Freezing forwarding functionality to make the network greener

Computer Networks 78 (2015) 26–41

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Freezing forwarding functionality to make the network greener Marco Polverini a, Antonio Cianfrani a,⇑, Angelo Coiro a, Marco Listanti a, Roberto Bruschi b a b

DIET Department, Sapienza University of Rome, Via Eudossiana, 18, 00184 Rome, Italy CNIT, Research Unit of the University of Genoa, Via all’Opera Pia 13, Genova 16129, Italy

a r t i c l e

i n f o

Article history: Received 28 February 2014 Received in revised form 23 September 2014 Accepted 1 October 2014 Available online 7 January 2015 Keywords: Green networks Energy aware routing Table lookup bypass

a b s t r a c t This work proposes a novel approach to reduce the power consumption of IP routers: freezing the forwarding engine of routers line-cards. In fact, recent studies showed that about 60% of the power consumption of a line-card is wasted to lookup the routing table during packet forwarding process. We first define the proposed approach, called Freezing Forwarding Functionality (F3). Then, we provide an ILP formulation of the energy minimization problem under F 3 mode and define a heuristic algorithm, referred to as Green Backbone Algorithm (GBA), to solve the problem in large networks. The performance of GBA is evaluated under different traffic scenarios in real ISP network topologies, and a comparison with the ILP solution is carried out for small networks. Results show that: (i) GBA performance, in terms of number of nodes in F 3 mode, are very close to optimal ILP solution ones; (ii) a large energy saving (up to 80% of nodes in F 3 mode ) is obtained in large networks during low traffic hours; (iii) a limited impact on paths length increase is achieved. Ó 2014 Elsevier B.V. All rights reserved.

1. Introduction The reduction of energy consumption of IP networks has been a fertile research topic in recent years. Green networking aims at reversing the principle that the network power consumption be constant even though traffic varies over the time. Many techniques have been proposed to adapt the network consumption to the actual traffic load. The most widely used strategy is to put in low-power standby mode a subset of routers and/or line cards according to traffic load variation [1] and to wake them up only if necessary. These mechanisms have to be supported by traffic engineering techniques [2,3] able to modify network paths so that links or routers to be put in standby mode can be bypassed. It has to be noted that they also need a modification or an adaptation of currently adopted routing protocols, for instance, enhancements of routing protocols as OSPF are under study [4]. Most of these studies exclusively ⇑ Corresponding author. E-mail address: [email protected] (A. Cianfrani). http://dx.doi.org/10.1016/j.comnet.2014.10.034 1389-1286/Ó 2014 Elsevier B.V. All rights reserved.

concentrates on links since it is practically infeasible to put in standby an entire node. In fact, in principle, if a whole router were put in standby, it would not be able to receive, to process and to forward packets any more. Consequently, it would be virtually removed from the network topology. This paper faces the problem of defining a low-power state for nodes, avoiding the virtual removal of them from the network. The idea is to define a router state, called Freezing Forwarding Functionality (F 3 ), able to obtain a significant energy saving, comparable to the case of complete ‘‘router standby’’, and, at the same time, able to limit the impact on network performance, stability, and reliability levels. This objective is achieved by introducing a mechanism aiming at bypassing lookup operations in router line-cards. This choice is supported by the consideration that these operations are the most power hungry [5] and a considerable energy saving can be obtained through their deactivation. A preliminary work on the definition of a low-power state for nodes was presented in [6], where the authors describe several theoretical states for network nodes.

M. Polverini et al. / Computer Networks 78 (2015) 26–41

Starting from the ‘‘bridged local’’ operation mode proposed in [6], we defined the ‘‘router standby’’ solution [7], taking into account real router implementation components. This work is an evolution of [7], since: (i) the F 3 mode of operation is defined, providing a more accurate evaluation of the internal architecture of IP routers; (ii) a novel formulation of the energy saving routing problem when F 3 state is available, with the specific constraints of IP routing, such as the destination-based forwarding mechanism and the shortest path routing policy, is proposed; (iii) an improved heuristic algorithm, to be applied in real network cases, is defined and evaluated. Our model proposes that a router can assume two modes of operation: full mode and F 3 mode. In full mode, all the router line cards operate normally; on the contrary, in F 3 mode the routing functionalities are frozen and router line-cards assume specific fixed configurations, making the router behave like a sort of multiplexer/de-multiplexer. With respect to energy saving mechanisms based on the standby approach, the main advantages of F 3 mode are: (i) a router in F 3 mode maintains its network presence, avoiding network connectivity problems and the reduced network reliability due to nodes disconnection; (ii) differently to the node standby approach, the F 3 mode can bring energy saving even in a network scenario where every router is source and/or destination of traffic. The problem of finding the set of nodes to be put in F 3 mode that minimizes the network power consumption and meets routing requirements is modeled as an optimization problem. Moreover, in order to find an approximate solution of the above mentioned problem even in case of large networks, a heuristic algorithm, called Green Backbone Algorithm (GBA), is proposed. The solution of the aforementioned problem will allow the network to work in a highly dynamic way: the nodes kept in full mode will compose a reduced Elastic Backbone that increases or decreases its size according to the needs due to the traffic load. Summarizing, the main contributions of the present paper can be summarized as follows:  the proposition of a low-power mode of operation for routers, called F 3 mode, and its specification according to the architecture of the currently adopted routers hardware;  the formalization of the energy minimization problem in case of F 3 mode taking into account the specific constraints of IP routing features;  the definition of the Green Backbone Algorithm heuristic, able to solve the energy minimization problem in case of large networks and to outperform previously proposed heuristics. The rest of the paper is organized as follows. In Section 2 the contribution of this work with respect to similar solutions already proposed in literature, is highlighted. In Section 3 a brief review of the energy consumption associated to router elements is presented. In Section 4 details of the F 3 mode of operation are given. Section 5 is devoted to the explanation of the topological and traffic requirements under the identification of a feasible network configura-

27

tion. Then, a MILP formulation of the energy minimization problem is presented. Section 6 is focused on the presentation of GBA heuristic algorithm. Finally, results of the performance evaluation study are discussed in Section 7.

2. Previous works In the last few years many works focused on the reduction of energy consumption in backbone networks [8]. Anyway only few of them are devoted to the definition of a low power state for the routers, considering the standby of links/line-cards as the only available option. The main reason of such a situation is that putting a whole device in standby state is equivalent to remove it from the network, with a considerable impact on network performance and reliability. The first work focusing on the definition of a new low power state for routers, different from a simple shut down, was proposed by Kist and Aldraho in [6], where a theoretical analysis of operational modes for routers is provided. The authors define several low power states for a network node; among them the most interesting one is the ‘‘bridged local’’, representing the starting idea of our work. The authors also define a MILP formulation for the detection of a minimal topology, i.e. the minimum number of active nodes to satisfy a specific traffic demand; the formulation is based on the node bypass transformation, leading to a new network topology with an higher number of nodes and links. Due to the high complexity of the MILP problem, in [9] the same authors provide two simple heuristics to find a feasible solution in a real network scenario. The heuristics differ for the sorting criterion used ‘‘to scan’’ the network nodes: (i) the Lightest Node First (LNF) uses a topology parameter, i.e. the node gravity; (ii) the Least Loaded Node (LLN) exploits the node traffic load. Both heuristics try to remove a node from the network following the nodes order, and use the Shortest Path algorithm for network paths computation; as detailed discussed in Section 7, the way to connect each ‘‘bridged local’’ node to the rest of the network is not clearly explained in the work. Starting from the ‘‘bridged local’’ model in [6], we defined the more accurate ‘‘router standby’’ model [7], taking into account the real router implementation components, i.e. those regarding IP packets processing and routing. In the work we also provide a new heuristic solution for the energy minimization problem when router standby is available. The heuristic, based on the wellknown Floyd-Warshall algorithm, is able to detect a subset of network nodes that must work in active state, while the ‘‘router standby’’ state can be enabled on the remaining ones; moreover the problem of detecting the active outgoing link of standby routers is deeply investigated by the introduction of a specific procedure, referred to as bandwidth reassignment phase. In this work we introduce our low power state for routers, referred to as F 3 mode. We provide a new MILP formulation of the energy minimization problem w.r.t [6]: in particular we formulate the problem of detecting the maximum number of nodes to put in F 3 mode, maintaining the classical IP routing among active nodes,

