Switching adaptable optimization of resource allocation for space division multiplexed elastic optical networks

Accepted Manuscript Switching adaptable optimization of resource allocation for space division multiplexed elastic optical networks Mohsen Yaghubi-Namaad, Akbar Ghaffarpour Rahbar, Behrooz Alizadeh, Amin Ghadesi PII:

S1573-4277(18)30064-X

DOI:

10.1016/j.osn.2018.08.001

Reference:

OSN 495

To appear in:

Optical Switching and Networking

Received Date: 7 April 2018 Revised Date:

26 June 2018

Accepted Date: 10 August 2018

Please cite this article as: M. Yaghubi-Namaad, A. Ghaffarpour Rahbar, B. Alizadeh, A. Ghadesi, Switching adaptable optimization of resource allocation for space division multiplexed elastic optical networks, Optical Switching and Networking (2018), doi: 10.1016/j.osn.2018.08.001. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Switching Adaptable Optimization of Resource Allocation for Space Division Multiplexed Elastic Optical Networks a

RI PT

Mohsen Yaghubi-Namaad a, Akbar Ghaffarpour Rahbar a, Behrooz Alizadehb , and Amin Ghadesi a Computer Networks Research Lab, Department of Electrical Engineering, Sahand University of Technology, Sahand New Town, Iran. b Department of Science, Sahand University of Technology, Sahand New Town, Iran

Abstract

EP

TE D

M AN U

SC

Space division multiplexed-elastic optical networking (SDM-EON) is considered as the promising solution to overcome the capacity crunch of optical transport networks. The resource allocation problem of SDM-EON includes the route, modulation level, space, and spectrum assignment (RMLSSA). In this paper, we first investigate the effect of fiber types, switching solutions, and networking approaches on the resource allocation problem of SDMEON, and try to consider comprehensive all-inclusive constraints. Then, a new generic formulation of switching adaptable (SA)-RMLSSA is proposed as an integer linear programing (ILP) for static traffic based on these comprehensive constraints. In addition, the heuristic switching adaptable resource allocation (SARA) algorithm is introduced. Finally, the paper evaluates the effectiveness of SARA, with two sorting policies of connection demands, to find the near-optimal solution of different networking approaches. This evaluation is performed for parallel spectral superchannel (PS-Ch), limited spatial-spectral superchannel (LS2-Ch), group limited spatial-spectral superchannel (GLS2-Ch), and free spatial-spectral superchannel (FS2-Ch) switchings (with both ribbon and ring configurations of multi-core fibers (MCF), and having or not having spatial guardband) with operational assumptions in regard to the quality of transmission (related to the used fiber type) and traffic profile. The effect of each networking approach, having modulation adaptivity tailored for each fiber type, enabling spatial guardbands for MCFs, and cores configurations are investigated by maximum utilized frequency slot index (MUFSI) and demand utilization ratio (DUR) as metrics of static traffic. Moreover, the use of SARA for dynamic traffic is investigated for real network experiment.

AC C

Index terms: Space Division Multiplexing, Elastic Optical Network, Network planning, Integer Linear Programming, Resource Allocation, RMLSSA, Multi-Core Fiber, Multi-Mode Fiber, Modulation Adaptivity, Static and Dynamic Traffic.

Yaghubi-Namaad, et al. / ACCEPTED MANUSCRIPT

2

List of acronyms and nomenclature Ascending SAL number Adaptive SAL selection for a Networking Approach Bandwidth blocking rate Bandwidth variable transponder Set of connection demands Descending FS number Demand utilization ratio Set of links Elastic optical network Ordered set of FSs The ith frequency slot Frequency slot Free S2-Ch switching Connected graph represents the network topology Group limited S2-Ch switching Spatial guardband Spectral guardband Maximum number of spatial paths in each networking approach Number of spatial paths in SAL q Integer linear programming Number of pre-determined routes for each connection demand Limited S2-Ch switching The highest attainable modulation level Multi-core fiber Multi-core multi-mode fiber Multi-input multi-output Multi-mode fiber Maximum utilized frequency slot index

MCF MC-MMF MIMO MMF MUFSI n d ,π d

M AN U

SC

RI PT

ASN ASNA BBR BVT D DFN DUR E EON F fi FS FS2-Ch G GLS2-Ch gs gw hmax hq ILP k LS2-Ch π M max

Connection demand required FS

Optical signal to noise ratio Polarization division multiplexing Physical layer impairment Parallel S-Ch switching

