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The paper deeply analyzes a novel network-wide power management problem, called Power-Aware Routing and Network Design with Bundled Links (PARND-BL), which is able to take into account both the relationship between the power consumption and the traffic throughput of the nodes and to power off both the chassis and even the single Physical Interface Card (PIC) composing each link. The solutions of the PARND-BL model have been analyzed by taking into account different aspects associated with the actual applicability in real network scenarios: (i) the time for obtaining the solution, (ii) the deployed network topology and the resulting topology provided by the solution, (iii) the power behavior of the network elements, (iv) the traffic load, (v) the QoS requirement, and (vi) the number of paths to route each traffic demand. Among the most interesting and novel results, our analysis shows that the strategy of minimizing the number of powered-on network elements through the traffic consolidation does not always produce power savings, and the solution of this kind of problems, in some cases, can lead to spliting a single traffic demand into a high number of paths.

Energy saving is one of the most important challenges of the twenty-first century for environmental and economical reasons. From an environmental perspective, due to the lack of diffusion and efficiency of renewable energy, the reduction of power consumption is important because the production of energy is directly related to the emission of carbon dioxide (

In this scenario, the research community is studying a set of approaches for improving the energy efficiency of the future Internet. Detailed and up-to-date surveys on the different strategies for energy-efficient networking are presented in [

The research activities can be classified into two main areas: local strategy and network-wide strategy. In the first case, power saving functions are executed locally by an entity. The strategies consist in monitoring the entity usage and dynamically adapting its power consumption according to the required performance. As an example, the entity may switch to a sleep state when it is not in use or out of scheduled business hours [

Starting from the seminal work on power-efficient network devices presented in [

The contribution of this paper is focused on the network-wide power optimization in the backbone network. In particular, the paper investigates a very general network-wide power management (NWPM) problem, called Power Aware Routing and Network Design with Bundled Links (PARND-BL) [

In the case of large network topologies, PARND-BL cannot be solved to optimality in an acceptable time, that is, few hours (see [

The performance analysis takes into account different actual network scenarios and diverse metrics, such as the number of powered-on network elements, the CPU time for solving the problem, and the number of paths per flow of the solution. To the best of our knowledge, none of the previous works presenting models for the minimization of the network power consumption has evaluated the actual applicability of the obtained solution in terms of number of paths used to route each single traffic demand. The relevance of this analysis consists in the fact that the solutions of the power reduction problems could entail a huge number of paths per traffic demand. The management of a high number of paths per traffic demand can be so expensive in terms of signaling to reduce the appeal deriving from the power savings. Finally, the extensive simulation analysis gives insights into the performance of the considered NWPM approaches under diverse network parameters, such as the power characterization of network devices, the traffic load, the network topology, and the QoS requirements.

The paper is structured as follows. Section

Generally speaking, NWPM consists in finding the design and the routing strategies that minimize the overall power consumption of a network by taking into account the power behavior of the network elements and the traffic demand. Therefore, three critical issues can be devised in NWPM: the time horizon of the traffic demands, the power behavior of the network devices, and the protocol architecture.

Regarding this issue, we can observe that in actual deployments the traffic matrix presents significant changes mostly between two periods: peak and off-peak. Just relatively small variations are usually registered within each period (see Figure

Byte volume on a domestic link in each direction (north/south)—source [

Daily

Weekly

The energy characterization of the network devices determines what can be exploited to minimize the overall network consumption. In this work, we have used a general power consumption model of a router, which is composed of three main components [

chassis;

Physical Interface Cards (PICs);

route processor.

The chassis can be powered off (i.e., it works in a low-power mode); hence, the power consumption can be assumed to be constant if the chassis is powered on and zero otherwise.

To model the power characteristics of the PICs, we have to dissect the communication process in more detail. The energy for transferring a bit from a node

Another aspect that will be included in the analysis is the fact that in modern core networks pairs of routers are typically connected by multiple PICs that form one logical bundled link [

In the route processor, the power consumption generally depends on the traffic load of the router in a nonlinear way. In [

In modern broadband communication networks, in order to apply the calculated traffic engineering solution, we should refer to protocol architectures such as MPLS (Multiprotocol Label Switching) [

A similar strategy can be implemented by means of emerging architecture paradigms such as the Software-Defined Networking (SDN).

