406 IEEE SYSTEMS JOURNAL, VOL. 9, NO. 2, JUNE 2015

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1 406 IEEE SYSTEMS JOURNAL, VOL. 9, NO. 2, JUNE 2015 HERO: Hierarchical Energy Otimization or Data Center Networks Yan Zhang, Student Member, IEEE, and Nirwan Ansari, Fellow, IEEE Abstract The raid escalating ower consumtion has become critically imortant to modern data centers. Existing works on reducing the ower consumtion o network elements ormulate the ower otimization roblem or a general network toology and require a centralized controller. As the scale o data centers increases, the comlexity o solving this otimization roblem increases raidly. Insired rom the hierarchical data center network (DCN) toologies and data center traic atterns, we design a two-level, od-level, and core-level ower otimization model, namely, Hierarchical EneRgy Otimization (HERO), to reduce the ower consumtion o network elements by switching o network switches and links while still guaranteeing ull connectivity and maximizing link utilization. Given a hysical DCN toology and a traic matrix, we illustrate that two-level ower otimizations in HERO all in the class o caacitated multicommodity minimum cost low (CMCF) roblem, which is NP-hard. Thereore, we design several heuristic algorithms based on dierent switch elimination criteria to solve the roosed HERO otimization roblem. The ower-saving erormance o the roosed HERO model is evaluated by several exeriments with dierent traic atterns. Our simulations demonstrate that HERO can reduce ower consumtions o network elements eectively with reduced comlexity. Index Terms Data center networks (DCNs), energy eiciency, green data centers, ower otimization. I. INTRODUCTION DATA center networks (DCNs) are revalent and essential to rovide a myriad o services and alications. In order to rovide a reliable and scalable comuting inrastructure, the network caacity o DCNs is esecially rovisioned or worst case or eak-hour workload, and thus, data centers consume a huge amount o energy. The Reort to Congress on Server and Data Center Energy Eiciency [1] indicated that data centers and servers consumed about 61 billion kilowatthours (kwh) in 2006 (1.5% o the total U.S. electricity consumtion) or a total electricity cost o about $4.5 billion, and the electricity usage o data centers has been almost doubled rom 2000 to As reorted in [2], the total ower consumtion o data centers in 2010 increases by about 56% rom 2005 to 2010 or worldwide data centers and increases by only 36% or U.S. data centers. It has been well established in the research literature that the average server utilization is oten below 30% o the maximum utilization in data centers [3]. At low levels o workload, servers Manuscrit received November 12, 2012; revised Setember 19, 2013; acceted October 1, Date o ublication October 28, 2013; date o current version May 22, The authors are with the Advanced Networking Laboratory, Deartment o Electrical and Comuter Engineering, New Jersey Institute o Technology, Newark, NJ USA ( yz45@njit.edu; nirwan.ansari@njit.edu). Digital Object Identiier /JSYST are highly energy ineicient because, even in the idle state, the ower consumed is over 50% o its eak ower or an energyeicient server [3] and oten over 80% or a commodity server [4]. Moreover, switches are not energy eicient currently either, and they consume 70% 80% o their eak ower in their idle state [5]. The high oerational costs and the mismatch between data center utilization and ower consumtion have surred great interest in imroving data center energy eiciency. The ower consumtion o network elements can account or 10% 20% o a data center s total ower consumtion [6]. Thus, reducing the ower cost o network elements without adversely aecting network erormance resents a great challenge. Several studies [7] [10] have investigated the ower savings o the network inrastructure in DCNs by switching o some unneeded network devices or by utting them into slee. In a recent work, a network-wide ower manager, ElasticTree [7], was roosed to otimize the energy consumtion o DCNs by dynamically otimizing the subset o active network elements, switches, and links to satisy dynamic traic loads while still meeting the erormance and ault tolerance requirements. Shang et al. [8] solved the energy-saving roblem in DCNs rom a routing ersective. Mann et al. [9] resented a network ower-aware ramework, the VMFLow, or the lacement and migration o virtual machines (VMs), taking into account the network toology as well as network traic demands to otimize the network ower consumtion while satisying as many network traic demands as ossible. A more general solution, the VMPlanner [10], has been roosed to reduce the network element ower consumtion by otimizing both VM lacement and traic low routing. A survey on ower consumtion in data centers along with solutions has recently been reorted in [11]. All o these rior works ormulated the ower otimization roblem or a general network toology and required a centralized ower management controller, which monitors and redicts traic demands at each network element and controls the ower status o all network elements. As the scale o DCNs increases, the comlexity o the ower otimization roblem o DCNs and the required comutational time to solve this otimization roblem increase raidly. Insired rom the hierarchical DCN toologies and data center traic atterns, we roose a Hierarchical EneRgy Otimization (HERO) model to reduce the ower consumtion o data centers. Given a DCN toology and a traic matrix, we evaluate the ossibility o turning o some network elements (i.e., routers, switches, and links) hierarchically, without violating the network connectivity and QoS constraints. In this aer, we extend the revious HERO model [12] by including the switching ower enalty. We also include detailed erormance IEEE. Personal use is ermitted, but reublication/redistribution requires IEEE ermission. See htt:// or more inormation.

