Michaela Novakova

Hana Glier

Naděžda Brdičková

Marcela Vlková

Ana Helena Santos

Margarida Lima

Mikaël Roussel

Juan Flores-Montero

Tomasz Szczepanski

Sebastian Böttcher

Michaela Nováková

Mikael Roussel

Vincent H J Van Der Velden

Paula Fernandez

Ester Mejstříková

Leire Burgos

Bruno Paiva

Jacques J M Van Dongen

Alberto Orfao

Tomáš Kalina

MD Tomas Kalina
email: tomas.kalina@lfmotol.cuni.cz

How to make usage of the standardized EuroFlow 8-color protocols possible

Keywords: flow cytometry, standardization, fluorochromes, EuroFlow, fluorescent spectrum

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Abstract

A critical component of the EuroFlow standardization of leukemia/lymphoma immunophenotyping is instrument setup. Initially, the EuroFlow consortium developed a step-by-step standard operating protocol for instrument setup of ≥ 8-color flow cytometers that were available in 2006, when the EuroFlow activities started. Currently, there are 14 instruments from 9 manufacturers capable of 3-laser excitation and ≥8 color measurements. The specific adaptations required in the instrument set-up to enable them to acquire the standardized 8-color EuroFlow protocols are described here. Overall, all 14 instruments can be fitted with similar violet, blue and red lasers for simultaneous measurements of ≥8 fluorescent dyes. Since individual instruments differ both on their dynamic range (scale) and emission filters, it is not accurate to simply recalculate the target values to different scale, but adjustment of PMT voltages to a given emission filter and fluorochrome, is essential. For this purpose, EuroFlow has developed an approach using Type IIB (spectrally matching) particles to set-up standardized and fully comparable fluorescence measurements, in instruments from different manufacturers, as demonstrated here for the FACSCanto II, and Navios and MACSQuant flow cytometers. Data acquired after such adjustment on any of the tested cytometry platforms could be fully superimposed and therefore analyzed together. The proposed approach can be used to derive target values for any combination of spectrally distinct fluorochromes and any distinct emission filter of any new flow cytometry platform, which enables the measurement of the 8-color EuroFlow panels in a standardized way, by creating superimposable datafiles.

Introduction

The EuroFlow consortium has been developing standardized ≥8-color immunophenotyping protocols since 2006, when only two manufacturers, Becton Dickinson (BD) Biosciences (San Jose, CA, USA) and DakoCytomation (Glostrup, Denmark), were producing instruments capable of ≥8-color measurements. Since complete standardization of instrument setup [START_REF] Kalina | EuroFlow standardization of flow cytometer instrument settings and immunophenotyping protocols[END_REF] , sample preparation, antibody panels [START_REF] Kalina | EuroFlow standardization of flow cytometer instrument settings and immunophenotyping protocols[END_REF][START_REF] Van Dongen | EuroFlow antibody panels for standardized ndimensional flow cytometric immunophenotyping of normal, reactive and malignant leukocytes[END_REF][START_REF] Flores-Montero | Next generation flow (NGF) for highly sensitive and standardized detection of minimal residual disease in multiple myeloma[END_REF][START_REF] Theunissen | Standardized flow cytometry for highly sensitive MRD measurements in B-cell acute lymphoblastic leukemia[END_REF] , and data analysis [START_REF] Costa | Automated pattern-guided principal component analysis vs expert-based immunophenotypic classification of B-cell chronic lymphoproliferative disorders: a step forward in the standardization of clinical immunophenotyping[END_REF][START_REF] Pedreira | Overview of clinical flow cytometry data analysis: recent advances and future challenges[END_REF] are cornerstones of the EuroFlow approach for robust and reproducible immunophenotyping 2 , the EuroFlow standard operating protocol (SOP) for instrument setup was developed in detail for the FACSCanto II flow cytometer (BD Biosciences), in a way, it could also be transferred and applied to BD LSRII, as well as to CyanADP (DakoCytomation) [START_REF] Kalina | EuroFlow standardization of flow cytometer instrument settings and immunophenotyping protocols[END_REF] . Later on, several other companies entered the multicolor flow cytometry market and at present there is a growing number of instruments capable of ≥8 color measurements. Thus, crucial questions have arised about the requirements for any cytometer to be used with the EuroFlow protocols and the parameters that need to be taken care of, to produce fully standardized signal linearity; and f) produce data conforming to Flow Cytometry Standard (FCS) data format without hidden features preventing their analysis by a third party software [START_REF] Spidlen | Data File Standard for Flow Cytometry, version FCS 3.1[END_REF] . In addition, the features of instruments that require specific adjustments to generate standardized data include: a) emission filters' specifications; b) data range (i.e., number of channels); and c) both data acquisition software and reliable fluorescence compensation calculation algorithms. Furthermore, should an instrument be used for diagnostic purposes it must conform to local legal requirements (e.g., CE marking, IVD regulatory status). Last, but not least, application and technical support from the vendor should be appropriate for the intended use at the user site. Spectrally matched beads (Type IIB) can be made ad-hoc by incubating immunoglobulin capture beads with fluorescence labeled monoclonal antibodies [START_REF] Maecker | Standardization of cytokine flow cytometry assays[END_REF] . However, they must be made for each channel separately using specific fluorescent conjugates and their stability is limited.

In order to control for the quality of data in individual laboratories, the EuroFlow Quality Assessment (EuroFlow QA) program has been developed [START_REF] Kalina | Quality assessment program for EuroFlow protocols: Summary results of four-year (2010-2013) quality assurance rounds[END_REF] . This program identifies a parameter measured in the example Lymphoid Screening Tube-QA (LST-QA) that provides an abnormal readout and quantifies its distance from the expected value. The EuroFlow QA approach has also been applied to test the quality of the data acquired on multiple different flow cytometer platforms. By December 2016, there were 14 distinct flow cytometers that have ≥3 excitation lasers and allow for the detection of ≥8 different fluorochromes (Table 1). So far only four of them are CE IVD approved (however, this may differ in different countries and will change over time). In principle, all instruments that have 405nm, 488nm and 633-640nm excitation lasers and at least two, four and two detectors for each excitation line, respectively, fulfill the technical requirements for acquisition of the complete set of 8 colors used in EuroFlow panels (Table 2). However, some instruments may be equipped with emission filters that are adjusted for optimal detection of manufacturer's proprietary fluorochromes (Table 2). If detection of the fluorescence emission of the EuroFlow reference and alternative fluorochromes is feasible by those filters, standardization can be achieved by adjusting the target MFI values for a given fluorochrome and its optical filter, as described below.