Qd ,πd

Set of possible SALs for required number of frequency slots

TE D

OSNR PDM PLI PS-Ch

Set of possible SALs for required number of frequency slots with guardbands

QoT Rd Rfs RMLSA RMLSSA ROADM RSA RSCA sd S2-Ch SAL SARA SA-RMLSSA

Quality of transmission Data rate of the connection demand FS base capacity Routing, modulation level, and spectrum assignment Routing, modulation level, space, and spectrum assignment Reconfigurable optical add/drop multiplexers Routing and spectrum assignment Routing, spectrum and core allocation The source node Spatial-spectral superchannel Space and spectrum assignment layouts Switching adaptable resource allocation Switching adaptable-routing, modulation level, space, and spectrum assignment

AC C

EP

Q%d ,πd

Ygahubi-Namaad, et al./ ACCEPTED MANUSCRIPT

Spectral superchannels Space division multiplexing Stepwise greedy heuristic algorithm Single mode fiber Spectrum selective switch Destination node Objective function of SA-RMLSSA formulation Set of nodes Frequency width in SAL q Wavelength division multiplexing Spatial path Ordered set of spatial paths on each link Number of spatial paths Set of all routes for every connection demand Set of pre-determined candidate routes for connection demand d Normalized traffic load Maximum number of FSs All the routes that go through link e

SC

RI PT

S-Ch SDM SGA SMF SSS td u V wq WDM δi ∆ θ Π Πd ρ ψ Ωe

3

1. Introduction

AC C

EP

TE D

M AN U

Currently, Elastic optical networking (EON) is considered as the promising flexible solution, against the conventional fixed-grid wavelength division multiplexing (WDM) networks, for evergrowing traffic in backbone networks [1-4]. The use of finer granularity of spectrum as frequency slots (FS) and adaptive modulation provides flexibility in EON by means of bandwidth variable transponders (BVT) and spectrum selective switches (SSS) [1, 5-8]. The aforementioned flexibility affords efficient use of spectrum, supports the sub-wavelength and super-wavelength for connection demands [2, 3], and provides quality of transmission (QoT) awareness [5, 9, 10]. However, the capacity requirement of current and future applications has forced researchers to exploit methods to overcome the capacity limitation of fibers. Thus, space division multiplexed EON (SDM-EON) has been proposed in which optical signals are transmitted over different spatial paths of optical links [11-15]. The single mode fiber (SMF) bundle, coupled or uncoupled multi-core fiber (MCF), multimode fiber (MMF), and multi-core multi-mode fiber (MC-MMF) are the main nominates to be used in SDM-EON [16-19]. Consequently, in SDM-EON, the spatial path of optical transmission could be either a fiber, a core, or a mode in a core. The SDM-EON enhances the spatial diversity and consequently provides more capacity and network throughput than simple EON. However, resource allocation that includes routing, modulation level, space, and spectrum assignment (RMLSSA) becomes more complex because of added degree of flexibility via spatial domain, in contrast with resource allocation problem of EON (routing, modulation level, and spectrum assignment (RMLSA) or routing and spectrum assignment (RSA)) which was investigated for static and dynamic traffic in many works such as [20-24]. The formulation of static resource allocation problem as an integer linear programming (ILP) for EON has been presented as link-based RMLSA in [25] and as path-based RSA in [26] which are proved to be NP-problem. In both works, the network planning of EON is investigated for a given traffic matrix with the requested transmission data rates of all connection demands. The objective of formulations was to find the optimal minimum number of utilized FSs to establish all the