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M. Polverini et al. / Computer Networks 78 (2015) 26–41

i.e. destination-based forwarding and shortest path routing. The MILP formulation here provided is applied to the original network, so there is no need for a graph transformation that increase the complexity of the problem. The implementation aspects of the solution, in terms of hardware architectures capabilities of commercial devices, are deeply investigated w.r.t. [7]: in the next Section the main subcomponents of a router line-card are described, showing the modules that can be turned off during F 3 mode. Finally, an improved heuristic algorithm is here proposed. As will be better explained in Section 6, the new algorithm performs a more accurate analysis of all possible routing solutions. From a physical level point of view, the Table Lookup Bypass (TLB) approach, proposed for the first time in [10] and then recalled in [11,12], can be considered as the general case of our F 3 mode functioning state. The TLB solution is based on the deactivation of processing capabilities at line-card level, similarly to F 3 mode; moreover each linecard can independently switch to the TLB state. In other words the TLB solution focus on line-cards standby and not on the definition of a standby state for the whole router: so we can state that F 3 mode problem is a constrained case of the generic TLB problem. In this paper we prove that our F 3 mode problem formulation has a lower complexity with respect to the TLB one, and we also show that our heuristic can be more easily implemented in a real network, representing in this way a short-term solution for the deployment of a greener Internet.

3. Anatomy of IP router energy consumption We consider commercial state-of-the-art IP router architectures based on line-cards and switching fabric [13,14]. In these architectures, operational power requirements arise from all the hardware elements realizing network-specific functionalities, like the ones related to data and control-planes, as well as from elements devoted to auxiliary functionalities (e.g., air cooling, etc.). In this respect, the data-plane certainly represents the most energy-starving and critical element in the largest part of network device architectures, since it is generally composed of special purpose hardware elements (packet processing engines, network interfaces, etc.) that have to perform per-packet forwarding operations at very high speeds. For instance, Tucker et al. [15] focused on Cisco IP routers [13], and estimated that the data-plane weighs for 54% on the overall device architectures, vs. 11% for the control plane and 35% for power and heat management. The same authors further broke out energy consumption sources at the data-plane. Switching fabric accounts for 18:5% of the power consumption at the data-plane, and the remaining and most relevant part (81:5%) is due to line-cards, which collect the most complex and energy consuming hardware blocs of the device. These indications from Cisco routers are confirmed also by the measurement campaign of the ECONET consortium [5], performed on heterogeneous high-end platforms (from routers to Ethernet and MPLS switches) coming from other vendors.

Fig. 1. Internal architecture of a router line-card.

Internal architectures and hardware solutions of linecards are well-known to sensibly differ among vendors, and often also among platforms of a same vendor. However, a generic scheme of a router line-card can be represented as in Fig. 1. Here, it can be noted that the main building blocks of a line-card can be summarized as follows:  interfaces to and from network transceivers, usually realized by means of widely used buses like the Serial Gigabit Media Independent Interface (SGMII), the 10 Gigabit Attachment Unit Interface (XAUI), etc.;  interfaces to and from the router switching matrix, sometimes realized with the same buses cited above;  hardware chips to perform packet buffering operations to the local memory, and to manipulate headers content (e.g., the IPv4 Time-To-Live field);  specialized hardware engines, often based on Ternary Content Addressable Memories (TCAMs), which perform routing and switching table lookups and Access Control List (ACL) operations. According to the Tucker’s study, internal packet processing (including both lookup and header processing operations) require about 60% of the power consumption at the data-plane of a high-end router, transceivers and buses interfaces weigh for 13%, and buffer management operations for 8:5%. Similar energy consumption figures are also reported in [16], where a 320 Gbps router equipped with four 40 Gbps line-card with optical interfaces is considered. Here, the packet processing is estimated to account about 60% of the energy consumption of a line-card. This huge energy consumption level in packet processor and lookup engines is not surprising, since they are well known performance bottleneck [17,18]. In fact, TCAMs and high-speed packet processors are hardware components that have to perform complex and heterogeneous operations with tight time constraints for large volumes of traffic [17,19]. 4. The F 3 mode The main contribution of this work is the definition of the F 3 mode, a new functioning state reducing the energy consumption of an IP router acting on the lookup operations performed at line-cards level. This new router state is: (i) feasible, i.e. implementable on actual device

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M. Polverini et al. / Computer Networks 78 (2015) 26–41

LE stub network

PP

Switching Fabric

LE

BM

BM LE

LE

PP

Internet

LE

PP

PP

PP

BM

BM LE

stub network

BM

BM LE

PP

LE

PP

Internet

PP

BM

BM

Fig. 2. Example of a node in F 3 mode.

architectures; and (ii) reliable, i.e. able to maintain the network presence of the node so that to not impact network performance and stability. The F 3 mode is based on the possibility for the linecards of a router to work in two modes, namely Full and Table Lookup Bypass (TLB). In the Full mode, the line-card behaves normally and performs all the usual operations on incoming and outgoing traffic. In the TLB mode, proposed in [10], table lookup and packet processing functionalities are frozen, allowing the line-card to enter a reduced power state. In this state, all packets entering the line-card are forwarded towards the same output port of the router regardless of the specific destination address of each of them and without any further packet header elaborations (e.g., changing the time-to-live field, calculating the checksumming, etc.). This simple redirection operation can be easily implemented outside the IP packet processor and the lookup engine. For instance, this operation may be included in the hardware chip performing buffer management operations, since this module usually drives I/O operations towards other line-cards and local ports. In this case, when the F 3 mode is enabled, functionalities provided by the lookup engine and the IP processor are no more needed, and these hardware components can enter low power sleeping states. Despite no physical prototypes of the F 3 mode have been developed, the experimental results and architectural solutions achieved by the ECONET project [20] provide a good demonstration of the implementation feasibility of the F 3 mode on commercial network devices. In the ECONET project, a number of solutions for making packet processing and lookup engines entering sleeping modes have been designed and experimentally tested under different hardware technologies (e.g., FPGA, network processors, etc.) [5]. Moreover, the project also developed a hierarchical interface, named Green Abstraction Layer (GAL), recently approved by ETSI as ES 203 237 standard, which allows setting the energy-aware states of the internal components of a network device [21]. Thus, this standard interface can be used to enable/disable the F 3 mode on a device line-card by sleeping or waking up its packet processing and look up engines. The ECONET experimentations also demonstrated that, also in the presence of almost legacy

hardware technologies and architectures, the energy saving obtainable by sleeping entire subcomponents can exceed 90% of the consumption level in the active mode [5]. Thus, considering the entire line-card and the energy consumption breakdown in Section 3, the F 3 mode can allows reducing the energy consumption level of 50% with respect to the active mode. As already discussed, differently from the generic TLB mode of operation [10], in which each line-card can be in Full mode or in TLB mode toward a specific outgoing port regardless of the state of any other line-card, the model here proposed foresees that the whole router can assume only two different states, namely full mode and Freezing Forwarding Functionality mode (F 3 mode). In the former, all the line-cards work as usual as well as the whole router. In the latter, line-cards assume a specific TLB configuration making the router behave like a sort of ‘‘aggregator’’. To better explain our approach, a simplified scheme of the status assumed by a reference router when F 3 mode is enabled is shown in Fig. 2. The router is equipped with four line-cards, each one with one network port. For the sake of clarity, we split each bidirectional router interface in two different unidirectional functional blocks associated to reception and transmission directions, respectively. We consider a simplified scenario where one of the ports connects the router to a stub network and the other ones to transit nodes (among which multiple paths exist). As shown in Fig. 2, when F 3 mode is enabled, the router can be configured to work in the following manner. The line-card connecting the stub network collects all the incoming traffic destined to the Internet, and, without performing any lookup operation, forwards it to one of the line-cards towards only one transit node. On the other direction, the line-cards connected to transit nodes collect all the incoming traffic, and they all forward it to the stub networks. In this way, the connectivity to and from the stub network is maintained, despite the standby of lookup hardware. It can be noted that, when the node is in F 3 mode, it is not able to manage transit traffic and paths crossing the node need to be rerouted elsewhere over the network. In more detail, in the considered scenario, the node in F 3 mode can manage only paths coming from or terminating at the stub network, since in this configuration