For this reason, we propose a centralized architecture where a Network Control Unit (NCU) provides the LPSs (see Figure

System diagram.

We focus our attention on the network-wide power saving strategies, which are able to exploit the energetic characterization of the power-aware network devices. As presented in [

A first set of activities has been aimed at defining models for the PAND problem. In particular, [

A second set of works has been focused on the definition and the solution of the PAR problem. In [

A third set of works has been devoted to jointly consider the power aware routing and the network design problems (i.e., PARND). The problem is discussed in [

On the other hand, to the best of our knowledge, none has deeply analyzed both the performance and the actual applicability of a general network-wide problem like PARND-BL, proposed in [

Let us introduce the parameters and the notation used in the paper. The starting point of the analysis is a network modelled as a directed graph

The following parameters are assumed to be given in order to characterize the power consumption of the network elements:

Since each logical link is generally composed of a set of PICs, the overall power consumption for the traffic transmission on a link

Concerning the traffic demand and the capacity of nodes and links, we define the following parameters:

Three sets of variables are defined:

The traffic throughput of node

For reducing the overall power consumption of a network with bundled links, we define the

The above introduced PARND-BL problem leads to a Mixed Integer Nonlinear Programming (MINLP) design and routing model, which can be formulated as follows:

Equations (

For solving PARND-BL, we propose a new heuristic, called

The FGH heuristic uses the Maximum Spare Capacity (MSC) problem as building block. Taking into account the notations introduced in the previous section, the MSC problem can be formulated as follows:

The initialization of the FGH heuristic consists in solving the MSC problem to obtain the flow

After the initialization, the link with the greatest spare capacity is identified; that is, FGH finds the

Focusing on the ability of powering off link/PICs, HPARND-BL mainly differs from FGH in two aspects: (i) at each iteration a PIC is removed if the overall power consumption is actually reduced, (ii) and the Power-Aware Routing (PAR) problem is used as a building block in place of MSC. Furthermore, HPARND-BL is able to power off nodes. Therefore, HPARND-BL can exploit the ability of the chassis to be powered off, and this is particularly relevant when the power consumption due to route processor is dependent on the node throughput. In this case, the power consumption due to route processor has to be explicitly addressed in the problem formulation, and just to power off links/PICs does not necessarily determine a reduction of the overall network consumption.

The considered PAR problem consists in determining the traffic routing strategy that permits to reduce the overall power consumption of the network by taking into account only the power consumption of the nodes concerning the route processor, that is,

PAR problem has been solved by means of Ipopt [

In Algorithm

(1) Solve PAR

(2) Remove PICs to match flows and set

(3) Initialize

(4)

(5) Sort vertices (greatest spare capacity);

(6)

(7) Disable the first vertex

(8) Set

(9) Solve PAR

(10)

(11) Remove vertex

(12) Update

(13)

(14) Enable vertex

(15)

(16)

(17)

(18)

(19) Sort links (greatest spare capacity);

(20)

(21) Select the first link

(22) Disable one PIC from selected link

(23) Solve PAR

(24)

(25) Remove PIC from

(26) Update

(27)

(28) Enable PIC and

(29)

(30)

(31)

In the following section, we present some implementation issues to enhance the computational efficiency of the approach, to take into account the Quality of Service (QoS), and to evaluate the applicability of the proposed solutions in a real network scenario.

In order to reduce the computational effort, we indeed considered and implemented aggregated versions of the flow variables, where all the commodities having the same origin node are considered to be “the same kind of flow.”

We have modified the constraints (

Consequently, the flow conservation constraints (

These modifications reduce the number of the flow variables from

In order to take into account the QoS in the considered problem, we have limited the link utilization by multiplying

The solution of the PARND-BL formulation and the related heuristic provides the set of flow variables. Therefore, for providing the LSPs, as discussed in Section

Note that the splitting of a traffic demand into too much LSPs can deteriorate the performance of the networks, due to the overhead of the signalling protocols used to create and manage LSPs. Hence, the solution should limit to few units the number of paths used to support the traffic of each origin-destination pair [

The Multidestination Flow Decomposition Heuristic (MD-FDH) is a new heuristic for decomposing a flow (one-source multiple destinations) into a set of paths that is based on a heuristic proposed in [

After initializing the

(1) Given a source

demand

(2) Residual topology

(3) Initialize

(4)

(5) Set

(6) Select the destination node

(7) Find the path

(8) Compute

(9) Update

(10) Set

(11)

(12)

The simulation analysis is devoted to evaluate the impact of the diverse parameters of the network scenario on the performance of the described solutions. In particular, we take into account the network topology, the energy behavior of the network equipment, the traffic load, and the QoS requirements.