Yaghubi-Namaad, et al. / ACCEPTED MANUSCRIPT

4

AC C

EP

TE D

M AN U

SC

RI PT

connection demands without blocking. Heuristic algorithms have been proposed to achieve nearoptimal solutions, too [20, 22, 25, 26]. However, the optimal or near-optimal solution depends on traffic matrix, network topology, connectivity degrees of nodes, and sorting policy of serving connection demands for heuristic algorithms, especially. The resource allocation of SDM-EON depends on the proposed switching solutions and fiber types which leads to different networking approaches [12, 27-29], that will be discussed subsequently in Section 2. Note that it is possible to switch each core spectrum independently (known as independent switching), but the energy coupling of MMFs forces to switch all the modes altogether known as joint switching/fractional joint switching [30, 31]. The performance of different SDM networking approaches are investigated in regard to the number of needed transponders [28], required number of SSS [31], and traffic profile effect [32, 33]. Moreover, the spectral efficiency versus transmission reach tradeoff is investigated in [31] for different switching granularities. Spatial group sharing is proposed to improve joint switching performance by equipping nodes with extra SSSs to provide limited independent switching as electrical/optical grooming enablers in [34, 35]. These works showed that independent switching brings out higher network performance for dynamic traffic, but cost savings from integrated components makes the joint switching (especially implemented by SMF bundles) an interesting approach to be used as a middle ground of migration from present backbone to future SDM networks. For static traffic, the ILP formulation of routing, spectrum and core allocation (RSCA) problem has been presented in [36]. This MCF-based formulation uses link-based view to assure no overlapping of connection demands over each core fiber along keeping the accumulated crosstalk smaller than a given threshold. In [37, 38], the ILP formulation for routing, modulation level, core, and spectrum assignment has been presented with considering the core continuity constraint which is provided by cost effective reconfigurable optical add/drop multiplexers (ROADM). In our previous work [39], we presented an ILP formulation for the RMLSSA problem to support SMFbundles, coupled and uncoupled MCFs. Then, a stepwise greedy heuristic algorithm (SGA) was introduced to achieve near optimal solution of the static RMLSSA problem. We also introduced four kinds of sorting policies for algorithm and investigated the performance of them in comparison with optimal solution. Overall, (1) the proposed ILP formulations have not considered the support of multi-mode fibers, and (2) have not included the switching and networking considerations. However, basic ILP modeling ways of SDM-EON resource allocation is surveyed in [15]. Different channel-based ILPs for networking approaches are introduced in [40] without performance evaluation. Moreover, one channel-based ILP is introduced and evaluated in [41, 42] considering the SMF bundles as transmission media. However, the channel-based approaches will not provide scalability (as reported out of memory error in some instances [41]), regarded to so many possible ways of allocating channels over available spatial-spectral resources [40]. This has motivated us to propose a new generic resource allocation formulation that considers the constraints forced by the type of fiber or possible switching solutions. Our objective in this work is to consider the forced constraints from switching solutions and fiber types to formulate the static switching adaptable- route, modulation level, space and spectrum (SARMLSSA) problem as an generic ILP that tries to minimize the utilized spectrum over the network. Since the optimal solution of ILP formulation cannot be solved efficiently for large networks, we propose a switching adaptable resource allocation (SARA) heuristic algorithm to find the near optimal solution with less complexity. We compare the performance of the proposed heuristic

Ygahubi-Namaad, et al./ ACCEPTED MANUSCRIPT

5

SC

RI PT

algorithm with the optimal solution through simulation. We also compare the effects of networking approaches and relative properties (such as tailored modulation adaptivity, core configuration, space and spectrum assignment layout (SAL) gain, and required guardbands) on the utilized spectrum and try to give a planning outline based on each fiber type. We also evaluate modified version of SARA’s performance for dynamic traffic to investigate networking approach effect on the bandwidth blocking rate. Our contribution is first to support all fiber types, switching solutions and networking approaches in resource allocation by: (1) defining and assuming some comprehensive constraints to manage crosstalk/energy coupling, (2) introducing one scalable generic SA-RMLSSA in regard to comprehensive constraints, (3) introducing SARA as a generic heuristic resource allocation tool, and (4) modeling all the physical layer impairments (PLI) of fiber with one parameter as an input for SA-RMLSSA and SARA. Second, we compare the performance of different networking approaches in static and dynamic scenarios in regard to the effect of practical assumptions about network operation. Third, we try to give a network planning outline based on our results. The rest of this paper is organized as follows. In Section 2, we discuss the fiber and switching constraints and networking approaches. In Section 3, the SA-RMLSSA formulation is presented. In Section 4, we introduce our heuristic algorithm to solve the SA-RMLSSA problem. The simulation results are demonstrated in Section 5. Section 6 concludes the paper.

M AN U

2. Network model

Here, we discuss the main concepts that should be considered to formulate the resource allocation problem. First, the spatial-spectral channel and SAL are discussed. Next, the type of fibers and crosstalk issue will be discussed. Then, four networking approaches and ways to manage or suppress crosstalk for each one is discussed. Finally, this section is concluded with identifying comprehensive constraints for generic formulation of resource allocation to support all fibers, switching solutions, and networking approaches. 2.1. Spatial- spectral superchannel

AC C

EP

TE D

The main idea for providing the spectral flexibility in EON is to have overlapped and modulation adaptive subcarriers [1, 3].Varying the number of subcarriers in a BVT enables us to create spectral superchannels (S-Ch). A superchannel is a group of subcarriers that their transmission, routing and receiving are performed as one lightpath [43, 44]. Accordingly, an S-Ch can support bandwidth requirement between one FS and maximum capacity of BVT. The routing of this end-to-end lightpath needs the bandwidth adaptive switches with fine resolution, along the route, i.e., SSS. Since SSS in each node tries to switch the spectral channels of connection demands, we call the EON networking approach as “S-Ch switching”. In SDM-EON, the spectral superchannel concept can be expanded to have spatial-spectral superchannel. The S2-Ch is used when a connection demand is transmitted in different optical spatial paths and has overlapped subcarriers in each spatial path. The space and spectrum assignment layout determines how a connection demand can be assigned through some spatial paths and with specified frequency width in each spatial path [39]. The S2-Ch provides flexibility of changing the layout for resource allocation, but entails more complexity.