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M. Polverini et al. / Computer Networks 78 (2015) 26–41

it behaves like a sort of ‘‘multiplexer’’ of the Internet traffic to the stub network. The introduction of the F 3 mode leads to three main advantages. First of all, the energy consumption can be highly reduced, as shown in Section 7. Besides energy saving capabilities, the F 3 mode can be implemented more easily than a solution based on node sleeping. In fact, a router in F 3 mode maintains its network presence, avoiding the network connectivity problem and the reduced network reliability due to nodes disconnection. A further positive aspect is that, contrary to the node sleeping approach, the F 3 mode can bring energy saving even in a network scenario where every router is source and/or destination of traffic. Even if this aspect is out of the scope of the paper, it is interesting to briefly describe the impact of our solution on the network reliability. In particular it is interesting to compare the F 3 solution with classical link switch off ones; anyway a more accurate study is required to experimentally prove the following considerations. When F 3 mode is enabled on a device, only the forwarding engines of its line-cards can be switched off: in this way the reactivation of the line-cards functionalities can be performed more quickly with respect to a complete switch-off of the linecard. Moreover, considering the limited reactivation time, it is possible to enable the F 3 mode on all devices used for protection purpose. A last aspect to consider is the network scenario where to implement our proposal. Considering that network paths of all routers must be modified on the basis of the traffic requirements, it is clear that a centralized network control is needed; in this scenario a single node is responsible for the traffic monitoring and for the activation of the F 3 mode on a subset of network routers. This is the classical scenario of an SDN network, where the controller manage the forwarding tables of network nodes. Anyway it is also possible to ‘‘adapt’’ a legacy IP network, so that to allow our F 3 solution. In such a scenario, the F 3 scheme reported in Fig. 2 should be slightly modified so that to allow the F 3 nodes to control packets of the routing protocols: in particular the forwarding engine and the packet processor of the line-cards connecting the F 3 node to the stub network must be activated, so that to manage control packets. Moreover the presence of a central node able to monitor traffic levels and enable F 3 mode on network nodes, by means of an ad-hoc signaling protocol, is needed. In the next section, we formalize the problem of detecting the set of nodes to be put in F 3 mode that minimizes the network power consumption according to routing and traffic requirements.

to define a sort of ‘‘core network’’ with a limited number of nodes. Let us explain this concept using as example the network topology shown in Fig. 3. For instance, let us suppose that the only router a is in full state. It is easy to see that such a configuration is unfeasible. This is because the router d is connected to the rest of the network by means of the router c, which however is in F 3 mode. Thus, since by definition the router c forwards all received packets toward the network stub c, it would cut out the node d from the rest of the network. Now, suppose that all nodes but c are in F 3 mode. In this scenario, the resulting network topology can be assimilated to a star, which is clearly connected. Therefore, this configuration represents a feasible solution. In particular, the node c represents the ‘‘core’’ and all other nodes are connected to it, making the resulting configuration feasible. Finally, let us suppose that nodes a and d are working normally, while b and c are in F 3 mode. Now, even though each node that is in F 3 mode is connected to a node in full state, the resulting network configuration is still disconnected. This is because the node c is cutting the ‘‘core’’ (that is composed by a and d) in two connected domains. The simple example discussed above shows which are the basic topological requirements that the ‘‘core network’’ must meet. As first, it must be connected, i.e., there must be a path connecting any two nodes in the ‘‘core network’’ that is whole contained in the ‘‘core network’’ itself. Secondly, nodes in F 3 mode must have at least one neighbor in the ‘‘core network’’. These requirements coincide with the definition of Connected Dominating Set (CDS). Specifically, given a graph G ¼ ðN ; LÞ, a CDS is a subset of nodes D that respects the following two constraints: 1. any node in D can reach any other node in D by a path that is entirely contained in D. That is, D induces a connected subgraph of G ¼ ðN ; LÞ; 2. every vertex in G ¼ ðN ; LÞ either belongs to D or is adjacent to a vertex in D. That is, D is a dominating set of G ¼ ðN ; LÞ. Thus, by a topological point of view, the nodes that are in F 3 mode are still connected (i.e., the stub networks connected to them can still exchange packets between them), if and only if the set of nodes that are in full state leads to a CDS. Over the CDS we also need to define a valid routing, i.e., a configuration of paths that respects all the features of classical IP routing [22], such as Destination Based

a

stub c

stub d

c

d

stub a

5. The elastic backbone In order to save energy through F 3 mode, a subset of nodes able to manage the routing of all packet flows exchanged between stub networks must be found. This subset of routers must meet specific requirements in order to obtain a feasible routing configuration and avoid some stub networks being unreachable. In more detail, we need

b stub b

Fig. 3. Example of a Connected Dominating Set (CDS).

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M. Polverini et al. / Computer Networks 78 (2015) 26–41

Forwarding (DBF) and Shortest Path (SP), and such that, by routing traffic flows over this set of paths, QoS requirements are satisfied. Referring to the previous example (see Fig. 3) where only the router c is in full state, let us suppose that the link between nodes a and c does not have enough bandwidth to support all the traffic starting from stub a and directed to all the other stub networks. Clearly, such a solution would be infeasible since traffic requirements would not be guaranteed. Then, we would need to insert the node a in the CDS, so that it could split the traffic originated in the stub a over all of its outgoing interfaces and possibly meet traffic requirements. The CDS can be associated to a reduced network, i.e. a backbone, that changes its size as a function of the traffic load. This Elastic Backbone increases (decreases) its size, i.e. the number of nodes, when traffic increases (decreases). The following sub-sections are focused on the problem of finding the optimum CDS able to minimize the energy consumption of a network.

Minimize

X X X þ ðð1  mÞyij þ xj mÞ ¼ ð1  mÞyij þ mjdi jxj ij2E

ij2E

ð2Þ

j2N

Subject to:

X

sd f ji



sd f ij

j2d i

j2dþ i

X

X

8 > < 1 i ¼ s ¼ 1 i¼d > : 0 i – s; d

sd

8s; d 2 K; 8i 2 N

8ij 2 L

f ij t sd 6 C ij yij

ð3Þ

ð4Þ

sd2K

X

sd

f ij 6 Mndij

8ij 2 L; 8d 2 N

ð5Þ

s;d2K

X

ndij ¼



1 ifi – d 0

j2V

8d 2 N ; ij 2 L

ifi ¼ d

8d 2 N ; ij 2 L

pdj þ wij  pdi P 0

ð6Þ

ð7Þ

5.1. Problem formulation In the following, we provide an ILP formulation of the problem of minimizing the energy consumption when nodes have F 3 mode capability. As first, we introduce the notation shown in Table 1. Then, we provide a simple power consumption model for network nodes. We consider the power consumption of the line-cards attached to each node; therefore, we refer to links in the following power consumption model. Indicating as PTOT the total power consumed by a line-card, we consider two contributions of power consumption for links: (i) the power consumed by the Forwarding Engine (FE), which is equal to mPTOT and (ii) the rest of power consumption (i.e. ð1  mÞP TOT ). Then, we consider that, when a node i is in F 3 mode, links ij that are unused can be switched off saving an amount of power equal to ð1  mÞP TOT . Therefore, the power consumption P ij related to a link ij is given by:

Pij ¼ ½yij ð1  mÞ þ xj mPTOT

ð1Þ TOT

According to the model above, and assuming P ¼1 for sake of simplicity, the problem can be formalized as follows.