2 ZHANG AND ANSARI: HERO: HIERARCHICAL ENERGY OPTIMIZATION FOR DCNS 407 evaluations using the emulated tyical data center workloads. The main contributions o this aer are described as ollows. First, a hierarchical energy otimization model or DCNs is roosed. One o the major advantages o the roosed hierarchical model is that it reduces the algorithm comlexity by transorming the whole network ower otimization roblem into several subnetwork ower otimization roblems. Second, several heuristic algorithms to solve the roosed HERO model are veriied. One more major advantage o the roosed energy otimization model is that dierent heuristic algorithms at dierent levels can be adoted. The rest o this aer is organized as ollows. Section II resents the background and motivation o the hierarchical aroach to reduce the ower consumtion o DCNs. Details o the roosed hierarchical aroach, the network connectivity with the roosed HERO model, and the algorithm comlexity are described in Section III. Then, the hierarchical heuristic algorithm is resented in Section IV. The erormance o the roosed HERO model is evaluated in Section V. Section VI concludes this aer. II. BACKGROUND AND MOTIVATION The main idea o the roosed hierarchical network element ower otimization model is insired rom the observations and analysis o the DCN architectures and traic atterns. In this section, we will discuss the architectures and the traic atterns in DCNs. A. Data Center Toology Conventional DCNs [13] tyically consist o a two- or threetier hierarchical switching inrastructure. Two-tier architecture only has the core and the edge switch tiers. In the three-tier architecture, an aggregation switch tier is inserted in the middle between the core and the edge switch tiers. All servers attach to DCNs through edge tier switches. The edge switches and aggregation switches can orm several switch grous, and the core switches can orm another switch grou as shown in Fig. 1(a). As analyzed in revious works, conventional DCNs have some well-known roblems, e.g., scalability and resource ragmentation, server to server connectivity, and cost. Several new toologies have been roosed or DCNs recently, and they can be divided into two categories, switch-centric toology, e.g., VL2 [14] and PortLand [15], and server-centric toology, e.g., DCell [16] and BCube [17]. VL2 [14] is a three-tier architecture, which shares many eatures with the conventional DCN architecture. The main dierence is that a Clos toology is ormed between the core tier and the aggregation tier switches. VL2 shares almost all o the eatures with the conventional DCN architecture excet the rich connectivity between the aggregation switches and the core switches. PortLand [15] is another three-tier architecture that orms a at-tree toology. The edge and aggregation switches orm a comlete biartite grah, i.e., a Clos grah. A collection o edge and aggregation switches is called a od in PortLand architecture. Each od is connected with all core switches and thus orms a second Clos toology. Thus, each od can orm a switch grou, and the aggregation switches and the core switches can orm another switch grou. Fig. 1. DCN toologies and traic categories. (a) Conventional DCN treelike toology. (b) Fat-tree DCN toology and traic attern. DCell [16] and BCube [17] are reresentative modular DCN architectures, which are constructed with new building blocks o shiing containers instead o server racks. Each container houses u to a ew thousands o servers on multile racks within a standard 40- or 20-t shiing container. The shiing container-based modular data center simliies suly management by hooking u ower, networking, and cooling inrastructure to commence the services, shortens deloyment time, increases system and ower density, and reduces cooling and manuacturing cost. Both DCell and BCube are multilevel recursively deined DCN architectures built with miniswitches and servers equied with multile network orts. A k-level DCell k and BCube k can be constructed recursively with several (k 1)-level DCell k 1 and BCube k 1, resectively. Thereore, each DCell k 1 and BCube k 1 can orm one switch collection, and the k-level switches can orm another switch grou. As analyzed earlier, we can observe that almost all the toologies o DCNs tyically consist o a two- or three-tier hierarchical switching inrastructure, including the conventional treelike switching inrastructure and newly roosed data center architectures. The networking elements, including switches and links, can be organized into several grous. B. Data Center Traic Patterns Traic in DCNs can be categorized into ive classes: intraedge switch traic, interedge but intraod traic, interod traic, incoming traic, and outgoing traic. For the intraedge switch traic shown as F1 in Fig. 1(b), it only requires the connected edge switch and links to be owered on to minimize the ower consumtion. The interedge but intraod traic goes within the same od but needs to go through dierent edge switches, shown as F2 in Fig. 1(b). Interod traic is the lows that go through dierent ods, shown as F3 in Fig. 1(b). The incoming (F4) and the outgoing (F5) traic are traic lows that go into and out o DCNs, resectively. The aorementioned observations on hierarchical DCN toologies and data center traic atterns suggest that a DCN can be divided into several od-level subnetworks and a

3 408 IEEE SYSTEMS JOURNAL, VOL. 9, NO. 2, JUNE 2015 od-level network element ower otimization. The otimizer s role in each level is to ind the minimum ower network subset to meet the erormance and ault tolerance goals by owering o the unneeded switches and links. In this section, we describe the hierarchical energy otimization algorithm and also analyze the algorithm comlexity. Fig. 2. Subnetwork toologies o a 4-ary at-tree network. (a) Pod-level subgrah. (b) Core-level subgrah. core-level subnetwork, and also, the traic can be reorganized accordingly. As an examle, Fig. 2 shows the subnetwork toologies o a 4-ary at-tree network as shown in Fig. 1(b). There are our ods (Pod0 Pod3), each o which contains edge switches, aggregation switches, and servers. As discussed earlier, the traic related to one od can be reorganized as intraedge switch traic, interedge but intraod traic, odincoming traic, and od-outgoing traic. The od-incoming traic is merged rom interod traic and incoming traic rom outside o the DCN destination to one o the servers belonging to this od, while the od-outgoing traic is merged rom interod traic and outgoing traic to outside o the DCN that originated rom one o