Yaghubi-Namaad, et al. / ACCEPTED MANUSCRIPT

6

2.2. Fiber types and crosstalk

M AN U

SC

RI PT

Optical fibers suffer from different physical layer impairments. However, the most important PLI that affects the resource allocation of SDM-EON is crosstalk/energy coupling between different lightpaths. As mentioned, the transmission media for SDM-EON may be available in many forms. The SMF bundle is parallelization of some fiber cores, with different cladding for each, designed to allow light guiding in one spatial path that is the fiber. In this case, there is usually no crosstalk between spatial paths. The MCF includes multiple cores placed within a single fiber cladding with one optical mode in each core. Consequently, the spatial path of MCF is a core. There is two commercial types of MCF: (1) uncoupled MCFs with no crosstalk between cores by means of core distance or trench assisted profiles for refractive index [14, 16], and (2) coupled MCFs with crosstalk between cores, yet could provide more number of cores at the same cladding diameter. On the other hand, the configuration of cores could have two main arrangement: a ribbon or ring. Other configurations of cores could be considered as ribbon especially for uncoupled MCFs. The MMF has multiple spatial paths as optical modes in one core. The crosstalk between modes are inevitable, however fiber designs with low group mode delay are favorable for SDM-EON [16, 19]. Finally, MC-MMF has multiple cores each with multiple modes. In this case, the designs with no crosstalk between cores are more favorable for SDM-EON. Furthermore, the existing crosstalk could affect QoT and consequently transmission reach [16, 19, 45]. However, by some consideration for each fiber kind, the multi-input multi-output (MIMO) processing alongside with coherent detection could be beneficial to suppress the accumulated crosstalk along the route [14, 39]. Therefore, the ways to tackle the crosstalk problem will be discussed separately for each fiber kind subsequently. 2.3. Switching solutions and networking approaches

AC C

EP

TE D

From the network planning view, the use of each fiber affects entirely the resource allocation. To understand the fiber effect on the network planning, we discuss four networking approaches and related switching solutions [27] proposed for SDM-EON briefly. • PS-Ch switching: The simplest idea to use spatial diversity is to have some parallel networks by using the SMF bundle between network nodes. In this approach, shown in Fig. 1.a., it is obvious that the resource allocation and switching is performed in each spatial path independently. The switching of this network could be performed as a layered EON network (e.g., parallel SSS is required). Consequently, the resource allocation includes route and spatial path selection, and after that spectrum assignment could be carried out like the EON. We call this approach “parallel S-Ch switching” (PS-Ch) that is equivalent to the flex grid-single spatial switching [12, 28]. This networking approach provides capacity and network throughput, but it cannot explore the provided SDM opportunities related to resource allocation such as SAL variety. Thus, the spatial flexibility of this approach is limited at selecting spatial path, but it has the spectrum flexibility in each spatial path. Moreover, the uncoupled MCF can be used in this approach, but coupled MCFs and MMFs are not suitable. Consequently the crosstalk is not an issue in this networking approach. • FS2-Ch switching: The full flexible spatial-spectral switching for SDM network requires fine

Ygahubi-Namaad, et al./ ACCEPTED MANUSCRIPT

7

S-Ch3

S-Ch2 S-Ch5

S-Ch4

S-Ch9

S-Ch6

S2Ch8

S2-Ch1

S-Ch8

S-Ch7

a)

S2-Ch5

S2-Ch2

S-Ch10

M AN U

S-Ch1

SC

RI PT

granularities in both spectrum and space domains. In other words, based on connection demand’s possible SALs, the S2-Ch establishment could be performed in every set of spatial paths and every set of FSs. The full spatial-spectral flexible networking must be capable of switching each frequency slot of each spatial path to any determined route. This kind of networking only switches the allocated resource to each connection demand as shown in Fig. 1.b. We call this networking approach “free S2-Ch switching” (FS2-Ch), also called flex gridflex spatial [12] or independent switching [28, 31, 32] in the literature. Due to the severe crosstalk between modes for MMF, the separation of modes for switching seems not to be possible. Consequently, there is not any feasible switching solution based on MMF for this networking approach till now. However, two different switching structures are proposed in [27] that could be used for both SMF-bundle and MCF with little change. For MCF, it is necessary to use multi-core fiber breakout (Fan in/Fan out device) to divide the spatial paths of MCF and make them separated like the SMF bundle spatial paths connecting to a high-port cross-connect switch. After that one SSS for each spatial path is used to switch each connection demand in the spectral domain [27]. In FS2-Ch, the crosstalk exists if coupled MCFs are used, but can be controlled by guardbands and providing the spatial contiguity [39]. It can also be suppressed by MIMO as discussed in [46].