pdj þ wij  pdi 6 ð1  ndij ÞM

8ij 2 L

wij P 1 X

8d 2 N ; ij 2 L

sd

f ij 6 Mxi

ð8Þ ð9Þ

8ij 2 L

ð10Þ

s;d2Kji–s;d

X yij 6 ðOi  1Þxi þ 1 8i 2 N

ð11Þ

j2d i

yij  xi P 0 8ij 2 E

ð12Þ

Eq. (2) is the objective function which minimizes the total consumed power according to the model defined in (1). Eqs. (3) and (4) respectively represents the set of classical flow conservation and capacity constraints. Constraints in Eqs. (5), (6) and Eqs. (7)–(9) respectively deals with the Destination Based Forwarding (DBF) and Shorthest Path (SP) feature of IP routing. Specifically, (5) constrains the traffic carried on link ij to be 0 if node i does not use node j as next hop to reach d while (6) constrains a node i to use

Table 1 Notation. Symbol

Description

G ¼ ðN ; LÞ T ¼ ðts;d Þ K C ij

The network graph, where N is the set of nodes and L the set of unidirectional links The traffic matrix indicating the amount of traffic t s;d requested between nodes s and d The set of commodities, i.e., all the pairs s; d 2 N such that tsd – 0 The capacity of the link ij The percentage of power consumed by the FE functionality þ The set of links leaving (d i ) or entering (di ) the node i The out-degree of the node i A binary variable equal to 1 if the node i is in full mode A binary variable indicating whether the flow destined to the node d and originated from node s is routed over the link ij or not

m di Oi xi sd

f ij

yij ndij wij pdi

A binary variable equal to 1 if the link ij is used to route the traffic, otherwise 0 A binary variable equal to 1 if the link ij is used to route the traffic destined to d, otherwise 0 An integer variable indicating the weight of link ij An integer variable indicating the cost of the path from i to d

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M. Polverini et al. / Computer Networks 78 (2015) 26–41

a unique next hop j to reach a given destination d. Eq. (7) assures that path costs are coherent with link weights while (8) constrains the variable ndij to be set to 0 if pdi < pdj þ wij . In fact, in this case, node i does not use node j as next hop to reach d. At the same time, Eq. (8) constrains pdi to be equal to pdj þ wij if ndij is equal to 1. Finally Eq. (9) forces the links weights to be positive. Constraints in Eqs. (10) and (11) are related to the F 3 mode. In particular, (10) constraint the flow s; d over all the links leaving node i to be equal to zero if node i is neither the source of the flow nor is in the CDS, assuring that node i will not manage transit traffic if in F 3 mode. Eq. (11) constrains a node i in F 3 mode to use only one outgoing link to forward the packets originated in the stub network connected to it. This constraint guarantees that a node in F 3 mode does not need to use the lookup functionality. Finally, (12) allows a link ij to be unused and then considered as in off state only if node i is in F 3 mode. The problem above falls in the category of capacitated multicommodity flow problems and, as such, is NP-hard [23]. In the next section, we present a heuristic algorithm to solve it in reasonable time even for large networks.

i

i

1-v v j

CDS

1-v

j

CDS

v n

n

(a)

(b)

i

i v j

n

CDS

j

CDS

n

(c)

(d)

Fig. 4. Network configurations for the line-card of a node in F 3 mode.

ter. To formalize the problem, a graph transformation based on nodes splitting is needed, leading to a new transformed graph having OðLÞ nodes and OðNLÞ links. 5.3. Evaluation of the overall energy saving due to F 3 mode

5.2. Comparison among the F 3 and the TLB formulations As already discussed in Section 2, the MILP formulation here proposed is a constrained case of the general TLB problem, proposed in [12]. To better highlight this aspect, we compare both formulations in terms of complexity. In the case of the F 3 mode formulation reported in Secsd tion 5.1, the number of variables, i.e. flow variables f ij , is equal to OðN 2 LÞ, since there are N 2 flows and L links; the number of constraints is equal to OðN 3 Þ. The total number of possible network configuration can be computed considering that each router can be in full state or in a specific F3 state; the number of F3 states for a router depends on the number of links outgoing from it, since for each F3 state a specific neighbor transit router is used to forward locally generated traffic. Indicating with K i the number of transit neighbor nodes of node i, and with K the average node degree of a network, we have that the number of network configurations is given by the following expression: N Y

N

ðK i þ 1Þ 6 ðK þ 1Þ

ð13Þ

i¼1

A similar evaluation can be performed for the TLB formulation reported in [12]: a comparison among the two formulations is reported in Table 2. In the TLB formulation the number of variables, constraints and network configurations increases. The reasons for higher values is that in the TLB case each line-card, and not each router, can independently be in full state or in TLB state toward a specific neighbor rouTable 2 Comparison among F3 and TLB formulations. #

F 3 formulation 2

TLB formulation OðN 3 LÞ

Variables

OðN LÞ

Constraints

OðN 3 Þ

Network configurations

O½ðK þ 1Þ 

OðN 2 LÞ N

L

O½ðK þ 1Þ 

In this subsection, we analyze the overall energy saving that a network can achieve, thanks to the introduction of the F 3 mode. Starting from Eq. (1), we report the network elements involved by this new energy saving approach. It is clear that the energy saving is due to nodes in F 3 mode, and in particular to the forwarding engine freezing on their line-cards. To better explain the overall network energy saving due to F 3 mode, we report in Fig. 4 all the possible network configurations that the generic line-card of a node in F 3 mode can assume. In Fig. 4 we indicate with i the node in F 3 mode we are focusing on, with n a different node in F 3 mode, and with j a node in full mode, i.e. belonging to the CDS, sharing a link with i. In Fig. 4(a) we focus on the link of i toward a node in full mode, that is not its designated router.1 In this case link ij is not used to carry traffic, so on node i the transmission-related functions of the specific line-card can be frozen, leading to an energy saving equal to ð1  mÞP TOT . Moreover, since the node j does not receive any incoming packet on the line-card, its forwarding functionality can be frozen, saving mPTOT . Then, globally, the configuration reported in 4(a), allows to save PTOT . The case reported in Fig. 4(b), regards the link connecting two nodes in F 3 mode. Considering that also in this case the link is not used to transmit packets, this situation is similar, in terms of energy saving, to the one already reported in Fig. 4(a); so the energy saving is equal to P TOT . In the case depicted in Fig. 4(c), a node in full mode is connected to a node in F 3 mode. Here, all packets received by the line-card of the node i are directly forwarded towards the local stub network; so the packet processing operations can be frozen, allowing a saving equal to mPTOT . Finally in the case shown in Fig. 4(d), a node in F 3 mode is connected to its designated router. It s clear that no energy saving is here possible. 1 the designated router of a node in F 3 mode is the node to which it sends all its local demand.

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M. Polverini et al. / Computer Networks 78 (2015) 26–41

In conclusion, the total energy saving achievable by using a solution based on F 3 mode can be expressed as:

ES ¼ K þ CðmÞ ¼

N N X N X X xi ðdi  1ÞP TOT þ aij xi yj mPTOT i¼1

ð14Þ

i¼1 j¼1

where xi is a coefficient equal to 1 if the node i is in F 3 mode, di is the out degree of the node i; aij is a coefficient equal to 1 if nodes i and j are adjacent and yj is a coefficient equal to 1 if node j is in full mode. As it can be seen from Eq. (14), the overall energy saving is composed of two terms: the first one only depends on the number of nodes in F 3 mode and on their link degree; the second one also depends on m, i.e. the percentage of power consumed by the forwarding engine. 6. The green backbone algorithm In this section, we describe a heuristic algorithm, called Green Backbone Algorithm (GBA ), able to find near optimal solutions of the problem formalized in the previous section. In more detail, GBA is able to find a set of nodes that can be put in F 3 mode respecting the following constraints: 1. a node in F 3 mode can be only source or destination of a path; 2. the set of paths must be chosen according to SP routing; 3. all paths starting from a node in F 3 mode must have the same next hop or, equivalently, a node in F 3 mode can use only one outgoing link; 4. the traffic matrix can be supported with this set of paths. A direct consequence of constraint 1 is that, as already discussed, the set of nodes in full state will be a CDS of the original network graph. However, due to constraints 2, 3, and 4, finding a CDS is not sufficient in order to obtain a feasible solution. This is why we cannot use one of the heuristics available in the literature to find a CDS [24,25] but need to define a new heuristic. GBA is based on an iterative process within which two main functions are used, namely the CDS computation algorithm and the F 3 nodes detection algorithm. The CDS computation algorithm takes as input the set of nodes I  N and the whole network graph G and is able to check whether or not I is a CDS for G. We refer to a connected state when the set I is a CDS for G. In this case, the CDS computation algorithm also returns as output a set of paths P, which respect SP routing, between each node pair within the network. The F 3 nodes detection algorithm is invoked only if a CDS has already been found; i.e., if a connected state has been reached. It takes as input the network graph G, the set of link capacities C, the traffic matrix T , the set of nodes S ¼ N n I , which is the set of candidate nodes to be put in F 3 mode, and the set of paths P, and return as output a subset of nodes S   S that can be actually put in F 3 mode according to constraints (3) and (4) identified above. It also

returns as output the set L that is a set of jS  j links each of which is the unique outgoing link used by each specific node s 2 S  . The details of this two algorithms will be provided in the next two subsections. The pseudo code of GBA is shown in Alg. 1. As first, GBA sorts network nodes in order to create a list L (line 3). Many criteria could be defined. Here, we sort nodes in decreasing order of their betweenness (i.e., the number of times that a node appears in a shortest path) considering the original network graph. At the beginning, I is an empty set. Then, at each step, a new node is inserted in I (line 4) according to list L (line 5) and the CDS computation algorithm is invoked (line 7). If the resulting state is connected (line 8), the F 3 nodes detection algorithm is invoked (line 10), otherwise another node is added to the set I . The set LOn , that is the set of all links that will be used to route traffic, is updated at each step according to the constraint (12) in Section 5.1 (line 6). When the second algorithm is invoked, it returns as output the set S   S along with the specific next hop that each of which will use, i.e., L (line 10). If the cardinality of S  is higher than the best solution found until that step, i.e., F3 N , than S  is stored as the new best solution (lines 11– 14). Then, another node is added to the set I until it is posF3 sible to find a solution better than the solution in N (lines F3 16–18). This depends on whether the cardinality of N is higher than the maximum possible cardinality of the set S  that could be found at the next step, which is equal to jSj  1. In the next subsections, we describe the two algorithms invoked by GBA. Algorithm 1. GBA pseudo code 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19:

INPUT: GðN ; L; WÞ; T ; C F3

Set I ¼ ;; N ¼ ;; LOn ¼ ; list L = sort_node(G) for i ¼ 1 : jN j do pick node LðiÞ and put it in I LOn ¼ fij 2 L : i 2 I g ðconnected state; PÞ ¼ CDS computation algorithm ðG; T ; C; I Þ if connected_state then S ¼N nI ðS  ; L Þ ¼ F 3 nodes detection algorithm ðG; P; T ; C; I ; SÞ 3

if jS j > jN F j then 3

N F ¼ S LOn ¼ LOn [ L end if end if F3

if jN j P jSj  1 then 3

return N F and LOn as output and stop the algorithm end if end for

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M. Polverini et al. / Computer Networks 78 (2015) 26–41

6.1. The CDS computation algorithm

traffic matrix can be supported with the current set of paths P r .

The CDS computation algorithm is based on the FloydWarshall (FW) algorithm, which is an algorithm able find shortest paths in a weighted graph [26]. During its execution, FW algorithm divides nodes in two sets: 1. I , the set of nodes, defined as transit nodes, that can be crossed by a path; 2. S, the set of nodes, defined as terminating nodes, that can be only source or destination of a path. FW works by iteratively updating a matrix D ¼ ðdsd Þ that contains the cost of each path at a given round r. When the algorithm starts, the set I is empty, S coincides with N and all elements of D have an infinite cost except those elements ðs; dÞ corresponding to adjacent nodes in GðN ; EÞ, for which dsd ¼ wsd . Then, at each round r, a new node k 2 S is removed from S an added to I , and the matrix D is updated. Specifically, since the node k becomes a transit node, a new path is available for each source–destination pair ðs; dÞ, which is given by the union of the paths found at the previous round from s to k and from k to d. Therefore, for each source–destination pair ðs; dÞ, the cost r1 of the path dsd computed at the previous round is compared with the cost of this new path and, if higher, both the path and the cost are updated. When all nodes have been inserted in I , the algorithm stops and the entire set of shortest paths is available. The FW algorithm has complexity equal to OðjN j3 Þ. It has to be noted that, since a node i 2 I (at a generic round r) may be crossed by a path, it cannot be put in F 3 mode. Here, we use the FW algorithm to state whether a set of nodes represents a CDS or not. In fact, given a generic round r of FW algorithm, nodes in I lead to a CDS if and only if the following condition is met: r

dsd < 1 8ðs; dÞ 2 N  N

ð15Þ

As already said, we refer to a FW round r that verify this condition as connected state, and to the related set of paths as P r . When a connected state is reached, all nodes in S could be potentially put in F 3 mode, since they all are not crossed by transit paths. Unfortunately, even if a CDS has been found, we have no guarantee that, according to the current set of paths P r , each node s 2 S uses always the same next hop. Specifically, the routing configuration found by FW may lead to the following situations.  Direct paths between two nodes in S. Note that, if a link exists between two nodes s1 ; s2 2 S, then FW may find a directed path between them instead of a path traversing a transit node i 2 I ;  More than one neighbor node i 2 I used as next hop by a node s 2 S. In both cases, the configuration of paths P r does not allows node s to be put in F 3 mode since it has to execute lookup operations on the routing table to find the right next hop router. Moreover, there is no guarantee that the

6.2. The F 3 nodes detection algorithm Let us consider a set of nodes I that is a CDS of G, and a set of paths P respecting SP routing. As already stressed in the previous subsection, nodes into the set S ¼ N n I could be potentially put in F 3 mode. The F 3 nodes detection algorithm deals with finding a subset of nodes S   S that can be put in F 3 mode along with the set of next hops L they have to use. As a preliminary step, it has to verify that all traffic flows between node pairs in I can be supported. If not, it will return as output S  ¼ ; and L ¼ fsj 2 L : s 2 S g as no node s 2 S can be put in F 3 mode. Moreover, for a node to be put in F 3 mode it must use a single next hop and all its traffic demand must be supported by the network. This correspond to assign the demand of a node s 2 S to one of its neighbors i 2 I . Therefore, the problem is to find the maximum number of nodes s 2 S whose demand can be assigned to one of its neighbors in i 2 I . We call this phase Demand Assignment Problem. 6.2.1. Demand assignment problem Let C ij be the residual capacity of link ij 2 L after the allocation of traffic demands of all nodes i 2 I using paths in P. For each node s 2 S, we indicate with I s the set of its P neighbors j 2 I such that C sj P t s , where ts ¼ d t sd . Note that nodes j 2 I s are the only full mode neighbors of node s that could support all its traffic demand. Let asj be a binary variable equal to 1 if the demand of node s is assigned to j 2 I s and bs a binary variable equal to 1 if the demand of node s is not reassigned to any node, i.e., if node s is kept in full mode. In addition, let Cnm sj be the amount of traffic routed on link nm according to paths in P when the demand of node s 2 S is assigned to node j 2 I s . Finally, let Hnm be the amount of traffic routed on link nm s according to paths in P when the demand of node s is not nm reassigned to any node. Note that Cnm can be eassj and Hs ily computed according to the traffic matrix T and the set of paths P. Using the notation introduced above, the Demand Assignment Problem can be formulated as follows:

min

X bs

ð16Þ

s2S

Subject to:

XX

X

s2S j2I s

s2S

Cnm sj asj þ

 Hnm 8nm 2 L s bs 6 C nm

X asj þ bs ¼ 1 8s 2 S

ð17Þ

ð18Þ

s2S

The objective function (16) selects the solution that minimizes the number of nodes kept in full mode. Eq. (17) represents capacity constraints. Finally, constraints in (18) are introduced to guarantee that every terminating node uses a unique next hop j 2 I or is kept in full mode. The Demand Assignment Problem is an ILP, and solving it in general could be not trivial. However, in our

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M. Polverini et al. / Computer Networks 78 (2015) 26–41 175

Execution Time (s)

simulations we solved it optimally (using CPLEX) even for very large networks, i.e. N > 100, and the execution time was in the order of milliseconds. Once the demand assignment problem has been solved, the F 3 nodes detection algorithm returns as output the set of nodes S  ¼ fs : bs ¼ 0gand the set of links  L ¼ sj : asj ¼ 1 .