Here, we present an overview of currently available instruments capable of ≥8-color measurements together with the EuroFlow approach to standardization of data measured across multiple flow cytometer platforms. For this purpose, the Navios and MACSQuant flow cytometers were used as example, based on their availability in EuroFlow member laboratories and both type IIB and type IIIA beads were employed for fine-tuning the photomultiplier tubes

Materials and methods

Instrument set-up for

Instrument set-up of the MACSQuant analyzer and Navios flow cytometers.

As a starting point, all PMTs of the two flow cytometers evaluated (MACSQuant® Analyzer, Miltenyi Biotec; and Navios, Beckman Coulter; Table 2) were set up so that the signal of the 7 th Rainbow particles peak matched the MFI of the reference flow cytometer, after rescaling to the common 18-bit scale. Thus, for Navios, that means that 7 th peak target values were recalculated (multiplied by four) to its 20-bit scale (Table 2), and Navios software "True view set 1" was selected in configuration to display 20-bit scale.

As previously described, peripheral blood (PB) samples from adult volunteers were stained using the LST-QA [START_REF] Kalina | Quality assessment program for EuroFlow protocols: Summary results of four-year (2010-2013) quality assurance rounds[END_REF] . Furthermore, single-antibody reagent stained tubes were prepared using antibodies conjugated with fluorochromes identical to those in the LST-QA combination (i.e., FITC, PE, PerCP Cy5.5, PE-Cy7, APC, APC-H7, PacB, and OC515). Either PB cells or capture beads were incubated with each single antibody-fluorochrome conjugated reagent used in the LST-QA for 30 minutes in the darkness, as described in Figure 1 and Evaluation of LST-QA data on different flow cytometers. All data were analyzed with the Infinicyt™ software. Data acquired derived from the Navios instrument were first rescaled to 18-bit. Then, data were merged, a common assignment of parameters was used and the analysis performed. LST-QA data was analyzed using Principal Component Analysis (PCA) and visualized through the Automatic Population Separator (APS) graphical representation, as previously described [START_REF] Kalina | EuroFlow standardization of flow cytometer instrument settings and immunophenotyping protocols[END_REF] .

Results

Scale of fluorescence intensity measurements. Each of the instruments

analyzed here uses a different data range (number of channels, referred to as "dynamic range"; Table 2). Thus, data generated on each instrument were rescaled by software to a common scale for further analyses. After rescaling of the FCS data, the analysis of the merged files from the reference Rainbow calibration particles measurements showed similar patterns for the 7 th peak fluorescence emissions on the three instruments tested (Figure 1 A). Indeed, for those channels that used similar emission filters (centered on the maximum emission wavelength of the fluorochrome used), the standard instrument setup according to the EuroFlow SOP and rescaling to a common scale (if needed) were sufficient to achieve the same level of signal without any additional adjustment required. This is documented by the results obtained for peripheral blood samples single-stained with CD8 FITC, as illustrated in Figure 1B.

Adjustment for different spectra and distinct emission filters. Whereas

different instruments use similar excitation lines (violet, blue and red) there can still be differences in some of the emission filters (Table 2). When filters transmitting different (non-identical) bands of the emission spectra are used (e.g., the FACSCanto II 510/50 filters vs the Navios 550/40 filters for OC515 fluorescence here collected), the instrument setup using the EuroFlow Target MFI value for the Rainbow calibration particles is no longer sufficient because they are not spectrally identical to the actual fluorochromes (Figure 2A). In that case, a shift in the signal intensity corresponding to the proportion of the fluorophore's emission spectra transmitted by a distinct filter, is observed (Figure 2A). Thus, for each different optical filter and each spectrally different fluorochrome, a specific target MFI correction factor was required, calculated and applied. For this purpose, we empirically adjusted the PMT voltages on the Navios and MACSQuant instruments using OC515-stained capture beads, to exactly match the signal obtained on the FACSCanto II instrument for the same fluorochrome. Next, we measured the Rainbow calibration particles and established OC515/Navios and OC515/MACSQuant specific Target MFIs. When PB samples stained with an anti-CD45 reagent conjugated with OC515 were measured on the three different type of instruments with the specific correction factors applied, we could see in the merged data files that the staining pattern was fully comparable and thus, standardized (Figure 2B).

Standardized data acquisition on different instruments. Finally, three

EuroFlow laboratories have used the Navios flow cytometer in parallel to the FACSCanto II instrument during the EuroFlow QA rounds, with fully comparable results (see Kalina et al. in this issue [START_REF] Kalina | Frequent issues and lessons learned from EuroFlow QA[END_REF] ). Results showed that by applying the channel/fluorochrome specific Rainbow calibration particles target values, the fluorescence staining patterns were fully matched and standardized. The resulting FCS files could also be merged an analyzed jointly and they were also fully comparable to a reference image of the expected staining/fluorescence emission patterns (Figure 3A). In addition, the complete immunophenotypes analyzed using APS projections of fluorescent parameters of the merged files acquired in different laboratories and in different instruments, were also fully comparable (Figure 3B). Merged files from FACSCanto II, Navios and MACSQuant instruments showed the same staining pattern in all 8 channels for both the positive and negative cell populations coexisting in the sample (Supplementary Figure 1).

Discussion

The EuroFlow concept is built on the analysis and direct comparison of flow cytometry data files against well-defined databases of standardized data files acquired in different laboratories with different instruments [START_REF] Kalina | EuroFlow standardization of flow cytometer instrument settings and immunophenotyping protocols[END_REF][START_REF] Van Dongen | EuroFlow antibody panels for standardized ndimensional flow cytometric immunophenotyping of normal, reactive and malignant leukocytes[END_REF][START_REF] Flores-Montero | Next generation flow (NGF) for highly sensitive and standardized detection of minimal residual disease in multiple myeloma[END_REF][START_REF] Theunissen | Standardized flow cytometry for highly sensitive MRD measurements in B-cell acute lymphoblastic leukemia[END_REF] . At present, at least fourteen different instruments from nine distinct manufacturers, potentially enable acquisition of e.g. the EuroFlow 8-color panels for the diagnostic screening and classification of hematologic malignancies 2 . However, to take full advantage of the EuroFlow approach, acquisition of data must be performed under standardized signal settings, and data must be saved in a common data format. Unfortunately, most manufacturers do not consider crossplatform standardization in their instrument development plans and even a compliance with a common FCS data format 7 doesn't guarantee that the data can be analyzed in a third party software (most FCS files contain additional features that need to be specifically handled by a third party software).

