Achieving Energy-Proportionality in Fat-tree DCNs

Transcription

1 Achieving Energy-Proportionality in Fat-tree DCNs Qing Yi Department of Computer Science Portland State University Portland, Oregon Suresh Singh Department of Computer Science Portland State University Portland, Oregon Abstract Fat-tree is a popular topology for data center networks (DCNs). Many recent papers propose new energyefficient techniques that reduce the power consumption of fattree DCNs by dynamically powering off idle network switches and links. However, fat-tree DCNs adopting those techniques still consume a significant amount of energy even when lightly loaded. In this paper, we examine the approach of merging traffic in a fat-tree DCN in order to consolidate the traffic into fewer switches. We first derive an analytical model for the lower-bound of active switches required in a fat-tree DCN as a function of load, assuming traffic merging. Then we formulate a power optimization model and propose a scalable heuristic algorithm to find the minimum subset of network switches and links that satisfies a variety of traffic patterns and loads in actual DCNs. Simulation results show that our approach can substantially reduce the number of active switches and lower the energy consumption of a fat-tree DCN when the load is light. We show that our solution achieves near energy proportionality. I. INTRODUCTION With the exponential growth of global Internet traffic in recent years, data center networks (DCNs) have increasingly adopted architectures that are capable of providing high communication bandwidth in order to accommodate heavy traffic requirements between servers. However, in most data centers, traffic loading levels vary from time to time. To meet the peak traffic requirements, most data centers are designed with redundant capacity, resulting in large part of the networks underutilized for significant length of time. Consequently, networking equipment becomes idle, but it still consumes energy and is a major contributor to the overall energy cost for a data center. In fact, networks in a data center normally consume -% of the total electricity the data center consumes []. However, during low loadings, this fraction can increase to 5% [7] because servers can be turned to lower power states automatically while network switches cannot. Many researchers have studied the DCN energy consumption problem. One notable approach is ElasticTree [], in which the researchers propose to force traffic in a network to the leftmost switches in a fat-tree topology in order to power off unused switches. In contrast to ElasticTree, [7] replaces larger switches with many smaller ones to enable better packing of traffic into fewer number of switches. There are a number of other approaches studied, including those focusing on link-rate adaptation. The approach in [7] is static and thus does not adapt to load or different loading patterns. Link-rate adaptation is very effective at minimizing link energy consumption but, given that a lion s share of energy is used by the switch, this technique is not very effective. The ElasticTree approach [] is the most energy-efficient of all but is still sub-optimal because, as we show, for many light loading patterns, a large number of switches still need to remain active. k/ aggregation switches k/ edge switches k/ servers k / k/ k/+ k / Pod Pod Fig.. Fat-tree model. k pods We use a k-ary fat-tree shown in Fig. as an example to illustrate the deficiency of the prior approaches and explain the motivations of our contribution. The k-ary fat-tree interconnects k 3 / servers using three layers of switches. The edgelayer switches and aggregation-layer switches are organized in k pods. Each pod includes k/ and k/ and each edge switch connects to k/ servers. There are k / and each core switch has k links connecting to k pods. In previous approaches, all the are always powered on as they are connected to servers and have to remain active to be able to forward traffic upward and downward at all times. Even if a server has very little traffic going to the connecting edge switch, the switch will be fully powered on although very lightly loaded. Our contribution in this paper is to enable powering off more switches and links by consolidating traffic at edge and aggregation layer. A. Our Approach: Merging Consider an m-port switch connected with m servers. Assuming each server offers a load of fraction, the total