the servers belonging to this od. For each od, a od-level subnetwork can be ormed with the original od, a virtual node reresenting the destination o the od-incoming traic and the source o the od-outgoing traic, and virtual links, each o which connects the virtual node with one o the aggregation switches belonging to this od as shown in Fig. 2(a). Similarly, by abstracting each od in Fig. 1(b) to a virtual od node, a core-level subnetwork can be ormulated with these virtual od nodes, the core switches, a virtual source/destination node reresenting the source o the incoming traic and the destination o the outgoing traic, and some virtual links, each o which connects the virtual source/destination node with one o the core switches as shown in Fig. 2(b). The traic or this core-level subnetwork can be reorganized rom the original traic or the whole DCN by removing the intraedge switch traic and interedge but intraod traic. The aorementioned observations and analysis call or hierarchical energy otimization. The ower otimization o data centers can be divided into two levels: core level and od level. The objectives o core-level ower otimization are twoold: to determine the core switches that must stay active to send the outgoing traic and the aggregation switches which serve the out-od traic in each od. The objective o od-level ower otimization is to determine the aggregation switches that must be owered to low the intraod traic. The otential beneit o hierarchical energy otimization is to simliy the network element energy otimization roblem by reducing the number o variables greatly. III. HIERARCHICAL ENERGY OPTIMIZATION ALGORITHM As analyzed earlier, the networking inrastructure ower otimization o DCNs can be divided into the core-level and the A. Problem Formulation Given the network toology, the traic matrix, and the ower consumtion o each link and switch, the designed core-level and od-level ower otimizations can be modeled as two caacitated multicommodity minimum cost low (CMCF) [18] roblems. The basic assumtions are given as ollows. 1) A hysical network toology is given. The DCN inrastructure can be modeled by a grah G =(V,E), where V and E are the set o vertices and edges, resectively. The vertices reresent network nodes while the edges reresent network links. We use N and L to denote the cardinality o V and E, namely, N = V and L = E, resectively. C ij denotes the caacity o link rom node i to node j, and α [0, 1] reresents the maximum link utilization. The core-level and od-level ower otimizations can be solved based on the core-level subgrah G c =(V c,e c ) and a series o od-level subgrahs G i = (V i,e i )(i [1,N ]), resectively, where N is the total number o ods. The core-level subgrah G c =(V c,e c ) as shown in Fig. 2(b) is ormulated in terms o the core switches, the links connecting the aggregation switches and core switches, and the virtual nodes, each o which reresents a od. V c and E c denote the set o core-level vertices and edges, and N c = V c and L c = E c are the total number o nodes and links in the core-level subgrah G c. A od-level subgrah G i =(V i,e i )(i [1,N ]) as shown in Fig. 2(a) is ormulated in terms o a od and a virtual node reresenting the destination o the out-od traic. V i and E i denote the set o od-level vertices and edges in the od-level subgrah G i or the od i (i [1,N ]), and N i = V i and L i = E i are the total number o nodes and links in the od-level subgrah G i or the od i. 2) The average amount o traic exchanged by any source/ destination node air is also given. Denote t sd as the average amount o traic or the source target air (s, d) V V, meaning the traic that goes rom source s to destination d. T = {t sd } ( s, d V ) reresents the traic demand matrix which seciies the amount o traic t sd to be transmitted or each source destination air (s, d) V V. By transorming the traic demand matrix T = {t sd } ( s, d V ), we can get the core-level traic matrix T c = {t c sd } ( s, d V c ) and a series o od-level traic matrices T i = {t i sd } (i [1,N ]), where i (i [1,N ]) denotes the ith od and N is the total number o ods. t c m n is the average amount o traic going rom source od m to destination od n. 3) The ower consumtion o each node and link is given. Denote Pi N and Pij L as the ower consumtion o node i and that o the link between node i and node j, resectively.

4 ZHANG AND ANSARI: HERO: HIERARCHICAL ENERGY OPTIMIZATION FOR DCNS 409 Based on the aorementioned deinitions, the core-level CMCF roblem can be ormulated as ollows. The objective unction is to minimize Ptotal c = x ij Pij L + y i Pi N (1) j=1 where Ptotal c denotes the total ower consumtion o network switches and links in the core-level subgrah G c. x ij {0, 1} and y i {0, 1} reresent the ower status o link (i, j) E and node i V, resectively. x ij {0, 1} is a binary variable that is equal to 1 i the link between node i and node j is owered on; otherwise, it is equal to 0. Similarly, y i {0, 1} is a binary variable that takes the value o 1 i node i is owered on. It is subject to the ollowing. 1) Flow conservation: Commodities are neither created nor destroyed at intermediate nodes sd c ij sd c ji =0, ( s, d, i, j V c,j s, d) (2) where ( sd ij )c denotes the amount o traic low rom node s to node d routing through the arc rom node i to node j in the core-level subgrah G c. 2) Demand satisaction: Each source and sink sends and receives an amount o low equal to its demand, resectively sd c ij { sd c t c ji = sd s, d V c,j = s t c sd s, d V c,j = d. 3) Caacity and utilization constraint: The total low along each link c ij ( i, j V c ) must be smaller than the link caacity weighed by the link utilization requirement actor α s=1 d=1 (3) ij c = sd c ij αcij x ij, i, j V c (4) where ij c reresents the total amount o traic lowing on the link (i, j) E c in the core-level subgrah G c. 4) Switch turno rule: A node can be turned o only i all incoming and outgoing links are actually turned o x ij + x ji My i, i V c (5) j=1 j=1 where M is twice the total number o links connected to node i in the subgrah G c. Similarly, the od-level CMCF ower otimization can also be ormulated as ollows. The objective unction or od m ower otimization is to minimize P m total = Nm Nm Nm x ij Pij L + y i Pi N (6) j=1 where P m total denotes the total ower consumtion o network switches and links in the od-level subgrah G m. It is subject to the ollowing. 