Flow cytometry instrument manufacturers could support standardization by using the same (or identical) optical filters (the benefit of a filter optimized to a particular fluorochrome in 8-color setup is minor, while the negative impact on the standardization is major) or by supporting custom optical filters that could be exchanged by the user whenever needed. Also, an embedded feature of any instrument's software that would allow the user to easily export FCS data in a particular scale range, without (additional) features that prevent analysis in third party software and that facilitate evaluation of academically developed Rproject based algorithms, [START_REF] Finak | OpenCyto: an open source infrastructure for scalable, robust, reproducible, and automated, end-to-end flow cytometry data analysis[END_REF] would greatly enhance collaboration and joint analysis of large data sets [START_REF] Kvistborg | Thinking Outside the Gate: Single-Cell Assessments in Multiple Dimensions[END_REF] .

Since different filters are used on distinct instruments, to achieve standardization across different flow cytometers, the optimal standardization tools would involve internally dyed beads which are spectrally matched to the actual reagents. However, such beads are not widely available (fluorochromes are often proprietary to the manufacturer) and they are rather difficult to produce (fluorescence emission spectra can shift when a given fluorochrome is conjugated to a particle, instead of an antibody molecule) [START_REF] Schwartz | Standardizing flow cytometry: a classification system of fluorescence standards used for flow cytometry[END_REF] . To circumvent these limitations, we used capture beads with spectrally matching fluorescence to the antibody-conjugated dyes (Type IIB beads); to adjust the level of the signal to the desired value provided by the reference instrument. We then proceeded to establish specific target MFI values for each individual combination of fluorochromes and optical setup, using the Rainbow calibration particles (Type IIIA beads). Thus, new target MFI values had to be established and used for each optical filter that deviated from the standard one, as well as for each spectrally distinct fluorochrome. Thus, target MFI values adjusted for the Navios At this point, Navios is the only non-reference cytometer used by EuroFlow members. We have created a SOP for its setup (available at www.euroflow.org). By using this protocol, Navios users have shown to perform very similar to FACSCanto II users in the EuroFlow QA scheme (Kalina et al, this issue [START_REF] Kalina | Frequent issues and lessons learned from EuroFlow QA[END_REF] ). By adhering to this SOP, data from FACSCanto II, Navios and MACSQuant, once merged together, showed the same staining patterns for all 8 fluorescence channels, as illustrated in Supplementary Figure 1 for the fluorochromes used for the development of the SOP. In the GEIL study, Solly et al.

reported superimposable data measured on FACSCanto and Navios [START_REF] Solly | Comparable flow cytometry data can be obtained with two types of instruments, Canto II, and navios. A GEIL study[END_REF] . They used Type IIIA beads only and observed some histogram shifts in the PE-Cy7 and APC-Cy7 channels (e.g., OC515/Pacific Orange/VH500 histogram was not shown) consistent with the emission filter differences specified in Table 2. Other published inter-laboratory studies did not attempt to standardize the measured signal [START_REF] Irving | Establishment and validation of a standard protocol for the detection of minimal residual disease in B lineage childhood acute lymphoblastic leukemia by flow cytometry in a multi-center setting[END_REF][START_REF] Johansson | Guidelines on the use of multicolour flow cytometry in the diagnosis of haematological neoplasms[END_REF][START_REF] Karawajew | Minimal residual disease analysis by eight-color flow cytometry in relapsed childhood acute lymphoblastic leukemia[END_REF] .

Of note, the presented list of instruments does not intend any endorsement of particular cytometers, nor does intends to evaluate their technical performance (e.g., linearity, sensitivity, background noise, speed of acquisition) or other important variables (e.g., ease of use, technical and application support) guiding a cytometer selection. In contrast, we tried to address the question whether the same standardized approach (PMT voltage setup to reach specific target MFIs) could be used for ≥8-colors experiments, which proved to be feasible and successful. An identical strategy is currently being evaluated with similar good results at the moment, in other flow cytometry instruments, such as the Attune Nxt (Thermo Fisher Scientific, Waltham, Massachusetts) and the FACSLyric (BD Biosciences). In fact, we have successfully adopted the same standardization scheme in a 16-color inter-laboratory study on 4-laser instruments (561nm excitation line added) (see Blanco et al. in this issue) [START_REF] Blanco | Selection and validation of antibody clones against IgG and IgA subclasses in switched memory B-cells and plasma cells[END_REF] . Further increase in the number of colors will likely require an addition of UV excitation (350-355nm), with (currently) up to 6 PMT detectors for UV excited fluorochromes [START_REF] Stall | Brilliant UltraViolet TM Dyes: A new set of high sensitivity fluorescence reagents for multicolor flow cytometry with a UV laser (P3301)[END_REF] . Of note, the ability to reach a specified target MFI-based instrument setup requires that PMT voltages are adjusted independently of each other (this is not the case for instruments that share PMT detectors for two differently excited fluorochromes). As a concept, the Target MFI standardization can be expanded, but it requires stable Type IIIA beads excited by all lasers and emitting in all fluorescence channels. Here, the Rainbow calibration particles come short at violet laser excited, far-red emitting fluorescence. While we show here that standardization of signal on instruments equipped with different emission filters is possible, it is advisable to attempt emission filter unification as it becomes very complex and challenging to maintain and correctly apply Target MFI when several filters differ and multiple spectrally different dyes are used.

The key question when executing the EuroFlow protocol on any flow cytometer instrument is whether the data can be superimposed against the data in the EuroFlow databases [START_REF] Flores-Montero | Data bases of normal samples as internal reference for automated gating and identification of abnormal cells[END_REF] . Ideally, the data generated on any instrument should pass the EuroFlow QA without a systematic deviation from the expected values for a given fluorochrome and cell subset. We have shown here that this is indeed possible when SOPs are developed to adjust for differences in the emission filters and data scaling. Thus, we show that a concept of standardized data generation can be applied across multiple instruments from different manufacturers. Information was collected from technical specifications given by the manufacturers. In the case where more similar instruments are produced by a manufacturer, only a representative is listed.

Table 2. Instruments that were used to evaluate the feasibility of standardized measurements across different flow cytometry platforms.

Differences in the data dynamic range (number of channels) and differences in the emission filters are highlighted in bold.

FITC channel

FITC fluorescence

(

  reproducible) data on different instrument platforms. In general, EuroFlow compatible instrument must a) be equipped with excitation lasers and collection optics (emission filters) to detect at least the 8 colors used in the panel combinations; b) have stable fluidics, c) sensitivity to discriminate fluorescence signals, d) reasonably low background (noise) and e)

For

  appropriate instrument set-up, different types of fluorescent beads are available. Reference internally dyed fluorescent particles (calibration standards) used by EuroFlow SOP are classified as Type IIIA beads 8 , which are environmentally stable for over several years when properly stored. They contain bright signal beads in every detector but their fluorescence is not spectrally matched to individual fluorochromes used in ≥8-color panels.