S-Ch11

S2-Ch6 S2Ch7

S2Ch3

b)

S2-Ch4

S2-Ch1

S2-Ch3 S2-Ch2

S2Ch4

S2-Ch1

c)

TE D

S2-Ch5

S2Ch6

S2Ch4

S2-Ch3

S2-Ch2

S2-Ch7 S2-Ch8

S2Ch9

d)

Fig. 1. Networking approaches: (a) PS-Ch switching (b) FS2-Ch switching (c) LS2-Ch switching (d) GLS2Ch switching.

EP

LS2-Ch switching: In multi-mode fibers, the same frequency slots of different spatial paths (modes) cannot be allocated to two connection demands because of existing extreme crosstalk between modes. Consequently, the use of MMF enforces to allocate FSs of every mode to only one S2-Ch. All the spatial paths are switched altogether only with spectrum granularity as one entity. This limitation of multi-mode fibers is the basis for another networking approach called “limited S2-Ch switching” (LS2-Ch) equivalent to the flex grid- fixed spatial [12] or joint switching [28], shown in Fig. 1.c. Then, the detection of all the spatial paths is performed coherently and with MIMO processing to reduce the crosstalk effect. Note that, the resource allocation of different connection demands could be performed with different width of spectrum for each S2-Ch. Therefore, this networking approach has only spectrum flexibility. The

AC C

•

Yaghubi-Namaad, et al. / ACCEPTED MANUSCRIPT

8

M AN U

SC

RI PT

separation of different modes in the switch is performed by devices known as photonic lantern [47]. Moreover, MCFs and SMF bundles can be used in this networking approach and switching concept. However, using multicore fibers with FS2-Ch switching provides more resource utilization and flexibility in contrast with LS2-Ch. • GLS2-Ch switching: Finally, the networking approach shown in Fig.1.d demonstrated the “group limited S2-Ch switching” (GLS2-Ch) founded on MC-MMF, also called fractional joint switching [28]. This approach is a special case of having groups of LS2-Ch switching. The switching solutions for GLS2-Ch and LS2-Ch switchings have been introduced in [27]. As mentioned, the designs with no crosstalk between cores are more appropriate for SDM-EON that confines the crosstalk just among the spatial paths of each core. Therefore, the crosstalk could be tackled like the MMFs. The SMF bundles and uncoupled MCFs could be used in networking approach, but coupled MCFs would not. To sum up, the use of MMF and MC-MMF is restricted to the LS2-ch and GLS2-Ch, respectively. Coupled MCFs should be used only in FS2-Ch or LS2-Ch. Finally, all the networking approaches could be implemented by SMF bundles or uncoupled MCFs. On the other hand, different switching solutions require different optical components, and different number of optical components leads to variable cost of switching nodes. The implementation of SDM switching is considered with different architectures in [27], and possible enabling technologies are surveyed in [47]. The details about required components, number of required SSS, and cost of switching nodes are discussed in [31, 32, 38, 48]. It is shown that the joint switching needs lesser SSS and could decrease the network cost. The summary of these networking approaches, the possible use of fibers, and required optical/electrical components are presented in the Table I. TABLE I Summary of networking approaches

Crosstalk management means

Fiber type

Flex grid-single spatial

SMF bundleuncoupled MCF

Spatial path selection flexibility

No crosstalk

SMF array/ MCF break- Parallel switches or Core continuity constraint ROADM

FS -Ch

Flex grid-flex spatial /Independent switching

SMF bundlecoupled/uncoupled MCF

Full flexibility (supports SAL variety)

Spatial contiguityspatial guardbandMIMO

High port cross-connect switch / high optical wiring - DSP

LS2-Ch

Flex grid-fixed spatial /Joint switching

SMF bundlecoupled/uncoupled MCF- MMF

No flexibility

Switching all the modes togetherMIMO

2-D SMF arrays combined by SSS, MMF-SSS, photonic lantern, DSP

GLS2-Ch

Fractional joint switching

SMF bundleuncoupled MCFMC-MMF

Fractional spatial flexibility (group selection)

Switching all the modes of one core together- MIMO

Same as LS2-Ch

PS-Ch

AC C

2

TE D

literature

Spatial flexibility

EP

Networking approach

Optical/electrical components

2.4. Comprehensive Resource allocation constraints After investigating network approaches and switching solutions, we determine the comprehensive