2 traffic to this switch from the servers is m. Normally the m switch interfaces remain active even when is small. If the traffic can be consolidated, we need at most m interfaces to be active. When the load is small, more switch interfaces of the switch can be powered off. In other words, there is potential power savings if traffic can be merged. In previous papers [] [8], we provided a hardware design of a device called merge network. Rather than repeat that discussion here, we provide a functional model of what such a network does and then use it in the remainder of this paper. We illustrate a m m merge network in Fig.. The merge network has m connections to the m servers and m connections to the m switch interfaces. A merge network has the property that it pushes all traffic from servers to the leftmost interface of the switch. If that interface is busy, then the traffic is forced to the next interface, and so on. This traffic merging behavior ensures that several switch interfaces can be put to low power mode without compromising connectivity. Of course, because of the fact that we are breaking the - association of a switch interface to a server interface, several layer protocols will break. In the previous paper mentioned above, we have addressed this issue as well and showed how the merge network and certain additional switch software can overcome this limitation. Some additional observations about the merge network are as follows: ) The merge network is a fully analog device with no transceivers and, as a result, its power consumption is below one watt. ) We note that merge networks do not cause any packet loss or increase in delay. 3) Consider the uplink from the servers to the merge network. All traffic coming into the merge network is output on the leftmost q m links connected to the q leftmost interfaces of the switch, where q = m (assuming a normalized unit capacity for links). This is accomplished internally by sensing packets on links and automatically redirecting them to the leftmost output from the merge network that is free. The network can be visualized as a train switching station where trains are re-routed by switching the tracks (rather than storeand-forward as is done in hubs or switches). ) On the downlink to the servers, traffic from the switch to the m servers is sent out along the leftmost r m switch interfaces to the merge network. The packets are then sent out along the m links attached to the servers from the output of the merge network. The manner in which this is accomplished is described in [] (note that the challenge is to correctly route the packets flowing through the merge network to the appropriate destinations). We can connect a merge network to multiple switches. In this scenario, traffic are merged to interfaces of the leftmost switches, and the right-end switches with all idle interfaces can be powered off, achieving more energy savings. In this work, we apply merge networks at two locations within a pod m-port switch m x m merge network m servers Fig.. Schematic of a merge network. of a fat-tree network one location is between the servers and the and the other location is between the and the. Fig. 3 shows a single pod of a fat-tree after applying merge networks. As shown, we utilize one k / k / merge network to connect all the servers in a pod to the interfaces of and apply another merge network to connect to. k/ ports k/ ports k/ ports k/ ports to k/ k-port k/ k X k merge network k/ k-port k/ k X k merge network k/ X k/ = k / servers Fig. 3. Merge network applied to pod in a fat-tree. B. Contributions and Paper Organization The primary contribution of this paper is to demonstrate that traffic merging yields near energy proportionality. The remainder of the paper is organized as follows. In Section II we introduce some related work and background. Section III presents the schematic of applying merge networks to a fat-tree network and derives the analytical model for the lower bound of energy consumption. Section IV formulates the power optimization model for computing routes with the goal of minimizing energy consumption. This model is different from those developed in previous papers because we also consider merge networks and our minimization function includes the number of active interfaces as a parameter. Section V presents an algorithm that computes routes every second based on traffic load. Lastly, in Section VI, we show the results of simulating realistic larger fat-tree DCNs and analyze the energy savings obtained when using merge networks and Section VII summarizes the conclusions and the main contributions. II. RELATED WORK The rapid increasing of Internet services and cloud applications requires DCNs to support higher bandwidth and