FWNS GBA

150 125 100 75 50 25

6.3. Comparison between GBA and FWNS

0

The GBA algorithm here proposed is an improved version of the Floyd-Warshall Node Standby (FWNS) algorithm described in [7]. Basically, both algorithms consist of two main modules. In the first module, both GBA and FWNS execute the Floyd-Warshall algorithm, looking for a subset of nodes composing a CDS. The goal of the second module is to detect, among nodes not belonging to the CDS, the nodes to put in F 3 mode along with a specific designated router. The main difference among the two algorithms involves the execution of the second module. In the case of FWNS, the second module receives from the first one a CDS as a starting data; the module tries to put in F 3 mode all nodes not belonging to the CDS. If this operation is successfully, then the FWNS algorithm stops, otherwise the computed CDS is discarded and a new run of the first step is performed in order to find a different CDS. In the case of GBA, the second module simply tries to maximize the number of nodes in F 3 mode, among those not belonging to the CDS computed by the first module, while guaranteeing constraints 17 and 18. If a feasible solution is found, i.e. a certain amount of nodes in F 3 mode with their designated routers, then the algorithm save it; then a new CDS is explored and the second module is executed again, until the terminating condition reported in line 16 of Algorithm 1 is verified: at this point the algorithm stops and the best configuration, in terms of number of nodes in F 3 mode, is returned. In general, we can say that the second module of FWNS is hard, i.e. only a complete solution of the problem is considered, and memoryless; on the other hand the second phase of GBA is soft, i.e. partial solutions are saved, and with memory. To conclude the comparison among GBA and FWNS, we report in Fig. 5 their execution time (in seconds) as a function of the size of the network in terms of number of nodes. In particular, we generate random topologies and, according to a uniform distribution, a traffic matrix for each topology. As it can be seen, the modification introduced in the second module of GBA do not impact on the algorithm complexity, since the execution times of both algo-

20

40

60

80

100

120

140

160

180

# of Nodes Fig. 5. Execution time of GBA and FWNS as a function of the number of nodes.

rithms are comparable. Moreover, it is also interesting to note that for networks of about 100 nodes the execution time is about 25 s, that can be considered negligible with respect to the time needed to appreciate a consistent traffic variation. 7. Performance evaluation This section deals with the performance analysis of GBA and F 3 mode in general. In order to asses the performance of GBA, we consider three real ISP topologies, namely Tiscali and Level3 retrieved from [27] and France Telecom (FT) [28], and two small test networks to solve the ILP model. Table 3 reports the main topological parameters of each considered network. For each network, we randomly generate 20 traffic matrices representing the peak traffic and mediate results over them. Link capacities are dimensioned by routing traffic demands according to SP routing and imposing them equal to the amount of traffic flowing on each link. To simulate the traffic variation over time, we introduce the scaling factor a. Two kinds of traffic are considered: (i) uniform and (ii) gravity. In the first case each traffic demand t sd is chosen according to a uniform probability in the interval ½0:5; 1:5. In the second case, it is computed according to a gravity model considering the degree of each node as in [2]. To evaluate the energy saving (ES ) of GBA we set m ¼ 0:5 in Eq. (2). Section 7.1 reports the results of the ILP model presented in Section 5.1, while the performance of GBA for large networks are shown in Section 7.2. 7.1. Comparison with ILP model Here, we evaluate GBA against the optimal solution of the ILP model defined in Section 5.1 by defining the GBA

Table 3 ISP topologies. ISP

Nodes

Links

Mean node degree

Diameter

Average path length

Tiscali FT Level3 Test1 Test2

41 38 63 11 10

87 72 285 34 18

4.24 3.79 9.05 6.18 2.91

5 4 4 3 3

2.15 2.64 2.29 1.27 2.21

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M. Polverini et al. / Computer Networks 78 (2015) 26–41

GBA efficiency

1

0.9 ν=0.25 ν=0.50 ν=0.75 ν=0.25 ν=0.50 ν=0.75

0.8

0.1

0.2

0.3

0.4

0.5

α

0.6

0.7

0.8

0.9

1

0.8

0.9

1

(a) Test1 network.

GBA efficiency

1 0.98 0.96 0.94 0.92 0.1

ν=0.25 − U ν=0.50 − U ν=0.75 − U ν=0.25 − G ν=0.50 − G ν=0.75 − G

0.2

0.3

0.4

0.5

0.6

0.7

α

(b) Test2 network. Fig. 6. GBA efficiency vs. a in case of Test1 and Test2 networks.

efficiency as ratio between the power consumption in case of ILP and GBA. Fig. 6 shows the GBA efficiency while in Fig. 7 the power saving percentage in case of ILP solution is depicted for both Test1 (left) and Test2 (right) network; both test networks are obtained solving the classical MILP

formulation provided in [12], so that to minimize the number of links given as input the peak traffic matrix and a full meshed topology. As far as the power saving of ILP is concerned, it can be seen that the two networks behave quite differently. Test1 is very meshed and, as such, it allows to save up to 70% of power when a is very low due to the small cardinality of the minimum CDS. However, since the nodal degree is quite uniform within the network, only few low-degree nodes can be put in F 3 mode as a increases, which however bring low power saving with respect to the total. On the contrary, the low K of Test2 network does not allow to reach the same savings as Test1 when a is low but allows to achieve better performance when a increases. Finally, it can be seen that no significant difference is experienced between gravity and uniform traffic, while increasing m just leads to a little performance increase for Test2. Concerning the efficiency of GBA, it can be seen that it is always higher than 78%, with values greater than 90% in quite all cases. Specifically, the lowest efficiency is experienced in case of Test1 network, gravity traffic, and a ¼ 0:1, when the saving of the ILP solution rapidly increases. This loss of efficiency is due to the fact that GBA tries to maximize the number of nodes in F 3 mode without considering the actual energy saving. Then, it generally leads to lots of low-degree nodes entering F 3 mode, especially when highdegree nodes originate/terminate a lot of traffic, as in case of gravity model. However, in these specific conditions, some high-degree nodes, which clearly bring more saving, could be put in F 3 mode. Finally, in case of Test2 network, GBA experiences higher efficiency than in previous case. The highest loss of efficiency, which however is less than 10%, is experienced when the increase of a makes the saving pass from high to moderate levels. 7.2. Performance of GBA in large ISP networks

ν=0.25 − U ν=0.50 − U ν=0.75 − U ν=0.25 − G ν=0.50 − G ν=0.75 − G

ES %

60

40

20

0.1

0.2

0.3

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α

0.6

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1

(a) Test1 network. 50

ν=0.25 − U ν=0.50 − U ν=0.75 − U ν=0.25 − G ν=0.50 − G ν=0.75 − G

ES %

40 30 20 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

α

(b) Test2 network. Fig. 7. Optimal power saving vs. a in case of Test1 and Test2 networks.