1) Flow conservation N m ( sd ij ) m N m ( sd ji ) m =0, ( s, d, i, j V m,j s, d) (7) where (ij sd) m denotes the amount o low rom node s to node d routing through the arc rom node i to node j in the core-level subgrah G m. 2) Demand satisaction N m ( sd ij ) m N m { sd m t m ji = sd s, d Vm,j=s t m sd s, d Vm,j=d (8) where ij sd denotes the amount o traic low rom source s to destination d that is routed through the arc between node i and node j in od m. 3) Caacity and utilization constraint m ij = Nm Nm s=1 d=1 sd m ij αcij x ij, i, j Vm (9) where m ij reresents the total amount o traic lowing on the link (i, j) Em in the od-level subgrah G m. 4) Switch turno rule Nm Nm x ij + x ji My i, i Vm. (10) j=1 j=1 In order to avoid switching requently between ON/OFF ower states, we introduce the switching ower enalty o each switch in our otimization model: The core-level and od-level objective unctions can be extended with (11) and (12), resectively, while the constraints in the core-level and od-level ower otimizations can be ket the same as described earlier P c total = P m total = N x ij Pij L + y i Pi N j=1 + P s [ y i (1 yi )+y i (1 y i) ] (11) m Nm Nm x ij Pij L + y i Pi N Nm + P s [ y i (1 yi )+y i (1 y i) ] (12) where P s reresents the switching enalty or turning a node o i it was on and or turning a node on i it was o and y i denotes the ower status o node i determined at the last ower otimization. B. Algorithm Descrition A ormal descrition o the HERO algorithm is shown in Algorithm 1. The HERO algorithm can be erormed in our stes. In the irst ste, the ower status o the edge switches and edge links connecting the end hosts and edge switches is determined according to traic matrix T. All edge switches, connecting to any source server or destination server in the traic matrix T, must be owered on, and others can be owered o. The ower status o the core switches and core-level links connecting the core switches and aggregation switches

5 410 IEEE SYSTEMS JOURNAL, VOL. 9, NO. 2, JUNE 2015 is determined by solving the core-level CMCF otimization roblem with the core-level subgrah G c, the traic demand matrix among ods T c, and the ower consumtions o each core switch Pi N and the core-level links Pij L. The aggregation switches serve the od-incoming and the od-outgoing traic, which are also the traic to be considered in the core-level ower otimization, so the aggregation switches with the lowest ower consumtions should be selected in the core-level ower otimization. However, the aggregation switches are not involved directly in the core-level ower otimization because they are contained in the virtual od nodes. The link connecting an aggregation switch and a core switch is unique, and HERO erorms ower otimization rom the core-level ower otimization to the od-level ower otimization; thereore, the ower status o the link connecting one core switch and one aggregation switch in the core-level ower otimization also determines the ower status o the aggregation switch that this link connects to since, i the link is owered u, the switch that it connects to must be owered on anyway. Thereore, in order to guarantee that the aggregation switches with the lowest ower consumtions are selected or lowing the od-incoming and the od-outgoing traic in the core-level ower otimization, the ower consumtion arameter o the core-level link uses the ower consumtion o the aggregation switch that it uniquely connects to instead o its own ower consumtion in the core-level ower otimization roblem. This is based on the observation that the ower consumed by one link is much smaller than one switch. The ower status o these selected aggregation switches will be used as the inut to the od-level otimization roblem in Ste 3. The ower consumtions o the virtual od nodes, the virtual source/destination node, and the virtual links connecting the core switches with the virtual source/destination node in the core-level ower otimization are assumed to be zero. Then, in each od, the ower status o the aggregation switches serving intraod traic and that o the od-level links connecting the edge switches and aggregation switches are determined by solving the od-level otimization roblem with the od-level subgrah G i, the traic demand matrix T i in od i, the ower consumtion o each link Pij L and node N i in od i, and the ower status o the aggregation switches that serve the out-od traic determined in Ste 2. The aggregation switches selected to be owered on in the second ste and the link connecting the selected aggregation switch to the virtual node in each od are switched on. Finally, in order to maintain the whole network connectivity, some ault tolerance, and QoS guarantees, a comlementary rocess is erormed. The basic network connectivity to route traic deined in the given traic matrix is ensured by the HERO algorithm, which will be illustrated in the next section. However, in some secial cases, the whole network connectivity could be broken. For examle, i all the traic lows in a traic matrix can be classiied into intraedge traic or interedge but intraod traic, the otimal solution obtained by the otimization roblem in HERO will ut all core switches into the idle state, and thus, the connection between the data center and the Internet outside the data center is broken. Similarly, the connection between a od and other ods in a data center or the connection between a od and the Internet outside the data center may be broken. In this aer, two basic rules are imlemented in the comlementary rocess. One is that at least one core switch is owered on. I none o the core switches is turned on, one core switch is randomly selected to be owered on. Another rule is that at least one aggregation switch that can connect to one active core switch must be turned on in each od. I no such aggregation switch is turned on in one od, the one which connects to a owered-on core switch will be switched on. Algorithm 1 Hierarchical Energy Otimization Algorithm Ste 1: Determine the ower status o edge switches and edge links according to traic demand matrix T. Ste 2: Solve the core-level CMCF otimization roblem. Ste 2.1: The ower status o core switches and core-level links connecting the aggregation switches and the core switches is decided by solving the core-level CMCF otimization roblem. Ste 2.2: The aggregation switches serving the out-od traic in each od are selected with the ower status o the core-level links, and the selected aggregation switches are owered on. Ste 3: Solve the od-level CMCF otimization roblem. ori =1to N do Determine the ower status o the aggregation switches and the od-level links connecting the edge switches and the aggregation switches by solving the od-level otimization roblem. end or Ste 4: In order to rovision the whole network connectivity and to meet QoS goals, a merging rocess is erormed. C. Connectivity Certiication In this section, we illustrate how the network connectivity can be ensured to route the traic deined in the given traic matrix by HERO. 1) The connectivity between the servers and edge switches is maintained since the ower statuses o edge switches and edge links are determined according to the traic matrix directly. 