(

  PMTs) voltage setup and for calibration of instrument-and fluorochromespecific Target mean fluorescence intensity (MFI) measurements, respectively. Data generated on the Navios and MACSQuant® Analyzer flow cytometers were compared with the FACSCanto II flow cytometer data for which the EuroFlow SOP had been originally developed. The settings were adjusted for fluorochromes used in the LST-QA: fluorescein isothiocyanate (FITC), phycoerythrin (PE), Peridinin chlorophyll protein-cyanin5.5 (PerCP-Cy5.5), PEcyanin 7 (Cy7), allophycocyanin (APC), APC-hillite7 (H7), Pacific Blue (PacB), and Orange Cytognos 515 (OC515).

  FACSCanto II flow cytometers. FACSCanto II flow cytometers were set up according to the EuroFlow SOP as published previously (Kalina et al. 1 and www.euroflow.org). Briefly, voltages of all PMTs were set to reach the target value for the 7 th peak of the Euroflow-validated lot of Rainbow Calibration Particles, 8 peaks (Spherotech, Lake Forest, IL) Type IIIA calibration particles. Evaluation of spectral differences among fluorochromes. Spectral differences of selected fluorochromes and emission filters were tested on the Sony SP6800 flow cytometer (Sony Biotechnology Inc., Tokyo, Japan) equipped with 405nm, 488nm and 638nm excitation lasers and detection of complete spectra on PMT array binned to 32 (for 488nm excitation) or 34 channels (for 405 and 638nm collinear excitation). Signal level of Pacific Orange (CD45 PacO, Exbio Praha, Prague, Czech Republic), OC515 (CD45 OC515, Cytognos SL, Salamanca, Spain) and Horizon V500 (BD Biosciences) was measured with either 550/40 (analogous to the filter set used in the Navios intruments) or 510/50 (analogous to the filter set of FACSCanto II cytometers) optical filters (AHF analysentechnik AG, Tuebingen, Germany) on a BD LSRII instrument (BD Biosciences) using the 405nm excitation laser line.

Figure 2

 2 Figure 2 legends). The following capture beads were used during the study: BD™

  instrument and the following FITC, PE, PerCP-Cy5.5, PE-Cy7, APC, APC-H7, PacB, and OC515 fluorochromes, were developed. Similarly, other alternative fluorochromes used in recently developed EuroFlow protocols (e.g. Brilliant Violet 421, Brilliant Violet 510) 3 would also require fluorochrome specific adjustment for any instrument with a different optical filter setup.

Figure 1 Rescaling

 1 Figure 1

Figure 2 Differences

 2 Figure 2

Figure 3 Results

 3 Figure 3

  Figure 2B

Table Legends Table 1 .

 Legends1 List of instruments with the hardware capable of measuring 8-color

	EuroFlow panels.

Table 1

 1

	Instrument name	Manufacturer	Lasers	Fluorochrome parameters	Acquisition speed (events/s)	CE IVD clearance
	BD FACSCanto II	BD Biosciences	3	10	10000	CE IVD
	Navios	Beckman Coulter	3	10	25000	CE IVD
	BD FACSLyric™	BD Biosciences	3	10	35000	CE IVD
	Novocyte	ACEA Biosciences	3	13*	35000	CE IVD
	Cyan ADP	Beckman Coulter	3	9	70000
	MACSQuant	Miltenyi Biotec	3	8	10000
	BD LSR Fortessa	BD Biosciences	4	18	70000
	BD FACSCelesta	BD Biosciences	3	12	25000
	Cytoflex	Beckman Coulter	3	13	30000
	Attune Nxt	Invitrogen™/ ThermoFisher	4	14	35000
	Yeti / ZE5	Propel Labs / Bio-Rad	5	30	100000
	SE520EXi	Stratedigm	4	18	10000
	SP6800	Sony Biotechnology Inc	3	2x PMT array*	20000
	CyFlow® Space	Sysmex / Partec	5	15	n.a.

*does not allow for independent PMT voltage settings

Acknowledgements:

This work is the main output of grant 15-28525A from Ministry of Health of the Czech Republic (T.K.). Instruments and infrastructure were supported by Ministry of Education, Youth and Sports, Czech Republic NPU I no. LO1604 (T.K.).

Sony SP6800 instrument was funded by European Structural funds CZ.2.16/3.1.00/24505 (T.K.). M.N. was supported by GAUK 802214. A.O. and J.F-M. were supported by grant DTS15/00119 from the Instituto de Salud Carlos II, Ministerio de Economía y Competitividad, Madrid, Spain. We wish to thank Christiane Siewert (Mitenyi Biotec) for a trial of MACSQuant Analyzer.

Supplementary Figure 1

Supplementary Figure 1 Analysis


Rihab Maaloul

Raouia Taktak

Lamia Chaari

Bernard Cousin

Two Node-Disjoint Paths Routing for Energy-Efficiency and Network Reliability

Keywords: Energy-aware routing, Two disjoint paths, Carrier grade networks, Reliability, Network optimization

Carrier grade networks are in general overdimensioned in order to protect against network resource failures and to handle probable traffic peaks. Such network design exhibits non-negligible energy waste. As well known, during network operation, the traffic load varies remarkably over day hours. Typically, a significant amount of energy saving can be achieved by turning off redundant and underutilized resources. Ensuring a sufficient level of reliability while taking into account energy saving objective is a very challenging task. In this paper, we study the multi-commodity reliable network design for carrier Ethernet networks. Each traffic demand is routed along one working path, and a corresponding backup path computed considering dedicated protection scheme. The primary and backup path must be node-disjoint. We also assume that the links of the carrier grade networks are made of multiple physical cables called bundles. We propose an exact method based on an Integer Linear Programming (ILP) formulation for the two node-disjoint paths with energy-aware routing (TNDP-EAR) problem. The studied problem is known to be NP-hard. In order to solve it efficiently, we propose a heuristic-based algorithm called GreenTNDP. Preliminary experimental results show the effectiveness of our algorithms to solve the problem.