In this section we first show the performance of GBA in the considered networks, then we compare it against other heuristics. In order to give more insights, we first show the percentage of nodes in F 3 mode as a varies in Fig. 8. The related power saving will be shown later in Section 7.3. The percentage of nodes in F 3 mode when the traffic is at the peak level is about 20% for Tiscali and Level3 and close to zero in case of FT. In fact, the first two networks have several nodes with K ¼ 1 which can always stay in F 3 mode. However, as it will be shown later, this nodes bring little saving considering the power consumption model here assumed. Then, as a decreases, up to 80% of nodes can be put in F 3 mode, leading to more than 40% of power saving. Tiscali and FT networks take advantage from the gravity traffic model, under which the percentage of nodes in F 3 mode for medium values of a increases with respect to the uniform traffic case. From the topological point view, the three large networks considered here can be seen as an intermediate case with respect to the two small test networks considered for the ILP model. In fact, they are sufficiently meshed and, as such, a very high percentage of nodes can be put in F 3 mode when a is low, and consequently significant savings can be obtained even in case of suboptimal heuristic solutions (up to 50%). From this point of view, they behave

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M. Polverini et al. / Computer Networks 78 (2015) 26–41

FT Tiscali Level3

40 30 20 10

0.1

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α

0.6

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0.9

FT Tiscali Level3

6

APL increase (%)

Percentage of nodes

50

4

2

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1

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α

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60

40

20

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α

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APL increase (%)

8

80

Percentage of nodes

0.4

1

(a) Uniform Traffic Matrix.

(a) Uniform Traffic Matrix.

0.1

0.3

FT Tiscali Level3

6

4

2

0.1

1

0.3

0.4

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0.6

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0.8

0.9

1

α

(b) Gravity Traffic Matrix.

(b) Gravity Traffic Matrix.

3

Fig. 8. Percentage of nodes in F mode.

Fig. 9. Average path length increase.

25

ES %

20 15 10 FT Tiscali Level3

5

0.1

0.2

0.3

ν

0.4

0.5

(a) Uniform Traffic Matrix. 30 25

ES %

similarly to Test1 network. On the other hand, the nodal degree is less uniform than in case of Test1 leading to better performance when the traffic increases around 50% of the peak value. Now, we want to evaluate how the average path length (APL) increases when F 3 mode technique is applied. Results are reported in Fig. 9 as a varies. It can be seen that the APL increase is vary small, especially if compared what is experienced in case of link switch-off techniques [2,3]. in fact, it is limited to about 7–8% even for a ¼ 0:1 for all networks and traffic scenarios. Moreover, as a varies, it roughly follows the same trend as the percentage of nodes in F 3 mode. The next analysis we propose is the evaluation of the Energy Saving (ES ) achievable enabling GBA over a period of 24 h, varying the m parameter. The traffic profile used in this simulation has been taken from [29]. The algorithm is executed when a traffic variation equal to the 10% of the peak traffic is observed. Fig. 10(a) and (b) report the energy saving achieved by GBA averaged over a period of 24 h varying the m parameter for the three considered ISP topologies. As explained in Section 4, a plausible value for m is 0:5; anyway to have a more accurate analysis, the range 0:1  0:5 is considered. In general, according to the analysis reported in Section 5.3, energy saving achievable by GBA grows linearly with respect m. Moreover, the slope of the plotted straight lines is quite smooth, in fact the impact of m over the final energy saving is about 5%. This is particularly remarkable, since state that the performance of GBA are almost independent from the value of m, while other solutions (e.g., [12,11]) strongly depend on its value. To conclude, in order to show the concept of the ‘‘Elastic Backbone’’, we report in Fig. 11 the shape of the various

0.2

20 15 10 FT Tiscali Level3

5 0.1

0.2

0.3

0.4

0.5

ν

(b) Gravity Traffic Matrix. Fig. 10. Energy Saving over 24 h varying

m parameter.

CDSs found varying a. As expected, the CDS depends on the traffic load, and it can be seen how the full mode nodes are mainly placed in the center of the network, i.e. where hogh-degree nodes are placed, forming a reduced core

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M. Polverini et al. / Computer Networks 78 (2015) 26–41 4

4 5

12

33

10

6 10 29

30

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33

25 19

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20 31

26 14

1

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20

(a) α = 20%.

19

20 31

14

36 27

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0

14

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(b) α = 50%.

18

32 21

2 3

17

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35 34

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23

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4 5

12

22

11

1

2 3

0

15

(c) α = 60%.

(d) α = 80%.

Fig. 11. CDS in FT network under different percentage of peak hour gravity traffic.

network that gives connectivity to nodes in F 3 mode. When the traffic load is high, the capacity constraints are stronger than topology ones, and this property is lost.

7.3. Comparison among different heuristics In the following, we compare GBA with three different heuristics. The first one is called Floyd-Warshall Node Standby (FWNS) and was presented in [7]. FWNS is still based on the Floyd-Warshall algorithm, which is used to find the CDS, but differs from GBA for the second phase. In more detail, the second phase of FWNS returns a solution only if every node not belonging to the CDS (after the r-th round of FW) can be put in F 3 mode, while the F 3 nodes detection algorithm of GBA always returns the solution with the maximum number of nodes in F 3 mode among those not belonging to the CDS. The other two heuristics we compare with are proposed in [9]. Basically Aldraho et al. propose a greedy approach that iteratively tries

50

60

GBA FWNS LNF LLN

50

GBA FWNS LNF LLN

40

ES %

40

ES %

to turn a node in F 3 mode following a sorted list. Authors propose two different sorting criteria: (i) Lighted Node First (LNF), based on the concept of node gravity, and (ii) Least Loaded Node (LLN), considering the amount of traffic crossing each node. Results are shown in Fig. 12–14 for the three considered networks. Tables 4–6 report the mean value and the confidence interval referred to the Figs. 12, 13 and 14 respectively. First of all, it can be seen that GBA always outperforms FWNS, especially for medium–high values of a and in case of uniform traffic model. The other two heuristics generally perform worse than GBA and FWNS, except in case of FT network in case of low values of a. In this case, LNF and LLN slightly outperform GBA and FWNS. On the contrary, it can be seen that the improvement of GBA with respect to the other heuristics is quite evident in case of uniform traffic, especially for Tiscali network for which it leads to an improvement up to 25%. In fact, the gravity traffic model tends to concentrate demands

30

30 20

20 10

10 0.1

0.2

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0.5

α

0.6

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0.8

0.9

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1

0.2

20

10

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0.3

0.4

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0.6

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0.8

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0.8

0.9

1

0.9

GBA FWNS LNF LLN

30

20

0.2

0.6

40

30

0.1

α

50

ES %

ES %

40

0.5

60

GBA FWNS LNF LLN

50

0.4

(a) Uniform Traffic Matrix.

(a) Uniform Traffic Matrix. 60

0.3

1

(b) Gravity Traffic Matrix. Fig. 12. Comparison among different heuristics in the case of the France Telecom network.

0.1

0.2

0.3

0.4

0.5

α

0.6

0.7

0.8

0.9

1

(b) Gravity Traffic Matrix. Fig. 13. Comparison with different heuristics in the case of the Tiscali network.

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M. Polverini et al. / Computer Networks 78 (2015) 26–41 50 40

a

0.1

0.2

0.3

0.4

0.5

α

0.6

0.7

0.8

0.9

1

(a) Uniform Traffic Matrix. 50

GBA FWNS LNF LLN

ES %

40 30 20 10

0.1

0.2

0.3

0.4

0.5

α

0.6

0.7

0.8

0.9

1

(b) Gravity Traffic Matrix. Fig. 14. Comparison with different heuristics in the case of the Level3 network.