2) The connectivity between the edge and aggregation switches in each od and the connectivity between the aggregation and core switches are guaranteed by the od-level otimization and the core-level otimization, resectively. 3) The otimal solutions o the od-level otimization and the core-level otimization may activate dierent aggregation switches. Thus, the connectivity or out-od traic might be broken. In order to ensure the connectivity or out-od traic, the links connecting the aggregation switches activated in the core-level otimization and the edge switches in each od are required to be activated in the od-level otimization. To realize this, the ower

6 ZHANG AND ANSARI: HERO: HIERARCHICAL ENERGY OPTIMIZATION FOR DCNS 411 TABLE I COMPARISON OF ALGORITHM COMPLEXITY status o the aggregation switches determined in the corelevel otimization is inut to the od-level otimization. I the letover caacity o the active aggregation switches is not enough to accommodate the intraod interedge traic, more aggregation switches will be activated in the od-level otimization. Thereore, the connectivity o out-od traic lows is ensured by introducing the ower status o aggregation switches obtained in the corelevel otimization as the initial condition or the od-level otimization. D. Algorithm Comlexity The algorithm comlexity o the CMCF otimization roblems increases with the increase o the total number o variables and the total number o constraints. As described in Section III-A, the total number o variables in the CMCF ower otimization roblem can be exressed as the sum o the roduct o the total number o traic demands and twice the total number o links considering two directions o communication, the total number o nodes, and the total number o links as ollows: N var = N links 2 N demands + N links + N nodes (13) where N var, N nodes, N links, and N demands denote the total number o otimization variables, nodes, links, and traic demands, resectively. The total number o constraints in the CMCF ower otimization roblem can be exressed as the sum o twice the total number o links, the roduct o the total number o nodes and the total number o demands, and the total number o nodes by the ollowing equation: N con = N links 2+N nodes (N demands +1) (14) where N con reresents the total number o constraints. Table I comares some major arameters related to the algorithm comlexity o the CMCF otimization with a K-ary at-tree toology. As shown in Fig. 1(b), a K-ary at-tree DCN is built u with 5K 2 /4K-ort switches, and the edges switches and aggregation switches are constructed to orm K ods, each o which consists o K/2 edge switches and K/2 aggregation switches. The edge and aggregation switches orm a comlete biartite grah in each od. Thereore, the total numbers o nodes and links in the od-level otimization are K +1 and K 2 /2+K/2, resectively. There are (K/2) 2 K-ort core switches, and each core switch has one ort connected to each o k ods, while each od is connected to all core switches, and thus, i each od is virtualized as a node, the core switches and these virtual nodes orm a second biartite grah. Thereore, the total numbers o nodes and links in the core-level otimization are K 2 /4+K +1and K 3 /4+K 2 /4, resectively. The total numbers o switches and links o the whole K-ary at-tree network are 5K 2 /4 and 3K 3 /4, resectively. The algorithm comlexities o hierarchical and nonhierarchical energy otimization roblems can be comared in terms o the ratio o the total number o variables and the ratio o the total number o constraints. Since the total numbers o links and nodes in each od are much smaller than those in the core level and the core-level and od-level otimization roblems can be solved serially, the algorithm comlexity o the core-level ower otimization roblem dominates the algorithm comlexity in the hierarchical ower otimization model. Hence, the ratio o the total number o variables and the ratio o the total number o constraints between the hierarchical and the nonhierarchical energy otimization algorithm in a K-ary at-tree DCN can be exressed as ρ var = K3 /2 N c D + K3 /4+(K 2 /4+K) 3/2K 3 N D +3/4K 3 +5/4K 2 (15) ρ con = K3 /2+(K 2 /4+K) (N c D +1) 3/2K 3 +5/4K 2 (N D +1) (16) where ρ var and ρ con denote the ratio o the total number o variables and the ratio o the total number o constraints, resectively. N D and ND c denote the total number o the traic demands o the entire network and the core-level traic demands, resectively. Fig. 3 resents the ratios o the total number o variables and the total number o constraints between hierarchical and nonhierarchical energy otimization algorithms with dierent values o K and the total number o lows. Under dierent K and N D values, it is obvious that the ratios o the total number o variables and the ratios o the total number o constraints between the hierarchical and the nonhierarchical model are smaller than 35% and 40%, resectively, imlying that at least 65% and 60% o variables and constraints in the CMCF otimization roblem can be reduced with HERO as comared to the nonhierarchical ower otimization model, resectively. The ratio o the total number o constraints decreases with the increase o arameter K with the same number o lows.