3 better scalability. During the past few years, many new DCN architectures have been proposed to address these challenges. For instance, hierarchical topologies, including fat-tree [3], Clos [5] and flattened butterfly [], are designed to maximize the network cross-section bandwidth and optimize the costefficiency ratio. Some server-centric DCNs, such as DCell [8] [3] and BCube [9], use servers as network routing devices, aiming to obtain better scalability and fault-tolerance. In general, these DCN topologies are intended to maximize network bandwidth and achieve optimal throughput and better scalability. With the growing size of data centers and rising energy costs, many have turned to the DCN energy efficiency problem recently. New energy-efficient network devices are used, including energy-proportional switches or links. Abts et al. [] propose to dynamically adapt the link rate according to traffic intensity to save energy. The earlier work of Gupta et al. [] inspired the study of energy-efficient DCN topology through powering off idle interfaces or devices. For example, Heller et al. present an ElasticTree [] that adapts the network topology to varying traffic loads. For a given traffic load, ElasticTree assigns traffic flows to routes and thus finds a minimal subset of network and powers off all unnecessary switches and links to save energy. CARPO [6] consolidates negative-correlated flows into a smaller set of links and power off unused ones. Adnan and Gupta [] propose a path consolidation algorithm to select the path that best overlaps with the other paths and thus dynamically form a minimum network topology. Recently, Widiaja et al. [7] compare different sizes of switches and conclude that it is more energy-efficient to use smaller-sized switches when the traffic is highly localized. Our work complements prior work by applying merge networks to edge-level switches and aggregation-layer switches to further reduce the number of active switches and achieve energy-proportionality for fat-tree DCNs. III. LOWER BOUND ON ENERGY CONSUMPTION In this section, we compute the minimum number of active switches required for two models to support different traffic and loadings. In the first model, we consider a fat-tree DCN without merge networks. Similar to ElasticTree, we force traffic to the left so that more aggregation and can be powered off. The second model uses merge networks to further merge the traffic to the left, so can be idle and powered off. A. Energy Minimization without Traffic Merging In order to derive analytical expressions for minimal energy consumption of fat-trees for different type of loadings, we use fraction of active switches as the metric for energy consumption and assume an underlying routing protocols that pushes traffic to the left. We use three parameters to model different types of loadings. A packet from a server goes to another server connected to the same edge switch with probability, which goes to a server in the same pod but another edge switch with probability p, and with probability p 3 = p it goes to a server in a different pod. Thus of the traffic is never seen by either the core or the while p of the traffic is not seen by the. By varying and p we can model very different types of traffic. Let denote the average load offered by each server expressed as a fraction of link speed (which we normalize to ). Thus, the total load in the data center is k 3 /. We have the following equalities for total traffic at the level of, pod and : Traffic per edge switch = k Traffic for all in a pod = ( p)k Traffic for all = k ( p p)k Note that traffic flow is symmetric and the numbers above correspond to both, traffic into and out of a switch or switches. We observe that all the need to remain active at all levels of loads to ensure servers have network connectivity. This gives us k / active. Within each pod we have total traffic equal to ( )k / going into/from the k/ from/to the. Given each link has a normalized capacity of, and that there are k/ interfaces per aggregation switch connected to the edge switches, we require at least ( p)k / k/ active aggregation switches per pod. Since there are k pods, the total number of active becomes k ( p)k. Finally, since every core switch is connected to an aggregation switch from each of the k pods, the number of active we require is simply, ( p p)k3 / k where we divide the total traffic passing through the by the number of links per switch and round up. Therefore, the total number of active switches can be written as: Active Switches = k + k ( p)k + ( p p )k Fig. plots the fraction of active switches as a function of load for five different scenarios when k =. The plot with the labels -o corresponds to the case when all traffic is between the servers connected to an edge switch. In other words, no traffic needs to flow to the or to the. As expected, the graph stays flat. However, what is relevant here is that even at light loads of., all the are fully active. At this load value, each server generates /th of the uplink capacity of traffic (similarly for downlink) but the energy consumed is the same as when the link is fully loaded. The total combined traffic from all the 6 servers is.6, which is less than the capacity of a single link. The plot with the labels corresponds to the extreme case when all the traffic is destined for servers in a different pod. Hence the core and will be utilized. Contrasting this with the case discussed above, we observe that energy scales approximately linearly with load, if we discount the. This is the desired behavior for energyproportional networking.