The first scenario is an European core network topology obtained from the Simple Network Description Library [

The nodes of all the tested networks are assumed to have the same energy behavior, and the links are supposed to be symmetric; that is,

Table

Statistics of the network scenarios.

nobel-eu | Exodus | Ebone | Abovenet | Sprintlink | ta2 | |
---|---|---|---|---|---|---|

# Nodes | 28 | 22 | 23 | 22 | 43 | 65 |

# Links | 41 | 37 | 38 | 42 | 83 | 108 |

# S.L.N. | 0 | 1 | 4 | 5 | 13 | 1 |

In all network scenarios, each node represents a core router. We assumed the use of the Juniper T1600 core router, which has a total throughput capacity of 1600 Gb/s and a maximum power consumption of 8352 W [

The results reported in [

In summary, we have considered the following setting for the model parameters:

Concerning the power consumption component of the route processor, we focused our attention on a

Power consumption of node

Based on the previously cited energy parameters of the routers, we have thus defined the power consumption concerning the route processing by considering cubic and logarithmic curves, respectively, as follows:

In the case of the

To obtain the traffic matrix for the other topologies, we set the mean value of the traffic demand from

The choice of a traffic matrix where each node of the network is both source and destination of traffic would imply that only links (or PICs) could be powered off. To introduce the presence of transit nodes that can be powered off, for each network topology we have selected the

The dataset used for the network topologies does not provide information on the capacity of the links and, in particular, on the number of PICs composing each link. Hence, the maximum number of PICs per link has been computed as follows:

Table

Number of line cards per link.

nobel-eu | Exodus | Ebone | Abovenet | Sprintlink | ta2 | |
---|---|---|---|---|---|---|

Max | 16 | 7 | 11 | 7 | 23 | 23 |

Avg | 4.66 | 3.46 | 3.58 | 2.5 | 3.46 | 4.7 |

# S.P.L. | 7 | 4 | 8 | 12 | 15 | 20 |

Taking into account the formula of the mean delay of the M/M/1 model assumed in Section

The first set of simulations is devoted to the performance analysis of the PARND-BL model and of the proposed heuristic in a fixed configuration of network parameters. In particular, all results refer to a simulation scenario characterized by

The PARND-BL formulation has been solved by the mixed integer non-linear programming solver BONMIN 1.5.0 [

The performance analysis has been carried out by taking into account the following indicators:

number of powered-on network elements;

overall power consumption of the network;

CPU time;

number of flow paths per origin-destination pair.

It is relevant to note that, for a fair comparison, we considered FGH under the setting

The number of powered-on network elements (i.e., nodes, links, and PICs) obtained applying the considered approaches in the case of cubic and logarithmic

Number of powered-on network elements (nodes/links/PICs)—Cubic

nobel-eu | Exodus | Ebone | Abovenet | Sprintlink | ta2 | |
---|---|---|---|---|---|---|

PARND-BL | 26/32/48 | 22/32/40 | 22/30/48 | 21/28/38 | 41/61/102 | N/A |

FGH | 28/39/50 | 22/32/40 | 23/32/49 | 22/31/40 | 43/67/103 | 65/99/172 |

HPARND-BL | 28/40/50 | 22/34/41 | 23/34/50 | 21/30/39 | 42/65/104 | 65/102/185 |

Number of powered-on network elements (nodes/links/PICs)—logarithmic

nobel-eu | Exodus | Ebone | Abovenet | Sprintlink | ta2 | |
---|---|---|---|---|---|---|

PARND-BL | N/A | 20/24/47 | 21/24/53 | 21/28/41 | N/A | N/A |

HPARND-BL | 26/30/52 | 22/28/47 | 22/28/52 | 21/30/41 | 41/53/108 | 64/72/201 |

The results reported in Table

The comparison of the results shown in Tables

Furthermore, in the case of cubic

In order to evaluate the impact of the power consumption of the chassis on the performance, we carried out further simulations by setting