Ygahubi-Namaad, et al./ ACCEPTED MANUSCRIPT

9

AC C

EP

TE D

M AN U

SC

RI PT

constraints that should be satisfied in resource allocation of connection demands. As spectral view, the spectrum contiguity requires that a contiguous spectrum (frequency slots) is assigned to provide spectrum efficiency of overlapping subcarriers. Besides the spectrum continuity constraint guarantees that each S2-Ch is assigned the same spectrum over the route, and consequently, there is no need to spectrum conversion in switches. Moreover, two connection demands must not have overlapped frequency slots over the links. As spatial view, since the change of optical modes is hard to be performed, to make generality of SA-RMLSSA formulation to include MMF and MC-MMF, the space continuity constraint is considered to eliminate any spatial path change (equivalent to lane change [47]) along a route. This space continuity constraint could provide reduction of SSS ports, number of required SSS, and splitting loss of ROADMs as discussed in [37, 38]. Therefore, the space and spectrum continuity constraints guarantee that each connection demand is assigned the same spatial paths and the same spectrum over the route links. On the other hand, separating S2-Chs from each other –spectrally and spatially- is necessary to reduce energy coupling between S2-Chs along a route, which leads to more accurate detection. Therefore, the spectral guardband is used to spectrally separating of S2-Chs in the same spatial path for all networking approaches. The spatially separating of S2-Chs is carried out differently for each networking approach. Consequently, we discuss them separately and consider the comprehensive constraint to include all. For PS-Ch, considering to be implemented with SMF-bundle or uncoupled MCFs, spatially separation of S2-Chs is not required. As the LS2-Ch and GLS2-Ch forces to switch all the modes of MMFs and MC-MMFs as an entity, there is no spatially adjacent lightpaths in the same spectrum. Therefore, the spatially separated S2-Chs is one of the inside characteristics of PS-Ch, LS2-Ch and GLS2-Ch networking approaches. To do spatially separation of S2-Chs in FS2-Ch, first the space contiguity is considered. This ensures that each connection demand is allocated with spatially adjacent spatial paths (cores) to confine the energy of each lightpath. This spatial contiguity assumption helps MIMO processing to suppress accumulated crosstalk [14, 46] when it is applied to the entire set of coupled spatial paths. This spatial contiguity could be expanded to MMFs too, as there is energy coupling between all the modes, i.e., all the modes are adjacent. Then, when there is a spatial energy coupling, e.g., coupled MCFs, spatial guardband is enabled between S2-Chs with the same allocated spectrum on the same link. The spatial guardband is actually an extra unused spatial path (core) placed between two spatially adjacent S2-Chs which provides protection from direct energy coupling for both. It is noteworthy to mention that enabling spatial guardband has no conflict with allocating the spectrum of all the modes for MMFs as the remaining unused modes could be considered as guardbands. On the other hand, the use of spatial guardband for MCFs is voluntary, but using the spatial guardband (equivalent to not using the empty modes) is compulsory for MMFs. To sum up, a generic resource allocation formulation must satisfy the space and spectrum continuity that ensures the same spatial and spectral resources are allocated over the route links, and eliminates the need for spatial path change or spectrum conversion. Therefore, the path-based approach of formulation is chosen that provides space and spectrum contiguity without requiring any mathematical constraints. In addition, path-based approach reduces the decision variables of formulation, as decision variables are defined for entire optical route and not for each hop. Next, it must satisfy the spectrum contiguity and non-overlapping constraints. Then, if the spatial contiguity

Yaghubi-Namaad, et al. / ACCEPTED MANUSCRIPT

10

constraints are ensured in the formulation, it could improve the crosstalk suppression by MIMO as discussed in previous paragraph. Moreover, spatial contiguity can be used for all networking approaches. Finally, this generic formulation must be capable of enabling/disabling the spectrum and spatial guardbands as a way to manage crosstalk. On the other hand, the slice-based approach of formulation is chosen that provides scalability in contrast with channel-based approach. 3. SA- RMLSSA

RI PT

After determining the comprehensive constraints for networking approaches, a path-based slicebased formulation for the switching adaptable-routing, modulation level, space, and spectrum assignment problem is presented with generality to support all fiber types, switching solutions and networking approaches. First, the notations and proper sets are explained as needed for each networking approach. Then, decision variables and the SA-RMLSSA formulation are presented. 3.1. Notations