4 Fraction of active switches =.,p =.,p 3 =. =.5,p =.5,p 3 =. =.5,p =.5,p 3 =.5 Active Switches for k =. p =.5,p =.5,p =.5 3 =.,p =.,p 3 = Fraction of active switches Active Switches for k = with Traffic Merging =.,p =.,p 3 =. =.5,p =.5,p 3 =. =.5,p =.5,p 3 =.5 =.5,p =.5,p 3 =.5 =.,p =.,p 3 = Fig.. Active switches for the model in Section III-A. Fig. 5. Active switches for the model with traffic merging. B. Energy Savings Due to Traffic Merging To save energy used by the, we apply a k k merge network between the k / servers and the k/. There are two consequences after applying the merge networks. First, the p traffic that goes to other subnets within the same pod has no necessity to go through the aggregation level. Instead, it is transferred directly to the destination servers. The traffic loading parameters are changed to p and p and p = + p and p =. Accordingly, the number of active required in each pod is ( p )k = ( p p)k. Second, traffic from servers is now sent to a merge network and consolidated to the leftmost edge switch and the idle can be put to low power mode to save energy. Therefore, The active in one pod can be calculated as ( k )/( k k ) =, which changes with the traffic load. The total number of active switches after applying the merge networks can be written as: Active Switches = k k + k ( p )k + ( p p )k = k k ( p p)k + k + ( p p )k Fig. 5 shows the fraction of active switches in a k = fat-tree with merge networks for the same traffic models as Fig.. It is very illustrative of the benefits of traffic merging. The number of active switches is reduced more when the traffic load is lower. It is noticeable that the flat line in Fig. becomes more linear with the load after the traffic merging. IV. OPTIMIZATION POWER MODEL We formulate a power model of network switches and links to compute the minimal power consumed by a DCN. Given a network G(V,E), where V is the set of nodes and E is the set of links (u, v) connecting node u and v. End hosts and switches are all considered nodes in the network so V = V + V where V is the set of end hosts and V is the set of switches. Assuming the power consumption of each switch and each link is P s and P l respectively. With n active switches and k u active interfaces for each active switch u, the power optimization problem is expressed as: Minimize P total = k u P l + n P s () u V Subject to s S, gs,w i gw,s i = t i s,d w V s w V s d D, gw,d i gd,w i = () ti s,d w V d w V d u, u S, D, f u,w f w,u = (3) w V u w V u (u, v) E, f u,v c u,v x u,v () u V, f w,u c u y u and f u,w c u y u (5) w V u (u, v) E, x u,v = x v,u (6) u V, w V u,x u,w y u and x w,u y u (7) u V, w V u,y u (x u,w + x w,u ) (8) We use binary variables y u and x u,v to represent the power state of node u and link (u, v) respectively. For example, if x u,v =, link (u, v) is active; else it is idle. We have k u = x u,w and n = y u where V u is set of switches w V u u V connect to node u. gu,v i represents individual flow of the ith traffic demand t i s,d routed through (u, v). f u,w is the total flow assigned to (u, w) and f u,w = gu,w. i S and D are the set i of source nodes and destination nodes and V s and V d are set of switches connect to source node s and destination node d, respectively. For given network topologies and traffic loads, the optimization model finds optimal flow assignments involving minimum number of switches and links ((n, k u ) that consume minimum total power P total. The optimization problem is a mixed integer linear programming problem (MIP) that

5 subjects to capacity constraint, flow conservation and demand satisfaction. Demand satisfaction () specifies that the traffic flow from/to a source/destination node equals to certain traffic demand. Flow conservation (3) ensures the same amount of traffic enters an intermediate node and exits from the node. Capacity constraint () makes sure flows go through active links and traffic flow not surpass the link capacity. After applying the merge networks, the capacity of a node is not necessarily equal to the sum of the capacities of links connected to it. Therefore, we define capacity constraint c u for each node u as in (5). In addition, the bidirectional link constraint (6) confirms that both directions of a link are powered ON if there is a flow assigned to either direction of the link. Constraints (7) and (8) correlate the power states of each switch and it connected