I. Introduction

Reducing electricity bills and energy consumption has become a crucial goal for all industries, including telecommunication operators and Internet Service Providers (ISP). At the moment, network operators tend simultaneously to optimize the energy expenditure of their network and to provide the high service level required by their users. However, these two objectives are contentious. A tradeoff between both becomes hence inevitable. As the traffic demand continues to grow, it requires additional network resources with higher capacities and faster processing speeds. On the other hand, some critical applications need to be protected against unexpected failure events. Additional resources and power are consequently needed when it comes to ensuring network reliability. Network resilience versus energy-efficiency is a key concern in carrier grade networks [START_REF] Ye | Energy-efficient resilient optical networks: Challenges and tradeoffs[END_REF], [START_REF] Gazo Cervero | Green Wired Networks[END_REF]. The terms 'resilience', 'survivability', and 'reliability' are interchangeably used in the literature of telecommunications networks to refer to networks that are able to survive in the face of different faults. Network resilience implementation implies a mechanism for fault detection and localization together with a set of recovery techniques to reroute traffic around the failed component.

The path used by default is called working path or primary path. The path used to replace the working path in case of failure is called backup path. Depending on whether backup paths are computed before or after a fault of the working path, recovery techniques can be implemented based on two general schemes, restoration or protection [START_REF] Ye | Energy-efficient resilient optical networks: Challenges and tradeoffs[END_REF]. Routing with node-disjoint backup paths is more resilient to failures than routing with link-disjoint backup paths, because it can protect against both node and link failures. Furthermore, routing with node-disjoint paths is also link-disjoint, but not vice versa.

For network devices (i.e., carrier Ethernet devices) that present ON-OFF power profile [START_REF] Chabarek | Power awareness in network design and routing[END_REF], [START_REF] Jc Cardona Restrepo | Energy profile aware routing[END_REF], energy savings can be achieved by turning off selected devices (enter into sleep mode). To this end, many energy-aware routing solutions have been proposed [START_REF] Wang | Energy aware routing with link disjoint backup paths[END_REF]- [START_REF] Fisher | Greening backbone networks: reducing energy consumption by shutting off cables in bundled links[END_REF] to route traffic over energy efficient paths, and turn off unused network elements. Of particular interest are approaches such as [START_REF] Wang | Energy aware routing with link disjoint backup paths[END_REF] and [START_REF] Lin | Energy aware two disjoint paths routing[END_REF] which propose an energy-aware routing with two disjoint paths maintaining the network reliability.

In addition, bundled link concept can help improve the network capacity along with an enhanced resilience in case of link failure. This technique of composite link, called also link aggregation, is standardized by the IEEE 802.1AX [START_REF]Ieee standard for local and metropolitan area networks-link aggregation[END_REF]. Two main reasons behind using bundled links are (i) allowing network operators to easily upgrade their network capacity, (ii) resilience in case of cable failures and congestion. In this paper, a single network link is referred to one bundled link that is composed of multiple cables (or ports). We assume, without loss of generality, that all the cables have the same capacity and the same power consumption, and each port can be turned off independently.

In this paper, we consider the problem called energyaware routing with two node-disjoint reliable paths (TNDP-EAR). To the best of our knowledge, this is the first work that jointly minimizes the number of active cables in bundled links whilst ensuring a two-node disjunction protection scheme. To tackle this problem, we use efficient optimization techniques. Our main contributions are:

• First, we model the TNDP-EAR problem as an integer linear program. This exact formulation provides optimal solutions for small networks.

• Second, we propose a heuristic-based method called GreenTNDP, suitable for large-sized networks.

The paper is organized as follows. We present related works in the next section. In Section III, we formally describe the problem and model it as an ILP formulation. In Section IV, we describe our heuristic algorithm. A performance analysis of the proposed resolution methods is presented in Section V. Finally, we give concluding remarks in Section VI.

II. Related Works

The first work proposed in the context of green networking was that of Gupta et al. [START_REF] Gupta | Greening of the internet[END_REF], where a network protocol is able to put network components to sleep. They propose coordinated sleeping solution that deals with routing protocol aggregating traffic into few routes, in order to enable some links to sleep. Chiaraviglio et al. [START_REF] Chiaraviglio | Minimizing isp network energy cost: formulation and solutions[END_REF] provide a basic formulation of the EAR problem as a capacitated multi-commoditiy flow (CMCF) problem. They also propose different heuristics based on several sorting policies to turn off both links and nodes. Capone, et al. [START_REF] Capone | An optimization framework for the energy management of carrier ethernet networks with multiple spanning trees[END_REF] propose an optimization model that aims at minimizing the energy consumption of nodes and links while considering load-balancing constraints. The main shortcoming of this approach is the use of the traditional Multiple Spanning Tree Protocol (MSTP) [START_REF]Ieee standards for local and metropolitan area networks virtual bridged local area[END_REF], which can not adhere any more to the needs of nowadays carrier Ethernet network. Fisher et al. [START_REF] Fisher | Greening backbone networks: reducing energy consumption by shutting off cables in bundled links[END_REF] were the first who consider that pairs of core routers are connected by bundled links consisting of multiple cables. They propose three heuristic solutions, based on linear relaxation, to quickly determine the sub-optimal set of cables to be turned off. Their heuristics reroute traffic demands in a splittable way, i.e., multiple paths can be used to transmit one traffic demand between a source and a destination. In another work [START_REF] Lin | Efficient heuristics for energy-aware routing in networks with bundled links[END_REF], the same problem is addressed but with single path routing, i.e., traffic demands are routed in unsplittable way. Computation of the k-shortest-paths is exploited to select the path routing which fulfills the maximum link utilization constraint. In addition to energy efficiency, many studies have been interested to reliability issues in the network design problems. In [START_REF] Aldraho | Enabling energy efficient and resilient networks using dynamic topologies[END_REF] and [START_REF] Addis | On the energy cost of robustness and resiliency in ip networks[END_REF], the authors provide a set of algorithms and optimization models suitable with IP networks, considering unsplittable routing. In both works, the network resilience requirements are taken into account while reducing the link and node consumption. In addition to network survivability, robust optimization model is proposed in [START_REF] Addis | On the energy cost of robustness and resiliency in ip networks[END_REF] to handle uncertain traffic demands. In [START_REF] Lin | Energy aware two disjoint paths routing[END_REF], Lin et al. have proposed an energy-aware routing with two disjoint paths, according to which each request can be routed via multiple paths (which may have common links) besides two disjoint paths, to provide higher protection against eventual failures. The same authors have proposed an interesting strategy [START_REF] Lin | Energy-aware traffic engineering with reliability constraint[END_REF] which considers reliability and protection constraints in the formulation. The authors propose a comparative study of green routing approaches using two reliability measures: Terminal Reliability (TR) and Route Reliability (RR). Finding primary and backup link-disjoint paths for each source-to-terminal request is proposed in [START_REF] Wang | Energy aware routing with link disjoint backup paths[END_REF]. Two heuristic algorithms based on the computation of Suurballe's algorithm [START_REF] John | A quick method for finding shortest pairs of disjoint paths[END_REF] to find the working and backup paths, while turningoff both nodes and links are presented and evaluated. The optimization model aims at minimizing the fixed energy cost paid to keep a router or a link in the active state. To obtain only a single active path routing, binary flow variables are introduced. Note that the solution proposed in [START_REF] Wang | Energy aware routing with link disjoint backup paths[END_REF] can protect against only link failures, i.e., it does not consider the node failure event. To the best of our knowledge, the closest works to ours are [START_REF] Wang | Energy aware routing with link disjoint backup paths[END_REF]- [START_REF] Lin | Energy aware two disjoint paths routing[END_REF]. Like ours, they all are intended to be run in a logically centralized manner. We report in TABLE I the main common and different points (assumptions and resolution method) between our work, and those of [START_REF] Wang | Energy aware routing with link disjoint backup paths[END_REF], [START_REF] Lin | Energy-aware traffic engineering with reliability constraint[END_REF] and [START_REF] Lin | Energy aware two disjoint paths routing[END_REF].