Table 4 Mean values and confidence interval of results shown in Fig. 12. Algorithms GBA

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

FWNS

LNF

LLN

m

r

m

r

m

r

m

r

44.10 44.10 38.89 31.81 22.01 4.62 2.71 1.56 0.35 0.35

0 0 3.65 1.05 1.88 2.02 0.97 0.72 0 0

44.10 44.10 36.77 23.61 8.96 3.44 1.67 0.35 0.35 0.35

0 0 4.68 8.84 5.03 1.25 1.43 0.87 0 0

51.91 51.91 35.17 18.37 10.83 2.40 1.18 0.28 0.03 0.03

0.55 0.55 5.93 6.12 3.85 1.85 1.26 0.59 0.11 0.11

51.49 49.48 32.26 17.22 11.01 2.40 1.18 0.28 0.03 0.03

0.59 4.27 4.93 6.11 3.29 1.85 1.26 0.59 0.11 0.11

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

r

m

r

m

r

48.68 26.86 16.89 13.12 7.75 4.80 2.14 1.49 1.49 1.49

0 2.52 1.94 1.49 1.10 0.64 0.42 0 0 0

48.68 14.16 8.47 5.96 4.42 3.26 2.03 1.49 1.49 1.49

0 3.18 2.04 1.29 0.81 1.00 0.42 0 0 0

38.92 16.61 9.51 3.96 2.02 1.74 0.67 0.31 0.31 0.08

5.36 5.02 2.01 2.71 1.22 1.25 0.60 0.11 0.11 0.03

37.74 16.55 9.51 3.96 2.02 1.74 0.67 0.31 0.31 0.08

6.77 4.90 2.01 2.71 1.22 1.25 0.60 0.11 0.11 0.03

on nodes with high degree, i.e., those nodes having a higher probability to be in a CDS, making the problem simpler (by construction) to solve for every heuristic. On the contrary, the uniform traffic model does not reflect any particular topological characteristic. In this situation, jointly finding a small CDS and meet traffic requirements becomes harder. Here the flexibility brought by the use of the F 3 nodes detection algorithm is emphasized, allowing GBA to achieve better performance than other heuristics. To complete the performance comparison, we show in Fig. 15 the average value of the energy saving over a period of 24 h, using the traffic trace reported in [29]. Average values and confidence intervals referred to Fig. 15 are reported in Table 7. The time analysis show how GBA outperforms the other algorithms, even though in the case of gravity traffic the improvement is less evident than in the case of uniform traffic. Two main results should be

30

GBA FWNS LNF LLN

25 20 15 10 5 France Telecom

Tiscali

Level3

(a) Uniform Traffic Matrix. 35

Algorithms FWNS

LNF

GBA FWNS LNF LLN

30

LLN

m

r

m

r

m

r

m

r

25

48.56 42.21 32.73 20.17 11.35 7.10 4.43 4.02 3.45 2.87

2.01 2.24 1.79 6.25 1.64 2.26 0.85 0 0.61 0

44.71 16.41 10.29 7.82 5.49 3.99 2.87 2.87 2.87 2.87

6.28 8.22 2.01 1.94 1.80 1.80 0 0 0 0

26.72 15.89 7.16 5.37 2.87 0.78 0.29 0.37 0.46 0.26

9.05 6.95 5.93 5.44 2.31 0.97 0.43 0.38 0.43 0.09

26.75 15.89 7.16 5.37 2.87 0.78 0.29 0.37 0.46 0.26

8.99 6.95 5.93 5.44 2.31 0.97 0.43 0.38 0.43 0.09

20

ES %

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

LLN

m

Table 5 Mean values and confidence interval of results shown in Fig. 13.

GBA

LNF

r

0

a

FWNS

m 20 10

a

Algorithms GBA

30

ES %

ES %

Table 6 Mean values and confidence interval of results shown in Fig. 14.

GBA FWNS LNF LLN

15 10 5 0

France Telecom

Tiscali

Level3

(b) Gravity Traffic Matrix. Fig. 15. Energy Saving over a period of 24 h.

40

M. Polverini et al. / Computer Networks 78 (2015) 26–41

Table 7 Mean values and confidence interval of results shown in Fig. 15. Topology

France telecom Tiscali Level3

GBA

FWNS

LNF

LLN

m

r

m

r

m

r

m

r

24.80 22.77 17.12

0.71 1.30 0.69

21.23 13.61 13.11

1.68 2.57 0.97

23.68 8.68 10.93

1.40 2.79 1.95

22.95 8.69 10.73

0.88 2.79 2.03

highlighted: (i) for both kinds of traffic, the gain in using GBA grows with the size of the network, and (ii) in case of uniform traffic, the energy saving of GBA is twice the one obtained by LNF and LLN. 8. Conclusions We have studied the application of low power states for IP routers based on the principle of avoiding lookup operations in the line-cards. We have highlighted that implementing the bypass of the table lookup operation is feasible according to the current HW architecture of linecards. We have first presented the proposed technique, called F 3 mode. Then, the problem of minimizing the network power consumption when F 3 mode is available has been formalized as an optimization problem considering the specific constraints related to SP routing. We have shown that the problem can be assimilated to the minimum CDS problem with further constraints related to routing and capacity requirements. Results in small example networks showed that F 3 mode is able to bring power saving up to 70%, depending on the network topology. A heuristic algorithm, called GBA, has been then proposed to solve the problem in large networks. The performance of GBA have been firstly evaluated comparing it with the optimum solution of the problem showing that GBA is able to achieve efficiency higher than 90% in almost all cases. Then, the performance in large ISP networks have been assessed. Results confirmed that F 3 mode technique can bring high power saving in different traffic conditions while leading to a quite negligible increase of the average path length. Finally, results showed that GBA is able to outperform other heuristics in several conditions while is outperformed only in few cases and when traffic load is very low. As next steps, we are moving toward the implementation of F 3 mode capability in network prototypes. Acknowledgment The work described in this paper was carried out with the support of the GreenNet FIRB ‘‘Future in Research Program’’ 2010 project, funded by the Ministry of University and Reseach (MUR). References [1] L. Chiaraviglio, M. Mellia, F. Neri, Minimizing isp network energy cost: formulation and solutions, IEEE/ACM Trans. Netw. (TON) 20 (2) (2012) 463–476. [2] A. Coiro, M. Listanti, A. Valenti, F. Matera, Energy-aware traffic engineering: a routing-based distributed solution for connectionoriented ip networks, Comput. Netw. (2013)

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Marco Polverini received his Laurea degree in Telecommunications Engineering, in April 2010 from University of Rome ‘‘Sapienza’’, Italy. Since November 2010 he is a Ph.D. Student in Information and Communication Engineering at the same Department. His current research interests are protocols and models for Energy Saving in IP Networks.

Antonio Cianfrani received his M.Sc. degree in Telecommunications Engineering in 2004 and the Ph.D. in Information and Communication Engineering in 2008. both from the University of Rome ‘‘La Sapienza’’. He is an Assistant Professor at the DIET Department of the University of Rome ‘‘La Sapienza’’. His field of interests includes routing algorithms, network protocols, performance evaluation of Software Routers and optical networks. His current research interests are focused on green networks and future Internet architecture.

Angelo Coiro received the his master’s degree in Telecommunication Engineering in September 2008 and the Ph.D. degree in Information and Communication Engineering in 2011, both from the University of Rome Sapienza. Since November 2011 he is a postdoc researcher at DIET department of the same University. His research interests are in the fields of green networking, routing algorithms, network management and optical networks.

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Marco Listanti received his Dr. Eng. Degree in Electronics Engineering from the University of Roma ‘‘La Sapienza’’ in 1980. In 1981, he joined the Fondazione Ugo Bordoni, where he was the leader of the group TLC Network Architecture until 1991. In November 1991 he joined the INFOCOM Department of the University of Roma ‘‘La Sapienza’’, where he is a Professor of switching systems. Since 1994, he has also collaborated with the Electronics Department of the University of Roma ‘‘Tor Vergata’’, where he holds courses in telecommunication networks. He participated in several international research projects supported by EEC and ESA and is author of several papers published on the most important technical journals and conferences in the area of telecommunication networks. His current research interests focus on traffic control in IP networks and on the evolution of techniques for optical networking. He has been representative of Italian PTT administration in international standardization organizations (ITU, ETSI). He is also a member of IEEE Communications and Computer Societies.

Roberto Bruschi received his M.Sc. degree in telecommunication engineering in 2002 and his Ph.D. degree in electronic engineering in 2006 from the University of Genoa. He is currently a researcher with the National InterUniversity Consortium for Telecommunications (CNIT) in the University of Genoa Research Unit. His main research interests include future Internet, green networking, and software routers.