AC C

EP

TE D

M AN U

SC

A connected graph G = (V,E ) represents the network topology, where V is the set of nodes and E is the set of links. The number of nodes and links are denoted by |V| and |E|, respectively. As discussed, different types of spatial paths can be used in SDM networks. For generality of our formulation, let denote each spatial path by δi. To ensure space contiguity, it is important to denote the spatially adjacent spatial paths by consecutive indices, e.g., i-1, i, and i+1, especially for coupled MCFs, where adjacent cores have the most coupling factors against non-adjacent cores [18]. For SMF bundles and uncoupled MCFs, the indexing of cores could be performed in total arbitrary. Because, there will be no need to MIMO processing at the destination. For MMFs, even though, all the modes could be considered adjacent, but this indexing could be performed arbitrarily because all the modes must be switched together. For example, it is possible to consider transmission mode LP0,1 as δ0, LP1,1 as δ1, LP2,1 as δ2, and so on. The same indexing could be carried out for MC-MMF. For example, consider a MC-MMF with 3 cores and 3 modes in each core. Here, the modes in the first core could be indexed as explained like MMF as δ0, δ1, and δ2. Then, the second core modes are indexed from δ3 to δ5 similarly. Note that δ2 and δ3 have no coupling, but it is not an important issue as well as for uncoupled-MCFs. Accordingly, there is an ordered set of spatial paths on each link denoted by ∆={δ0,δ1,…, δθ-1}. Here, θ is the number of spatial paths and is an intrinsic property of network. Note that in the ring configuration of MCFs, the spatial paths δ0 and δθ-1 are adjacent. Also, spatial paths set ∆ differs based on types of spatial paths. For example, spatial paths set for MCF includes cores, but spatial paths set for MMF includes modes. For each spatial path, there is an ordered set F={f1, f2, … , fψ} of FSs. For static traffic, maximum number of FSs ψ must be set in a way to ensure no blocking of connection demands. Let D denote the set of connection demands as in (1), where each item of the set corresponds to a connection demand between a pair of network nodes. A triple (sd, td, Rd) determines connection demand d, where s d ∈V is the source node, t d ∈V is the destination node, and R d ∈ Z + is the data rate of the connection demand.

Ygahubi-Namaad, et al./ ACCEPTED MANUSCRIPT

D =

U

sd ,td ∈ V Rd ∈ Z +

11

d ( s d ,t d , R d ).

(1)

Πd =

RI PT

We assume that there are k pre-determined routes for each connection demand by using a shortest path algorithm. For each connection demand d ∈ D , the non-empty set of pre-determined candidate routes between sd and td is denoted by Πd as in (2). Let Π denote the set of all routes for every connection demand as defined in (3). Each route π ∈ Π can be specified with a subset E π ⊆ E . Accordingly, all the routes that go through link e could be determined by subset Ωe as in (4). π s t , d (s d , t d , R d ) ∈ D .

U ( s d ,t d )∈V

2

(2)

d d

Π = U Πd .

(3)

d ∈D

Ωe ={ π π ∈Π, e ∈Eπ } .

SC

(4)

For each connection demand d and candidate route π d ∈Πd , equation (5) determines the required number of FSs nd ,π , where Rd is the required data rate and Rfs is the FS base capacity. The frequency slot base capacity Rfs is specified according to the FS bandwidth if one bit per symbol modulation BPSK is used for each subcarrier without polarization division multiplexing (PDM). Note that increasing the FS capacity could be performed by increasing the modulation level (accordingly the bit per symbol rate), and could be doubled by using PDM. For example, the FS capacity is multiplied by 2 when the QPSK is used, and multiplied by 3 and by 4, if 8-QAM and 16QAM are used, respectively.

M AN U

d

TE D

 R  nd ,πd =  π d  M R ×  max fs  .

(5)

AC C

EP

π is the highest attainable modulation level that could achieve the optical signal to Parameter M max noise ratio (OSNR) margin to guarantee QoT for candidate route πd. The ceiling function provides more capacity for connection demands that their data rates are not an integer multiplier of FS capacity. The OSNR at the receiver side is generally depends on different linear PLIs, e.g., the attenuation and dispersion. Moreover, the accumulated crosstalk of SDM could affect ONSR for coupled MCFs and MMFs and decrease the OSNR like the other PLIs. Besides, the required OSNR margin for higher modulation level is higher to detect specified bit error rate. Consequently, higher modulation level, PLIs and crosstalk leads to shorter transmission reach. Studies are still ongoing to determine transmission reach in regard to the modulation level and other linear/nonlinear PLI’s of SDM fibers [49-54] especially based on Gaussian noise model. Since PLIs, accumulated crosstalk, and modulation level requirements are assumed to be a function of route length. Thus, the route length is considered the dominant factor of OSNR. Moreover, it is assumed that the suppression of other PLIs is possible by optical components along the route or electrical processing at the destination

Yaghubi-Namaad, et al. / ACCEPTED MANUSCRIPT

12

π node. Therefore, the value of M max depends on the route length and tolerable OSNR margin of specified bit error rate. Moreover, the highest level is considered in regard to the inverse relation of π nd ,π and M max in (5). Overall, after considering spatial guardbands to control crosstalk in MCFs, or similarly, allocating all the modes to one S2-Ch in MMFs, and space contiguity constraints to make π must the MIMO processing at the destination more efficient to suppress crosstalk, the value of M max ensure the required OSNR. Note that to ensure no blocking of all connection demands, the upper bound of ψ can be calculated as (6), where the BPSK modulation is considered for all the routes.