Number of powered-on network elements (nodes/links/PICs)—

nobel-eu | Exodus | Ebone | Abovenet | Sprintlink | ta2 | |
---|---|---|---|---|---|---|

PARND-BL-cub | 26/31/55 | 20/27/46 | 21/25/51 | 21/28/38 | 41/58/101 | N/A |

PARND-BL-log | N/A | 20/25/46 | 21/24/53 | 21/28/41 | N/A | N/A |

HPARND-BL-cub | 28/40/50 | 22/34/41 | 22/30/49 | 21/30/39 | 42/65/104 | 65/104/184 |

HPARND-BL-log | 26/30/52 | 22/28/47 | 22/29/50 | 21/30/41 | 41/53/108 | 64/74/197 |

Table

Power consumption (W) versus topology—cubic curve,

nobel-eu | Exodus | Ebone | Abovenet | Sprintlink | ta2 | |
---|---|---|---|---|---|---|

SPR | 30974 | 21422 | 22962 | 18533 | 48325 | 86673 |

PARND-BL | 11807 | 9864 | 11164 | 9581 | 23286 | N/A |

FGH | 12397 | 9876 | 11469 | 9828 | 24114 | 41835 |

HPARND-BL | 12364 | 9985 | 11521 | 9657 | 23585 | 40782 |

As shown in Table

In the case of the logarithmic

Power consumption (W) versus topology—logarithmic curve,

nobel-eu | Exodus | Ebone | Abovenet | Sprintlink | ta2 | |
---|---|---|---|---|---|---|

SPR | 175646 | 141605 | 148226 | 134683 | 283933 | 449419 |

PARND-BL | N/A | 121322 | 129370 | 120927 | N/A | N/A |

FGH | 160319 | 130922 | 138710 | 122026 | 261318 | 408726 |

HPARND-BL | 148630 | 128795 | 133621 | 121220 | 250021 | 393972 |

The results obtained with

Power consumption (W) versus topology—

nobel-eu | Exodus | Ebone | Abovenet | Sprintlink | ta2 | |
---|---|---|---|---|---|---|

SPR-cub | 137245 | 104928 | 110133 | 101976 | 210786 | 330447 |

SPR-log | 214479 | 169088 | 177006 | 163984 | 336568 | 524101 |

PARND-BL-cub | 107451 | 86282 | 91101 | 89200 | 178273 | N/A |

PARND-BL-log | N/A | 145484 | 154069 | 148825 | N/A | N/A |

FGH-cub | 118691 | 93374 | 98669 | 89455 | 186591 | 285929 |

FGH-log | 197660 | 157995 | 166597 | 149352 | 313224 | 481796 |

HPARND-BL-cub | 118674 | 93493 | 94661 | 89318 | 182477 | 286018 |

HPARND-BL-log | 183756 | 157288 | 160078 | 148983 | 299713 | 475801 |

We evaluated the CPU times required by the different approaches for calculating the energy-aware solutions. The measured data have been collected referring to a 3.07 GHz Intel 4-Core i7 CPU (with hyperthreading enabled). The obtained results are summarized in Tables

CPU times (s)—cubic curve.

nobel-eu | Exodus | Ebone | Abovenet | Sprintlink | ta2 | |
---|---|---|---|---|---|---|

SPR | 0.01 | 0.01 | 0.01 | 0.01 | 0.06 | 0.26 |

PARND-BL | 56.59 | 236.27 | 21.49 | 40.47 | 87784.79 | N/A |

FGH | 130.13 | 58.38 | 65.82 | 51.39 | 944.19 | 4412.29 |

HPARND-BL | 165.15 | 72.33 | 91.00 | 60.54 | 1420.37 | 7394.30 |

CPU times (s)—logarithmic curve.

nobel-eu | Exodus | Ebone | Abovenet | Sprintlink | ta2 | |
---|---|---|---|---|---|---|

PARND-BL | N/A | 553.21 | 209.52 | 1588.55 | N/A | N/A |

HPARND-BL | 294.51 | 143.28 | 210.56 | 100.33 | 2329.84 | 13095.59 |

Observing the results obtained for the logarithmic

The analysis of the scenario with

A relevant indicator to be considered in actual networks is the number of paths, which are used to support the computed multicommodity flows, as indicated in Section