7 412 IEEE SYSTEMS JOURNAL, VOL. 9, NO. 2, JUNE 2015 Fig. 3. Ratios o the total number o (a) variables and (b) constraints between hierarchical and nonhierarchical energy otimization algorithms or the at-tree network toology. (a) Ratio o the total number o variables. (b) Ratio o the total number o constraints. The results shown in Fig. 3 are the worst case because the ratio values are calculated under the condition that the total number o the core-level lows is the same as that o the entire network, while in act, the total number o the corelevel lows is usually much smaller than that o the whole network. In general, there are multile indeendent ods in a data center. Since the od-level otimization roblems can be solved in arallel, the total comutational time to obtain the otimal solution o the HERO model is roughly the sum o the comutational time to solve the core-level otimization roblem and one od-level otimization roblem. As comared to the nonhierarchical otimization model, the comutational time to obtain the otimal solution o the HERO model can also be cut down because both the total number o variables and the total number o constraints are reduced in the otimization roblems o the HERO model. IV. HEURISTIC ALGORITHMS The roosed HERO model or DCNs alls in the class o the CMCF roblem. CMCF is NP-hard, so exact methods can only be used to solve trivial cases. Simle greedy heuristics o node otimization and link otimization were roosed [19] by trying to switch o an additional network node or link. An imroved version o this heuristic algorithm was reorted in [20] by exlicitly considering the ower consumtion amount o the devices. The basic idea is to iterate through the node set or link set by sorting the nodes or links according to their ower consumtion in the node otimization or in the link otimization stage. An energy-aware greedy heuristic routing algorithm or DCNs was resented in [8]. The basic idea o this heuristic routing is to gradually eliminate the lightest loaded switch rom those involved in the routing, based on the total throughut o lows carried by each active switch. The roblem o this heuristic is that it does not take the switch ower consumtion model into consideration while dierent switch models may coexist in a data center. In this aer, several simle greedy heuristic algorithms based on dierent switch elimination criteria are designed to solve the hierarchical otimization roblem or large DCNs. The roosed energy-eicient heuristic algorithm is based on the observation that the ower consumed by one link is much smaller than that o one switch. The switch elimination criterion could be switch throughut, switch ower consumtion, and switch ower eiciency that gradually eliminates the lightest loaded switch based on the total throughut o lows carried by each active switch, the switch with the highest maximum ower consumtion er ort, and the lowest ower-eicient switches, resectively. The ower eiciency o a switch is deined as the total throughut o lows carried by the switch divided by its ower consumtion. The basic idea o the roosed heuristic algorithms is to try to turn o the core switches and core-level links iteratively as well as the aggregation switches and odlevel links iteratively in the core-level and the od-level ower otimization, resectively, so that as ew switches and links as ossible are owered on in DCNs to meet the traic demands and QoS goals. We assume that all switches and links are owered on initially and the traic is routed as normal, and then, we try to selectively ower o the switches and links hierarchically in the core-level and od-level energy otimizations. In the corelevel heuristic, we sort the core switches based on dierent criteria and then try to switch o the selected core switches by checking i the traic can be lowed through other active core switches; i so, we turn them o. Based on the throughutbased criterion and switch-ower-eiciency criterion, the core switches are sorted in the ascending order, while the core switches are sorted in the descending order i the switch ower consumtion criterion is adoted. Thereore, the core switch with the lowest throughut, the lowest ower eiciency, or the highest ower consumtion model is eliminated irst. A similar heuristic is alied to the od-level otimization excet that it tries to turn o aggregation switches in each od. As an imrovement to the switch ower consumtion-based criterion, another switch ower consumtion-based criterion is roosed by sorting the core switches in the descending order o the total ower consumtion o each core switch and its connecting aggregation switches in the core-level ower otimization.

8 ZHANG AND ANSARI: HERO: HIERARCHICAL ENERGY OPTIMIZATION FOR DCNS 413 V. P ERFORMANCE EVALUATION In this section, we irst comare the otimal ower consumtions o network elements o the HERO model and those o the nonhierarchical otimization model. Then, we investigate the ower-saving erormance o dierent heuristic algorithms. The relationshi o the ower consumtions and the network utilization is urther studied with a diurnal traic variation over a day. Moreover, the eects o the ower enalty when owering on or o network elements in the ower otimization model is examined. Three dierent switch ower consumtion models investigated in [7] are reerenced to build a DCN in each evaluation exeriment. Each switch selects its switch model randomly (uniorm distribution) rom these three tyes. In [7], the ower consumtions o three dierent 48-ort switch models with all orts staying at the idle state are measured as 151, 133, and 76 W, resectively. Also, a 1/3 extra ower consumtion required to turn on all orts is observed in [7]. A ositive linear relationshi between the switch ower consumtion with all orts staying at the idle state and the number o switch orts is assumed in our evaluations, meaning that a switch consumes more ower with the increase o the number o switch orts. A. Traic Patterns In the absence o commercial DCN traic traces, we generate several traic atterns to veriy the ower-saving erormance o HERO. 1) Random elehant: An end host sends large elehant lows to any other end host in DCN with uniorm robability. 2) All-to-all data shule: Every end host transers a large amount o data to every other hosts. 3) Staggered (P out, P edge, and P od ): A source host sends traic out o a DCN with robability P out to an end host which is connected by the same edge switch as the source host with robability P edge, to an end host which is within the same od as the source host but connected by dierent edge switches with robability P od, and to the rest o the end hosts with robability 1 P edge P od P out. 4) Diurnal traic variation: The data center traic variation over one day exhibits a clear diurnal attern, in which traic eaks during the day and alls at night. B. Simulation Results 1) HERO Versus Nonhierarchical Model: Thetraicatterns random elehant and all-to-all data shule are two extreme cases with large elehant traic lows only and with small traic lows only, resectively. In order to comare the otimal ower savings o the roosed HERO model and those o the nonhierarchical otimization model, CPLEX [21] is used to obtain the solutions o the CMCF roblems in the evaluations with these two traic atterns. Since current commodity switches are not ower roortional to work loads (even more than 80% o its eak ower consumtion at idle state) and the