III. Problem formulation A. Basic assumptions and notations

Our network model is based on the following assumptions: (i) each link consists of B cables that can be turned off independently, we assume to turn off only cables. (ii) we consider that for any pair of network nodes, it is possible to compute at least two node-disjoint paths. (iii) single link/node failure (the probability of simultaneous failures is very rare because failures are very quickly solved).

Let G = (V, A) be a directed graph that model the network topology, where V is the set of nodes (Ethernet switches), and A is the set of links. Each link (u, v) represents a bundled link with B uv 1 cables. The capacity of each link, i.e., C uv 1, is the total capacity of its cables, and each cable has the same capacity. The power consumption of each link is the total consumption induced by its operational cables. The number of turned-on cables in any given link (u, v) is denoted n uv B uv . When n uv = 0, it means that the whole link (u, v) is turned off. Let D be the set of all traffic demands (traffic matrix) in G, and the triplet (s

d , t d , h d ) denote the traffic demand indexed by d = 1, 2, ..., |D| from source node s d ∈ V to destination node t d ∈ V , where h d is the amount of traffic exchanged from s d ∈ V to t d ∈ V .
Given G and D as input, the TNDP-EAR (Two Node Disjoint Paths energy-aware routing) problem consists in routing each demand in an unsplittable way through a primary path P d p and a backup path P d b , while minimizing the number of powered-on cables. Additionally, the routing solution has to respect the maximum link utilization rate threshold that is denoted as U T . We denote by f uv the total flow assigned to link (u, v) ∈ A, y notations for the parameters and decision variables.

To illustrate the TNDP-EAR problem, we consider an example of 6-nodes network as shown in Fig. 1. We assume that each link is made of four cables (B=4). The capacity of each bundled link is assumed to be 24 units. Assume that there are two demands on the network, i.e., D = {(0, 2, 2), (0, 5, 3)}. Fig. 1b presents an optimal solution for TNDP-EAR problem. For demand d = 1, the primary path P 1 p = 0 → 2, and the backup path

P 1 b = 0 → 1 → 3 → 2.
For demand d = 2, the primary path P 2 p = 0 → 2 → 4 → 5, and the backup path

P 2 b = 0 → 1 → 3 → 5.
As we consider 1 + 1 protection, the traffic is duplicated over the two disjoint paths. In this case, we obtain f 01 = f 02 = f 13 = 5; f 32 = 2; f 35 = f 24 = f 45 = 3. Dashed lines correspond to links that are totally turned off, whereas turned off cables are not illustrated. As the spare capacity on each arc can be turned off by rounding up to discrete number of cables, we obtain n 01 = n 02 = n 13 = 2; n 32 = n 35 = n 24 = n 45 = 1; n 14 = n 34 = 0.

n uv E uv + β{ ∑ (u,v)∈A (B uv -n uv )E uv } (1)
x uv ≤ n uv ∀(u, v) ∈ A, ( 2
)
B uv x uv ≥ n uv ∀(u, v) ∈ A, (3)
∑ (u,v)∈A y d uv - ∑ (v,u)∈A y d vu =    1 if u = s d , -1 if u = t d , 0 if u ̸ = s d , t d , ∀d ∈ D, (4)
∑ (u,v)∈A z d uv - ∑ (v,u)∈A z d vu =    1 if u = s d , -1 if u = t d , 0 if u ̸ = s d , t d , ∀d ∈ D, (5)
∑ d∈D h d (y d uv + z d uv ) ≤ U T (n uv /B uv )C uv ∀(u, v) ∈ A, ( 6
)
y d uv + z d uv ≤ x uv ∀(u, v) ∈ A; d ∈ D, ( 7
)
g d u + k d u ≤ 1 ∀u ∈ V \ {s d , t d }; d ∈ D, ( 8
)
y d uv + y d vu ≤ g d u ∀u ∈ V ; (u, v) ∈ A; d ∈ D, ( 9
)
z d uv + z d vu ≤ k d u ∀u ∈ V ; (u, v), (v, u) ∈ A; d ∈ D. ( 10
)
The objective function (1) minimizes the total power consumption induced by cables. It is composed of two parts. The first part computes the power consumption of powered on cables. The second part computes the consumption of powered-off cables. It is weighted by parameter β that is set to 0.1, assuming that the powered-off cables consume 10% of the power spent in the active mode. Inequalities (2) make sure that all cables of link (u, v) are powered-off when x uv = 0. Inequalities (3) make sure if link (u, v) has at least one cable powered-on (i.e., n uv ≥ 1) then x uv = 1. Equations ( 4) and ( 5) express for each demand the classical flow conservation constraints for the primary and backup paths, respectively. Constraints (6) ensure that the total flow going through each link (u, v) of the primary and backup path cannot exceed the tolerated link capacity, i.e., U T (n uv /B uv )C uv . Inequalities (7) make sure that the primary and backup paths are link disjoint. While, inequalities [START_REF] Moulierac | Optimizing igp link weights for energy-efficiency in multi-period traffic matrices[END_REF] guarantee that for each demand the primary and the backup paths are node-disjoint. Finally, inequalities ( 9) and ( 10) are for two node-disjoint paths. They guarantee that if node u is used by primary path (g d uv = 1), then node u should be excluded from the backup path (k d uv = 0), and vice versa.