Number of paths per flow (Avg/Max)—cubic curve.

nobel-eu | Exodus | Ebone | Abovenet | Sprintlink | ta2 | |
---|---|---|---|---|---|---|

PARND-BL | 1.04/2 | 1.10/3 | 1.08/2 | 1.07/2 | 1.04/3 | N/A |

FGH | 1.42/6 | 1.49/7 | 1.40/7 | 1.28/5 | 1.41/7 | 1.43/10 |

HPARND-BL | 1.26/4 | 1.53/5 | 1.35/4 | 1.22/7 | 1.23/5 | 1.34/7 |

Number of paths per flow (Avg/Max)—logarithmic curve.

nobel-eu | Exodus | Ebone | Abovenet | Sprintlink | ta2 | |
---|---|---|---|---|---|---|

PARND-BL | N/A | 1.02/2 | 1.02/2 | 1.03/2 | N/A | N/A |

HPARND-BL | 1.10/3 | 1.19/3 | 1.12/2 | 1.17/3 | 1.12/4 | 1.01/2 |

In the case of a logarithmic

The results obtained with

Number of paths per flow (Avg/Max)—

nobel-eu | Exodus | Ebone | Abovenet | Sprintlink | ta2 | |
---|---|---|---|---|---|---|

PARND-BL-cub | 1.03/3 | 1.05/2 | 1.04/3 | 1.07/3 | 1.05/3 | N/A |

PARND-BL-log | N/A | 1.03/2 | 1.02/2 | 1.03/2 | N/A | N/A |

HPARND-BL-cub | 1.26/4 | 1.53/5 | 1.35/4 | 1.22/7 | 1.23/5 | 1.3/6 |

HPARND-BL-log | 1.09/3 | 1.19/3 | 1.16/3 | 1.17/3 | 1.12/4 | 1.09/3 |

In this section, we report the results of the simulation study aimed at evaluating the behavior of the considered solutions under different traffic load conditions and QoS requirements. As described in Section

The results of this analysis are summarized in Figure

Power consumption versus load factor

Ebone

ta2

The results of the overall power consumption as a function of the maximum link utilization are summarized in Figure

Power consumption versus maximum link utilisation.

Ebone

ta2

The paper deeply analyzed the PARND-BL problem, proposed the related heuristic HPARND-BL, and presented the performance evaluation carried out by taking into account diverse network parameters and metrics. The simulation results show that the power saving is more evident in the case of a cubic

The analysis of the results indicates that the energy saving depends on the network size (in terms of links and nodes). In the case of large topologies, the solution of the PARND-BL model and HPARND-BL provide the best results, whereas for small topologies, FGH permits to achieve interesting power savings, near to the optimal solution obtained by solving the PARND-BL model. Anyway, in these cases, the solution of PARND-BL is the more profitable; that is, it has highest energy savings and lowest CPU times.

The analysis of the number of powered-on network elements obtained by the diverse solutions highlights that in some cases the strategy of powering off the network elements is not always the best choice for saving network energy. As an example, by referring to the ta2 topology results shown in Tables

Furthermore, the paper presented the MD-FDH, a heuristic to decompose the single-source/multidestination flows into a minimal number of paths. The analysis of the obtained results points out that the optimal solution of the PARND-BL model leads to the split of a single traffic demand into a limited number of paths. Therefore, the solutions can be easily applied in an actual network. On the contrary, HPARND-BL splits some traffic demands into a number of paths that can be critical for an actual implementation. From this perspective, the worst case is represented by the FGH solutions. Furthermore, the results highlighted that in the case of a logarithmic

Finally, the extensive simulation analysis carried out with different power characterizations of network devices, traffic load, network topology, and QoS requirements points out that the proposed HPARND-BL represents a profitable solution of the most general NWPM approach by producing significant power savings in all network scenarios.

There is no conflict of interests between the authors and the mentioned commercial identities.

R. G. Garroppo and G. Nencioni have been supported by the Italian Ministry of Instruction, University and Research (MIUR) in the framework of the Project GreenNet (Greening the Network) under the FIRB "Future in Research" program, and of the project "GATECOM" under the PRIN 2009 program. M. G. Scutellà has been supported by MIUR under the PRIN 2009 research project “Approcci integrati per l’Ottimizzazione Discreta e Non Lineare”.