links. We implement the power optimization model for fat-tree in CPLEX. For a given traffic matrix, the model outputs the active switches and links, plus the total flow assignment to each link. For simplicity, we allow flow splitting in our implementation. V. GREEDY FLOW ASSIGNMENT ALGORITHM The formal optimization model finds the optimal flow assignments for a given network topology and traffic load. However, the optimization problem with a large scale DCN is a NP-hard problem and cannot be solved in a reasonable time frame. We propose a heuristic greedy algorithm in order to find a near-optimal route assignment. Our greedy flow assignment algorithm is based on the Dijkstra s algorithm that solves the shortest path problem. For each flow, the algorithm finds a route with sufficient bandwidth between the source node and the destination node with the lowest cost. The cost function is defined as the sum of the cost of switches and links along the route. By carefully defining the cost value of each node and each link, our greedy algorithm finds the lowest-cost route for each flow incrementally, and ultimately obtains the optimal routing for all the flows. The greedy algorithm is described as in Algorithm. Each link and each node has a fixed capacity. We only assign a flow to a link when there is available bandwidth at that link and also at the source and destination node. Once a flow is assigned, the amount of traffic demand is subtracted from the bandwidth of the link and the nodes on both ends. Link cost cost(u, v) is defined as a constant value of for all links while node cost cost(v) is initialized as. Each link is counted in the cost of the route and we are ensured to find the shortest route. Once node v is used in a route once, cost(v) is updated to. This makes sure that a switch that has been used in a previous route will have higher priority to be reused. As a result, we can achieve the minimum overall number of active switches. We use higher link cost than node cost in order to avoid detour routes between switches. The greedy algorithm is not optimal, but we verified that the results produced by the algorithm are very close to those from the CPLEX optimization solver in Section 3 for all traffic types and loads. However, the optimization model can only Algorithm Flow Assignment algorithm : function FLOWASSIGN(source, sink, demand) : for each vertex v in Graph do 3: dist[v] Infinity : dist[source] 5: insert (source, dist[source]) to Q 6: while Q is not empty do 7: u first pair in Q 8: if u == sink then 9: break : for each neighbor v of u do : if (capacity(u, v)!=)and : (capacity(u)!=)then 3: alt dist[u]+cost(v)+cost(u, v) : else 5: alt Infinity 6: if alt < dist[v] then 7: dist[v] alt 8: previous[v] u 9: update (v, dist[v]) in Q : for v = sink; v! = ; v = previous[v] do : insert v to route : return route scale to k =fat-tree networks. In the next part of this paper, we use this greedy algorithm to simulate larger scale fat-tree networks. VI. SIMULATION RESULTS We simulate a k =fat-tree network consisting of 3 servers and 8 switches. We apply merge networks between servers and, and between and. The merge network switches traffic flows to the left switches in each pod. Flow splitting is allowed for simplicity. The experimental traffic traces are generated following the On/Off pattern derived from production data centers [5] []. The duration of the On/Off period and the packet interarrival time follow the lognormal distribution. We generate different traffic type including Random, Stride(n), and Staggered(n), each of which has different patterns of near and far traffic. For instance, a flow in Stride(n) goes from node i and to node [(i + n) mod N] (N is the total number of servers). Source and destination nodes in Random type are uniformly distributed. Staggered(n) is staggered probability traffic and assigns fixed probabilities for traffic going to the same subnet and to the same pod. We generate 8 traffic suites with parameters, p and p showed in Table I. Flows in Stride() always go to the next server. In a k =fat-tree, each edge switch connects to 6 servers and forms a subnet. Flows from the first 5 servers go to the same subnet. While flow from the 6th server travels to the next subnet or the next pod. Therefore, 5/6 of the traffic goes to the same subnet. Flows in Stride(6) always travel cross subnets. Stride(36) have all flows traveling to other pods.