IV. Heuristic algorithm

As the EAR link disjoint path is proven in [START_REF] Wang | Energy aware routing with link disjoint backup paths[END_REF] to be NP-hard even for only two different demands. Thus, we can conclude that TNDP-EAR problem is an NP-hard problem as well. Hence, heuristic methods are preferred to quickly find efficient solutions for this problem. We propose, GreenTNDP, a heuristic algorithm that includes a nodedisjoint path computation phase and an EAR phase. The implementation of GreenTNDP can be run on a logicallycentralized power monitor such as in Software Defined Network (SDN) architecture. The idea of our heuristic is as follows (see Algorithm 1). Sort all demands in a descending order of their traffic h d ; create the residual graph for each demand by removing all links with residual capacity lower than h d ; find the primary path and backup path (using algorithm 2 that computes node-disjoint paths [START_REF] Iqbal | Disjoint paths in networks[END_REF]) for each demand. Then, the energy aware routing phase is initialized; select iteratively a link with maximum residual capacity to turn off; find all demands that contain the deleted link and reroute traffic for affected demands. If any of the affected demands fails to be rerouted, the candidate link must be turned on. Repeat the process until all links are considered. Finally, turn-off the unused cables using [START_REF]Ieee standard for local and metropolitan area networks-link aggregation[END_REF]. The GreenTNDP heuristic runs in a polynomial time and has a complexity of O(|A| 2

+ |A||V |log(|V |))

.

n uv = ⌈ f uv B uv µC uv ⌉ (11)

V. Experimental results

In this section, we evaluate the flow based ILP formulation for directed graphs and the heuristic-based algorithm GreenTNDP. We use the following experiments setup (i) bundle size B uv = 4; (ii) the maximum tolerated link utilization U T = 100%; and (iii) each cable has the same power consumption E uv = 100 watts. To evaluate the performance of our algorithms, we use the following metrics. Algorithm 2: Basic 2-node-disjoint-paths in directed graphs [START_REF] Iqbal | Disjoint paths in networks[END_REF] η% is the percentage of power savings related to the cables turned off by the EAR algorithm. It is computed as follows:

Input: A weighted-directed graph G = (V, A),
η% = (1 - ∑ (u,v)∈A n uv ∑ (u,v)∈A B uv ) × 100%. (12)
ρ is used to measure the mean traffic utilization of the used links in G ′ .

ρ% = 100 × ∑ (u,v)∈A ′ ρ uv |A ′ | , ( 13
)
where ρ uv is the traffic utilization of link uv.

Finally, we evaluate the effect of our EAR algorithms according to the reliability of each demand. We measure route reliability as in [START_REF] Lin | Energy-aware traffic engineering with reliability constraint[END_REF]. Let p uv = 0.9 be the probability of a cable in link (u, v) being functional. The reliability of a link (u, v) denoted by l uv is computed as follow:

l uv = 1 -(1 -p uv ) nuv . ( 14
)
Let RR d denote the global route reliability for a demand d routed through two node-disjoint paths (i.e., represented by variables y and z). RR d is computed as follows:

RR d = 1 -(1 -R dy )(1 -R dz ), (15)
where R dy and R dz are the route reliability of the primary and back-up paths respectively. R dy and R dz are calculated by the following formula :

R d{y/z} = log -1 ( ∑ (uv)∈R d{y/z} log l uv ) , ∀d ∈ D. ( 16
)
We can also compute the average route reliability (ARR) for a given traffic matrix D as follows.

ARR = ∑ d∈D RR d |D| . ( 17
)
We test our algorithms the ILP and GreenTNDP on six network topologies collected from the SNDlib [START_REF] Orlowski | Sndlib 1.0-survivable network design library[END_REF]. We choose network instances where two node-disjoint paths always exist. We solve the ILP model using the CPLEX solver [START_REF]Ibm ilog cplex optimization studio[END_REF], with a time limit set to 3 hours. Cplex is used for a branch-and-bound resolution, cuts are deactivated. TABLE III and TABLE IV report the computational results. The gap column reports the energy performance of the resulting network topology, if the gap equals to zero, it means that the optimal solution was found.

The obtained results confirm the effectiveness of our heuristic GreenTNDP. For instance, the ILP model cannot find an optimal solution for Atlanta, Dfn-bwin, Di-yuan, and Nobel-germany networks within 3 hours, meanwhile GreenTNDP provides feasible solutions in reasonable time (within at most 11 seconds). Moreover, we notice that the heuristic algorithm outperforms the ILP model for Atlanta, Di-yuan, and Nobel-germany instances, not only in terms of computational time but also in terms of energy savings. For Atlanta 73% of cables are turned off in 19.31 seconds by GreenTNDP, whereas 67% of cables are turned off in 3 hours by the ILP. Concerning Pdh network instance, ILP model and GreenTNDP find the same solution (optimal). This result shows that GreenTNDP may reduce the computation time. Finally, ILP model can find the optimal solution for Polska instance within 1529 seconds. Meanwhile GreenTNDP find feasible solution (with 19.43% of gap to optimality) in only 6.86 seconds. We can hence conclude that our heuristic should be improved in order to get approximative solutions close to the optimal ones. Note that once some of the links are turned-off, the same traffic is rerouted on a fewer set of links, which impact the traffic capabilities (i.e., network congestion). This trade-off between energy-saving and network congestion is clearly demonstrated by ρ parameter. We notice that the mean link utilization ρ% increases when η% increases as well. For example, when evaluated on Atlanta, the ILP can turn off 67.6% of cables having a smaller impact on the mean traffic utilization (ρ = 23%), compared to (ρ = 52.72%) when GreenTNDP achieved higher energy saving, i.e., η = 73.29. Figures 2 to 4 present the topologies before and after the execution of Green TNDP for Atlanta, Dfn-bwin and Diyuan network instances. TABLE V highlights the trade-off between minimizing energy usage and enhancing network reliability. We show the route reliability for GreenTNDP, ILP model and SP (Shortest Path routing without disjoint backup path) for the six network instances. Note that SP is an energy aware routing that minimizes the total number of cables that route each demand along only one path (the primary one). The results inTABLE V show that ILP model and GreenTNDP produce topologies with highest reliability (ARR) as compared to SP, since this later uses a fewer number of paths to route the demands. In the other hand, we observe that ARR increases when η% decreases for all the algorithms. These results are expected because when rerouting traffic on fewer cables this increases (resp. decreases) energy saving (resp. route reliability).

VI. Conclusion

To the best of our knowledge, this is the first study that deals with the energy-aware routing with two nodedisjoint paths problem. In this paper, we formally defined the reliable energy-aware routing problem and modeled it using an ILP formulation. We then proposed a greedy heuristic algorithm GreenTNDP. Our evaluation of the ILP model TNDP-EAR and the heuristic GreenTNDPbasic on six realistic networks showed that the heuristic is efficient to produce a network with a low energy usage under a high-reliability level in reasonable time. However, several improvements would be interesting to consider in order to enhance the heuristic algorithm and get close-to-optimal solutions. In this context, a theoretical analysis of the bounds of the heuristic algorithm could be considered consider the case where the path-disjunction is not always feasible. The objective can hence consist in maintaining a predefined threshold of routing reliability subject to constraints that limit the number of turned-off cables.