elehant lows dominate the traic volume in DCNs, we investigate the erormance o the HERO model with elehant lows only irst, the traic Fig. 4. Power consumtions o a 4-ary at-tree DCN with dierent number o elehant traic lows. demand o which or each source destination air will consume the whole edge link caacity. Fig. 4 shows the average ower consumtion o a 4-ary at-tree network with dierent numbers o traic lows. For each number o traic lows, 1000 simulations are erormed with randomly generated traic lows, and the ower consumtion is normalized with resect to the maximum ower consumtion o the whole network. The ower consumtions o the nonhierarchical ower-saving model and traic-load roortional ower consumtion model are also lotted or comarison. The nonhierarchical owersaving model takes the whole DCN toology as an inut to the otimization roblem and does not consider the hierarchical roerty o the DCN toology. ElasticTree [7] is a tyical examle o the nonhierarchical ower otimization model. The traic-load roortional ower consumtion model is a rimary design goal or ower otimization schemes, and thus, this model rovides the lower bound o ower consumtions under dierent traic loads. Such an energy-roortional model ideally consumes no ower when idle, nearly no ower when very little traic is transmitted through the network, and gradually more ower as the traic increases. As shown in Fig. 4, smaller than 5% more o the maximum ower consumtion o the whole network is consumed in HERO than that o the nonhierarchical model. Owing to the QoS and ault tolerance rotection rules imlemented in the comlementary rocedure, more than about 20% o the maximum ower consumtion o the whole network is needed as comared to the traic-load ower roortional model under the worst case. The lower bound and the uer bound ower consumtion under dierent numbers o elehant lows are also shown in Fig. 4, which relects the inluence o source and destination locations on the ower consumtion. Since no aggregation and core switches are required to be owered on or intraedge switch traic lows, the ower consumtion under some seciic number o traic lows is minimized i all the lows are intraedge switch traic. Similarly, the ower consumtion is maximized i all the lows are interod traic. A data shule is an exensive but necessary oeration or some data center oerations. Fig. 5 shows the normalized ower consumtion o a 4-ary at-tree network with all-toall traic under dierent traic loads. With all-to-all traic,

9 414 IEEE SYSTEMS JOURNAL, VOL. 9, NO. 2, JUNE 2015 Fig. 5. Power consumtions o a 4-ary at-tree DCN with all-to-all data shule under dierent traic loads. Fig. 6. Power consumtions o dierent heuristic algorithms in a 16-ary attree DCN with staggered (0.2, 0.4, and 0.24) traic. any host will have a traic low to any other end host. The traic load generated at any host will be distributed to other hosts uniormly. As shown in Fig. 5, the ower consumtions o HERO and the nonhierarchical model are almost the same under dierent traic loads. The ower consumtion at low traic load is much higher than that o the traic-load ower roortional model because every edge switch is active with all-to-all traic. 2) Perormance o Heuristic Algorithms: The staggered traic attern is a mix o intraedge traic, interedge but intraod traic, interod traic, and outgoing traic as discussed in Section II-B, and it is generated to emulate tyical data center traic atterns based on the ublished work [14], [22], [23]. With the staggered traic attern, exeriments are conducted to study the DCN ower consumtions with dierent heuristic algorithms. The ower consumtions o our heuristic algorithms under dierent traic loads with staggered traic attern (0.2, 0.4, and 0.24) in a 16-ary at-tree DCN are shown in Fig. 6. Traic demands are generated randomly. Around 20% o the traic leaves the data center, and 50%, 30%, and 20% o the remaining traic are intraedge switch traic, interedge but intraod traic, and interod traic within a DCN, resectively. As shown in this igure, throughut-based and owereiciency-based switch elimination criteria consume almost the Fig. 7. Power consumtions over a day with a diurnal traic variation attern in a 16-ary at-tree DCN with staggered (0.2, 0.4, and 0.24) traic. same ower. The switch ower consumtion method based on the total ower consumtion o the core and aggregation switches in the core-level ower otimization, labeled with Switch Power (Core + Aggregation), achieves the minimum ower consumtion among these our heuristics. At low utilization, about 37% and 53% o the original DCN ower consumtion can be saved by using this heuristic algorithm in a 16-ary at-tree DCN, resectively, which are quite close to the corresonding 38% and 60% otimal ower savings analyzed in [7]. Also, a linear relationshi between the ower consumtion and the traic load in the range o 20% 70% o the maximum traic load can be observed using this heuristic algorithm. Thereore, the ower consumtion achieved by this heuristic algorithm is very close to that o the otimal solutions o HERO and the nonhierarchical model. 3) Diurnal Traic Variation and Switching Power Penalty: The erormance o HERO with a diurnal traic variation over a day is urther studied. The ower consumtions with the roosed HERO model over one day in 10-min intervals with a diurnal traic variation attern with staggered traic attern (0.2, 0.4, and 0.24) in a 16-ary at-tree DCN are deicted in Fig. 7. In this evaluation, the heuristic algorithm based on the total ower consumtion o the core and aggregation switches in the core-level ower otimization is used. From this igure, we can see that the ower consumtions also show a clear diurnal attern and ollow the network utilization curve. In revious evaluations, the ower enalty when owering on or o network elements is ignored. We investigate such total ower enalty in a 16-ary at-tree DCN over a one-day diurnal traic variation with the HERO model and its extended otimization model, which considers the switching ower enalty o each switch, resectively. In this evaluation, we conduct several exeriments with dierent settings to the switching ower enalty arameter P S in (11) and (12) in the range o [10%, 50%] o the switch s ower consumtion. The results show that the total switching ower enalty in a day with HERO is more than ive times larger than that o its extended otimization model which takes the switching ower enalty into account. We also ound that, by taking the switching ower cost into the ower otimization model, the unnecessary switching ower enalty can be minimized.