6 TABLE I PROBABILITIES OF FLOW GOING TO THE SAME SUBNET ( ), TO THE SAME POD (p ) AND TO DIFFERENT PODS ( p ) FOR ALL TRAFFIC SUITES STUDIED Traffic Suite p p Random.% 7% 9.8% Stride() 83.3% 3.9%.8% Stride(6) % 83.3% 6.7% Stride(36) % % % Stride(6) % % % Staggered() % % % Staggered() 5% 3% % Staggered(3) % 3% 5% For each traffic suite above, we generate packet traces from each server with the load fraction varies from. to.7. The packet traces in every one-second interval are organized as a traffic matrix. In simulation, we feed the traffic matrix to the greedy algorithm and output the number of active switches and the number of active interfaces. A. Fig. 6 compares the number of active switches at each level before and after applying traffic merging. As we can find, for all traffic suites, the number of active switches at edge level reduces significantly after applying merge networks. For aggregation-level switches, we observe obvious reduction for Stride(6), Staggered() and Staggered(3). We notice from table I that these three traffic suites have higher p, and as we discussed in Section III-B, a amount of p of traffic is switched away from aggregation level after traffic merging, which means a substantial part of the traffic originally going to aggregation layer has been cut short to be transferred directly through with merge networks. Fig. 7 illustrates the fraction of total active switches of the DCNs before and after using merge networks. The fraction of active switches reduced from % 6% to % 35% for light traffic loadings (..). B. Energy cost The above discussions focused on reducing the number of active switches. The overall energy cost a DCN consists of the cost incurred by switches and links. However, cost incurred by links is negligible and can be incorporated within the cost of interfaces of switches. Generally speaking, the energy cost of a switch can be roughly partitioned into the cost of chassis and the interfaces. As described in [7] [6], a reasonable approximation to the cost of a k-port switch is: Switch Cost = C + k log k + k The constant C accounts for static costs of the switch such as fan etc. The second term corresponds to the cost of the interconnection fabric within the switch which is a significant contributor to energy consumption (typically 3% %). This cost scales as k log k for a k-port switch. The last term is the contribution to the cost from the active interfaces. This term folds into itself the cost of the linecards that the interfaces are Compare the number of active switches for Stride() Compare the number of active switches for Stride(36) Compare the number of active switches for Staggered() Compare the number of active switches for Staggered(3) Compare the number of active switches for Stride(6) Compare the number of active switches for Stride(6) Compare the number of active switches for Staggered() Compare the number of active switches for Random Fig. 6. Compare number of active switches with vs. without traffic merging. on. For the purposes of comparing the overall cost reduction of traffic merging, we set C to 5% of the maximum switch cost. That is: C = k log k + k If the traffic load fraction going to a switch is, the merge network will switch the traffic to the leftmost m = k interfaces. The cost of a switch with merge networks is thus: Switch Cost = C + m log m + m Fig. 8 shows the overall cost improvement over approaches without merge networks. It demonstrates that our traffic merging method can save up to 9% of energy cost when the traffic load is low. Fig. 9 shows that the traffic merging can achieve better energy efficiency that is closer to the ideal energy proportionality. VII. CONCLUSIONS We present the approach of traffic merging at edge-layer and aggregation-layer switches in fat-tree DCNs in order to save energy. We formulate the analytical power model for fattree DCNs with merge networks and find the lower bound