Fig. 1 :

 1 Fig. 1: Example of a routing solution for TNDP-EAR problem

7 P 8 if P d exist then 9 10 Paths=Paths 20 A 22 D

 789102022 Input: A weighted-directed graph G = (V, A), a set D of demands with traffic requirements h d for all d ∈ D, Output: G ′ = (V, A ′ ): the output graph containing only links used to route the demands. 1 Initially, A ′ = A; 2 /*Phase 1*/ Two Node Disjoint Path 3 Paths=∅; 4 Sort demands in a descending order of traffic h d ; 5 for each d ∈ D do 6 Compute the residual graph Gr for d by removing the links with ruv ≤ h d , ∀(u, v) ∈ A ′ ; d = call find-TNDP(Gr, d) /*Algorithm 2*/; Update residual capacity of links of P d on G ′ ; ∪P d ; P d = {P d p , P d b } ; Phase 2*/ Energy Aware Routing 18 //Step 1 19 for each link (u, v) ∈ A ′ in a descending order of its residual capacity do ′ = A ′ -{(u, v)}; // turn off candidate link (u, v) 21 //Find affected demands by turning off (u, v) a ={d|P d ∩ (u, v) ̸ = ∅, d ∈ D}; 23 Release the bandwidth of D a ; 24 feasible=Reroute traffic of D a on G ′ by repeating Phase 1; 25 if feasible==false then 26 put (u, v) back to A ′ ; 27 assign bandwidth of D a on G ′ ; 28 end 29 end 30 //Step 2 31 for each each link (u, v) ∈ A ′ do 32 turn off unused cables using (11); 33 end Algorithm 1: Pseudo-code description for the proposed heuristic (GreenTNDP)

Fig. 2 :

 2 Fig. 2: Atlanta network

Fig. 3 :

 3 Fig. 3: Dfn-bwin network

Fig. 4 :

 4 Fig. 4: Di-yuan network

TABLE I :

 I Main properties of this study with respect to the closest proposals h h h h h h h h h h

	Properties	Proposals	[5]	[6]	[7]	This work
	Routing	Unsplittable	Free splittable	Splittable	Unsplittable
	Path computation	Suurballe's algorithm [18]	Yen's algorithm [19]	Yen's algorithm [19]	Basic disjoint path algorithm [20]
	Exact formulation	0 -1 ILP	MILP	MILP	ILP
	Backup paths	Dedicated	Dedicated and shared	Dedicated and shared	Dedicated
	Failure assumption	Link	Link	Node and link	Node and link
	Bundled links	-		-

TABLE II :

 II Summary of notations and parameters Set of all traffic demands D = {(s d , t d , h d ), s d ∈ V, t d ∈ V } Binary variable to indicate whether node u is used to route d by primary path P d p , u ∈ V \ {s d , t d } k d

	Notation	Description
	G=(V, A )	Directed graph where V is the set of vertices (nodes) and A is the set of arcs (links)
	G'=(V, A ′ )	graph solution used to route D
	Euv	Power consumption of a powered cable in link (u, v) ∈ A
	β	Parameter set to 0.1, assuming that a powered-off cables consumes 10% of the power spent in the active mode
	Cuv	Capacity of link (u, v) ∈ A
	U T	Maximum tolerated link utilization, U T ∈]0, 1]
	ruv	Remaining capacity of link (u, v)
	D
	D t	Set of all demands having t as destination node t ∈ V
	h d	Demand of the traffic flow from node s d to t d
	Buv	Number of cables in link (u, v) ∈ A
	nuv	Integer variable to indicate the number of powered-on cables in link (u, v)
	xuv	Binary variable to indicate if the link (u, v) has at least one powered-on cable or not
	y d uv	Binary variable to indicate whether link (u, v) is used to route d by primary path P d p
	z d uv fuv	Binary variable to indicate whether link (u, v) is used to route d by backup path P d b Total flow of link (u, v); fuv ≥ 0
	g d u

u

  Binary variable to indicate whether node u is used to route d by backup pathP d b , u ∈ V \ {s d , t d }

  a pair of source and destination nodes (s, t).Find the shortest path Pi from node s to node t ;

	Output: 2 node-disjoint paths P1, P2.
	1 for i=1,2 do

2 3 Delete intermediate node of Pi from G; 4 end

TABLE III :

 III ILP formulation

					Power	Optimality	Power consumption	Mean links	Execution
	Network	|V |	|E|	|D|	Saving	gap	Upper bound	Utilization	Time
					(η%)	(%)	UB (W)	(ρ)	(s)
	Atlanta	15	44	132	67.61	5	5147.6	23.29	10800
	Dfn-bwin	10	90	90	90.83	21	3006	22.46	10800
	Di-yuan	11	84	22	88.39	6	3543.6	22.09	10800
	Nobel-germany	17	52	121	55.28	2	8390.8	43.89	10800
	Pdh	11	68	24	88.06	0	1917.2	11.05	30.25
	Polska	12	36	66	71.52	0	3704.4	27.66	1529.89

TABLE IV :

 IV Heuristic algorithm (GreenTNDP)

					Power	Power consumption	Mean links	Execution
	Network	|V |	|E|	|D|	Saving	Upper bound	Utilization	Time
					(η%)	UB (W)	(ρ)	(s)
	Atlanta	15	44	132	73.29	4247.6	52.72	19.31
	Dfn-bwin	10	90	90	87.22	4176.0	25.32	31.92
	Di-yuan	11	84	22	91.66	2553.6	11.94	8.96
	Nobel-germany	17	52	121	75	5061.8	13.90	30.54
	Pdh	11	68	24	88.06	1917.2	11.05	8.20
	Polska	12	36	66	65.97	4424.4	18.84	6.86

TABLE V :

 V Energy saving and average route reliability

			SP	ILP model	GreenTNDP
	Atlanta	η%	80.68	67.61	73.29
		ARR	0.7379	0.9661	0.9503
	Dfn-bwin	η%	94.72	90.83	87.22
		ARR	0.9084	0.9646	0.9732
	Di-yuan	η%	94.64	88.39	91.66
		ARR	0.9365	0.9969	0.994
	Nobel-germany	η%	76.44	55.28	75
		ARR	0.8403	0.9418	0.8926
	Pdh	η%	92.27	88.06	88.06
		ARR	0.8568	0.9486	0.9486
	Polska	η%	81.94	71.52	65.97
		ARR	0.8692	0.8813	0.9923