10 ZHANG AND ANSARI: HERO: HIERARCHICAL ENERGY OPTIMIZATION FOR DCNS 415 VI. CONCLUSION With the increase o scale o DCNs, existing centralized ower management schemes to reduce the ower consumtions o network elements in DCNs suer rom the scalability roblem. Insired rom the hierarchical architectures and traic atterns o data centers, we have roosed and evaluated the HERO model to reduce the ower consumtion o network elements without violating the connectivity and QoS constraints. In articular, the ower otimization o networking elements by switching o the idle switches or links can be divided into the core-level and the od-level network element ower otimization. Given a hysical DCN toology, the traic matrix, and the ower consumtion o each link and switch, the designed corelevel and od-level ower otimization roblems in the roosed HERO model all in the class o CMCF roblem, which is NP-hard. We have designed several heuristic algorithms based on dierent switch elimination criteria to solve the hierarchical otimization roblem or large data centers. We have evaluated the erormance o the roosed HERO model by generating several traic atterns, including random elehant, all-to-all data shule, staggered (P out, P edge, and P od ), and diurnal traic variation. The simulation results showed that the roosed HERO model can achieve otimized ower consumtions o a DCN similar to that o the nonhierarchical model but with much less comutational eorts. REFERENCES [1] Environmental Protection Agency, Reort to Congress on Server and Data Center Energy Eiciency Public Law , U.S. Environmental Protection Agency, Washington, DC, USA, Tech. Re. ENERGY STAR Program, Aug [2] J. G. Koomey, Growth in Data Center Electricity Use 2005 to 2010, Aug. 4, [3] L. A. Barroso and U. Hölzle, The case or energy-roortional comuting, Comuter, vol. 40, no. 12, , Dec [4] S. Dawson-Haggerty, A. Krioukov, and D. Culler, Power Otimization A Reality Check, EECS Det., Univ. Caliornia, Berkeley, Berkeley, CA, USA, Tech. Re. UCB/EECS , Oct [5] P. Mahadevan, P. Sharma, S. Banerjee, and P. Ranganathan, A ower benchmarking ramework or network devices, in Proc. 8th Int. IFIP-TC 6 Netw. Con., Aachen, Germany, 2009, [6] A. Greenberg, J. Hamilton, D. A. Maltz, and P. Patel, The cost o a cloud: Research roblems in data center networks, Sigcomm Comut. Commun. Rev., vol. 39, no. 1, , Jan [7] B. Heller, S. Seetharaman, P. Mahadevan, Y. Yiakoumis, P. Sharma, S. Banerjee, and N. McKeown, ElasticTree: Saving energy in data center networks, in Proc. 7th Sym. Netw. Syst. Design Imlementation, San Jose, CA, USA, Ar. 2010, [8] Y. Shang, D. Li, and M. Xu, Energy-aware routing in data center network, in Proc. SIGCOMM, New Delhi, India, Aug. 30 Se. 3, 2010, [9] V. Mann, A. Kumar, P. Dutta, and S. Kalyanaraman, VMFlow: Leveraging VM mobility to reduce network ower costs in data centers, in Proc. 10th Int. IFIP TC 6 Con. Netw., Valencia, Sain, May 9 13, 2011, [10] W. Fang, X. Liang, S. Li, L. Chiaraviglio, and N. Xiong, VMPlanner: Otimizing virtual machine lacement and traic low routing to reduce network ower, Comut. Netw., vol. 57, no. 1, , Jan [11] Y. Zhang and N. Ansari, On architecture design, congestion notiication, TCP incast and ower consumtion in data centers, IEEE Commun. Surveys Tuts., vol. 15, no. 1, , First Quarter, [12] Y. Zhang and N. Ansari, HERO: Hierarchical energy otimization or data center networks, in Proc. IEEE ICC, Ottawa, ON, Canada, Jun , 2012, [13] Cisco Data Center Inrastructure 2.5 Design Guide. [Online]. Available: htts:// ccmigration_09186a d.d [14] A. Greenberg, J. R. Hamilton, N. Jain, S. Kandula, C. Kim, P. Lahiri, D. A. Maltz, P. Patel, and S. Senguta, VL2: A scalable and lexible data center network, in Proc. SIGCOMM,Barcelona,Sain,Aug.17 21, 2009, [15] R. Niranjan Mysore, A. Pamboris, N. Farrington, N. Huang, P. Miri, S. Radhakrishnan, V. Subramanya, and A. Vahdat, PortLand: A scalable ault-tolerant layer 2 data center network abric, in Proc. SIGCOMM, Barcelona, Sain, Aug , 2009, [16] C. Guo, H. Wu, K. Tan, L. Shi, Y. Zhang, and S. Lu, DCell: A scalable and ault-tolerant network structure or data centers, in Proc. SIGCOMM, Seattle, WA, USA, Aug , 2008, [17] C. Guo, G. Lu, D. Li, H. Wu, X. Zhang, Y. Shi, C. Tian, Y. Zhang, and S. Lu, BCube: A high erormance, server-centric network architecture or modular data centers, in Proc. SIGCOMM, Barcelona, Sain, Aug , 2009, [18] I. Ghamlouche, T. G. Crainic, and M. Gendreau, Cycle-based neighbourhoods or ixed-charge caacitated multicommodity network design, Oerations Res., vol. 51, no. 4, , Jul [19] L. Chiaraviglio, M. Mellia, and F. Neri, Reducing ower consumtion in backbone networks, in Proc. IEEE ICC, Dresden, Germany, Jun , 2009, [20] L. Chiaraviglio, M. Mellia, and F. Neri, Energy-aware backbone networks: A case study, in Proc. IEEE Int. Con. Commun., Dresden, Germany, Jun , 2009, [21] IBM ILOG CPLEX Otimizer. [Online]. Available: htt://www-01.ibm. com/sotware/integration/otimization/clex-otimizer [22] S. Kandula, S. Senguta, A. Greenberg, P. Patel, and R. Chaiken, The nature o data center traic: Measurements and analysis, in Proc. 9th ACM SIGCOMM Con. IMC, Chicago, IL, USA, 2009, [23] T. Benson, A. Anand, A. Akella, and M. Zhang, Understanding data center traic characteristics, in Proc. ACM Worksho Res. Enterrise Netw., Barcelona, Sain, Aug. 2009, Yan Zhang (S 10) received the B.E. and M.E. degrees in electrical engineering rom Shandong University, Jinan, China, in 2001 and 2004, resectively. She is currently working toward the Ph.D. degree in comuter engineering in the Deartment o Electrical and Comuter Engineering, New Jersey Institute o Technology, Newark, NJ, USA. Her research interests include congestion control and energy otimization in data center networks, content delivery acceleration over wide area networks, and energy-eicient networking. Nirwan Ansari (S 78 M 83 SM 94 F 09) received the Ph.D. degree rom Purdue University, West Laayette, IN, USA. He is a Proessor o electrical and comuter engineering with the New Jersey Institute o Technology, Newark, NJ, USA. He has contributed over 450 technical aers, over one-third ublished in widely cited reereed journals/magazines. He is the holder o over 20 U.S. atents. He has guest edited a number o secial issues, covering various emerging toics in communications and networking. His current research ocuses on various asects o broad-band networks and multimedia communications. Pro. Ansari has assumed various leadershi roles in the IEEE Communications Society, and some o his recognitions include the Thomas Edison Patent Award (2010), New Jersey Inventors Hall o Fame Inventor o the Year Award (2012), and a coule o best aer awards.

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