7 Fraction of active switches Fraction of active switches Fraction of Active Switches out of 8 Random.3 Stride() Stride(6). Stride(36) Staggered(). Staggered() Staggered(3) Fraction of Active Switches out of 8 after Traffic Merging Random Stride() Stride(6) Stride(36) Staggered() Staggered() Staggered(3) Fig. 7. Fraction of active switches before using traffic merging (Top) and after using traffic merging (Down). % Cost improvement Cost Improvement using Traffic Merging Random 3 Stride() Stride(6) Stride(36) Staggered() Staggered() Staggered(3) Fig. 8. Reduction in total cost after using traffic merging. of the minimum number of switches for different traffic load. We simulate large-size fat-tree DCNs with the merge networks and present a heuristic greedy algorithm to find near-optimal subset of switches for different traffic patterns and load. The results show that our approach achieves up to 7% 9% total energy savings through traffic merging and achieves almost perfect energy proportionality. REFERENCES Fraction of cost Cost Improvement with Random Traffic Without traffic merging With traffic merging Ideal energy proportionality Fig. 9. Fraction of total cost without traffic merging vs. using traffic merging. [] Muhhamad Abdullah Adnan and Rajesh Gupta. Path Consolidation for Dynamic Right-sizing of Data Center Networks. In Proceedings IEEE Sixth International Conference on Cloud Computing, 3. [3] Mohammad Al-Fares, Alexander Loukissas, and Amin Vahdat. A Scalable, Commodity Data Center Network Architecture. In SIGCOMM, pages 63 7, 8. [] Theophilus Benson, Aditya Akella, and David A. Maltz. Network Traffic Characteristics of Data Centers in the Wild. In IMC,. [5] Charles Clos. A Study of Non-Blocking Switching Networks. The Bell System Technical Journal, 3():6, March 953. [6] V. Eramo, A. Germoni, A. Cianfrani, E. Miucci, and M. Listanti. Comparison in Power Consumption of MVMC and BENES Optical Packet Switches. In Proceedings IEEE NOC (Network on Chip), pages 5 8,. [7] Albert Greenberg, James Hamilton, David A. Maltz, and Parveen Patel. The Cost of a Cloud: Research Problems in Data Center Networks. In SIGCOMM CCR, pages 68 73, 9. [8] Chaunxiong Guo, Haitao Wu, Kun Tan, Lei Shi, Yongguang Zhang, and Songwu Lu. DCell: A Scalable and Fault-tolerant Network Structure for Data Centers. In SIGCOMM, pages 75 86, 8. [9] Chuanxiong Guo, Guohan Lu, Dan Li, Haitao Wu, Xuan Zhang, Yunfeng Shi, Chen Tian, Yongguang Zhang, and Songwu Lu. BCube: A High Performance, Server-centric Network Architecture for Modular Data Centers. In SIGCOMM, pages 63 7, 9. [] Maruti Gupta and Suresh Singh. Greening of the Internet. In Proceedings of ACM SIGCOMM, 3. [] Brandon Heller, Srini Seetharaman, Priya Mahadevan, Yannis Yiakoumis, Puneet Sharma, Sujata Banerjee, and Nick McKeown. ElasticTree: Saving Energy in Data Center Networks. In NSDI,. [] John Kim, William J. Dally, and Dennis Abts. Flattened Butterfly: A Cost-Efficient Topology for High-Radix Networks. In ISCA, pages 6 37, 7. [3] Markus Kliegl, Jason Lee, Jun Li, Xinchao Zhang, Chuanxiong Guo, and David Rincon. Generalized DCell Structure for Load-Balanced Data Center Networks. In INFOCOM,. [] Suresh Singh and Candy Yiu. Putting the Cart Before the Horse: Merging Traffic for Energy Conservation. In IEEE Communications Magazine. June. [5] Theophilus Benson and Ashok Anand and Aditya Akella and Ming Zhang. Understanding Data Center Traffic Characteristics. In WREN, 9. [6] Xiaodong Wang, Yanjun Yan, Xiaorui Wang, Kefa Lu, and Qing Cao. CARPO: Correlation-aware Power Optimization in Data Center Networks. In INFOCOM, pages 5 33,. [7] Indra Widjaja, Anwar Walid, Yanbin Luo, Yang Xu, and H. Jonathan Chao. Switch Sizing for Energy Efficient Datacenter Networks. In Proceedings GreenMetrics 3 Workshop (in conjunction with ACM Sigmetrics 3), Pittsburgh, PA, June 3. [8] Candy Yiu and Suresh Singh. Merging Traffic to Save Energy in the Enterprise. In E-Energy,. [] Dennis Abts, Michael R. Marty, Philip M. Wells, Peter Klausler, and Hong Liu. Energy Proportional Datacenter Networks. In ISCA,.