The throughputs are equalized in terms of weight. On the other hand, with WRFQ, the throughput ratio to the fair value diverges from the ideal value along with the weight. This is because the TCP frames are more likely to be marked with the colors to be discarded with WRFQ. The TCP flows whose frames are discarded in succession reduce the transmission rate with the congestion control algorithm. The throughputs of the flows decrease along with the number of the SWs that the flows pass, because of the increase in RTT caused by the accumulation of queuing delay. We confirmed that WNRN+1CM can realize weighted fairness in realistic situations. V. C ONCLUSION This paper described weighted NRN+1CM (WNRN+1CM). Simple bandwidth fairness can be realized with NRN+1CM. However, it is important to employ different configurations for different subscribers. Network operators often provide services that limit the maximum bandwidth or ensure the weights for bandwidth allocation. For example, it is assumed that a larger bandwidth will be ensured for subscribers with higher weights who use more expensive services.
In this paper, we proposed WNRN+1CM, which enables us to set the maximum bandwidth and the weight for each subscriber. With WNRN+1CM, the color generation probability is modified with the weight. If the input rate exceeds the maximum rate, frames are discarded to limit the output rate. When the link is congested, the bandwidth is allocated based on the weights. The throughput ratio between subscribers is equal to the weight ratio. We confirmed with computer simulations that WNRN+1CM can realize weighted fairness. The throughput ratio matches the weights and the throughput is limited to the maximum rate whatever the changes in the traffic. Although we assumed that there are only two priority classes, WNRN+1CM can be applied regardless of the number of classes as long as all of the higher priority classes are managed to avoid congestion and transmitted prior to BE. The application of WNRN+1CM to various network topologies and for deciding the appropriate parameters for realistic access networks will constitute future work. R EFERENCES [1] Information and Communications in Japan, Ministry of Internal Affairs and Communications, Japan, 2011. [2] Information and Communications in Japan, Ministry of Internal Affairs and Communications, Japan, 2007. [3] R. Kaneko, A. Ishikawa, F. Ishii, T. Sasai, M. Iwasawa, F. Mita, and R. Moriizumi, “Population projections for Japan: 2006-2055 outline of results, methods, and assumptions,” The Japanese Journal of Population, vol. 6, no. 1, pp. 76–114, 2008. [4] Y. Nakayama and N. Oota, “Fairness with n rate n+1 color marking on cascade aggregation for access network,” in IEEE Global Telecommunications Conference (GLOBECOM 2011), December 2011, pp. 1–5. [5] ——, “N rate n+1 color marking: Fair bandwidth sharing in cascade aggregation for access networks,” IEEE/ACM Transactions on Networking, submitted for publication. [6] J. Prat, J. Lazaro, P. Chanclou, R. Soila, P. Velanas, A. Teixeira, G. Beleffi, I. Tomkos, and D. Klonidis, “Hybrid ring-tree WDM/TDMPON optical distribution network,” in 11th International Conference on Transparent Optical Networks, 2009. (ICTON ’09), June 28 – July 2 2009, p. 1. [7] F.-T. An, K. S. Kim, D. Gutierrez, S. Yam, E. Hu, K. Shrikhande, and L. Kazovsky, “Success: a next-generation hybrid WDM/TDM optical access network architecture,” Journal of Lightwave Technology, vol. 22, no. 11, pp. 2557–2569, November 2004.
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5 Ideal value WNRN+1CM SW1 WNRN+1CM SW2 WNRN+1CM SW3 WNRN+1CM SW4 WNRN+1CM SW5 WNRN+1CM SW6 WRFQ SW1 WRFQ SW2 WRFQ SW3 WRFQ SW4 WRFQ SW5 WRFQ SW6
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[8] I. Stoica, S. Shenker, and H. Zhang, “Core-stateless fair queueing: a scalable architecture to approximate fair bandwidth allocations in highspeed networks,” IEEE/ACM Transactions on Networking, vol. 11, no. 1, pp. 33–46, February 2003. [9] Z. Cao, Z. Wang, and E. Zegura, “Rainbow fair queueing: fair bandwidth sharing without per-flow state,” in Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies. (INFOCOM 2000), vol. 2, 2000, pp. 922–931. [10] K. Pauwels, S. De Cnodder, and O. Elloumi, “A multi-color marking scheme to achieve fair bandwidth allocation,” in Quality of Future Internet Services. Springer, 2000, pp. 221–232. [11] A two rate three color marker, RFC2698, September 1999. [12] A. Demers, S. Keshav, and S. Shenker, “Analysis and simulation of a fair queueing algorithm,” in ACM SIGCOMM Computer Communication Review, vol. 19, no. 4, 1989, pp. 1–12.
[13] Network Simulator ns-2, available: http://www.isi.edu/nsnam/ns/.
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