RI PT

d

ψ = ∑  R d R  . fs  d ∈D 

Let

Qd ,πd

(6)

be the possible SALs for required number of frequency slots nd ,π given by (7). d

Q d ,π = {( hq ,w q ) | n d ,π d = hq × w q , hq ,w q , n d ,π d ∈ Z , 1 ≤ hq ≤ h max ,

SC

d

.

(7)

M AN U

1 ≤w q ≤ψ }

Note that SAL determines how Rd and accordingly nd ,π FSs can be assigned through hq spatial paths with wq frequency slots width. Note that wq is bounded to maximum number of frequency slots ψ in each spatial path and hq is bounded to maximum number of spatial paths hmax which varies to each networking approach (see Table II). The value of hmax equals to 1 for PS-Ch, as each spectral channel is allocated thorough one spatial path, e.g., a fiber of SMF bundle or a core of uncoupled MCF. The value of hmax equals to the number of spatial paths θ for FS2-Ch and LS2-Ch. At last, hmax equals to the number of spatial paths in each group of GLS2-Ch. For example, if MCMMF with c cores and m modes in each core is used to implement the GLS2-Ch, we have hmax = m.

TE D

d

TABLE II Values of hmax and hqg for each networking approach

Networking approach PS-Ch

EP

FS2-Ch

AC C

LS2-Ch ( c=1 group of m=θ spatial paths) GLS2-Ch ( c group of m spatial paths)

hmax

hqg

1

1

θ

hqg = hq + gs   hqg = hq

θ

θ

m

m

hq < θ hq = θ

To illustrate SALs for each networking approach, consider a connection demand with four FSs request and three possible SALs. In the simplest way, especially used in PS-Ch, spectrum

Ygahubi-Namaad, et al./ ACCEPTED MANUSCRIPT

13

assignment can be carried out by hq=1 spatial path which includes wq=4 FSs. Similarly, spectrum assignment can be performed by selecting wq=1 FS in hq=4 spatial paths, suitable to use for LS2-Ch. Another spectrum assignment could be performed with hq=2 spatial paths and wq=2 FSs in each spatial path, suitable to use for GLS2-Ch. Note that each of these different SALs could be used for FS2-Ch. Enabling the spectral and spatial guardbands requires some changes to wq and hq. The required spectral guardband gw can be added easily to wq as (8).

w qg = w q + gw .

RI PT

(8)

d ,πd

d

M AN U

d ,πd

SC

The networking approaches LS2-Ch and GLS2-Ch require that all of the spatial paths (modes) are allocated to the same connection demand. Similarly, enabling spatial guardbands requires that one more spatial path is allocated to the connection demand. Accordingly, Table II summarizes the changes that should be carried out to hq based on the selected networking approach. For FS2-Ch switching, note that when hq=θ, all the spatial paths are assigned to one lightpath and there is no need to spatial guardband. The value of gs could be either 1 to enable spatial guardband for coupled MCFs, or 0 to eliminate spatial guardband for uncoupled MCFs. Finally, set Q%d ,π is created with new values hqg and wqg as in (9), especially and differently for each networking approach. Q% = {(hqg ,w qg ) | (hq ,w q ) ∈ Q } . (9)

3.2. The ILP formulation

Here, the SA-RMLSSA ILP formulation is presented to determine the minimum FS index that could serve all the connection demands without any blocking. This formulation tries to solve the network planning phase with static traffic matrix as input. Table III lists the required decision variables.

TE D

Decision variable

TABLE III Decision variables of the RMLSSA problem Description

Boolean variable, indicates whether route π is selected to route connection demand d.

βqπ ∈{0,1}

Boolean variable, indicates whether SAL q is selected from different SALs of route π to allocate connection demand d. If frequency slot f is selected from spatial path δ as the corner FS of the allocated spectrum for connection demand d along route π by SAL q, this equals to 1; otherwise, equals to 0. If frequency slot f is selected from spatial path δ to allocate the spectrums of connection demand d along route π by SAL q, this equals to 1; otherwise, equals to 0. Boolean variable indicates whether frequency slot f from spatial path δ is occupied on link e ∈ E .

χ δπ,,fq ∈{0,1} γ δπ,,fq ∈{0,1} ζ δe , f ∈{0,1}

Boolean variable indicates whether frequency slot f is occupied on at least one spatial path over the network.

AC C

οf ∈{0,1}

EP

απ ∈{0,1}

π To allocate the connection demand d, if route π is chosen ( α π = 1 ), the modulation level ( M max ) is specified and accordingly the number of FSs ( nd ,π ) will be calculated based on (5). Then, the d

Yaghubi-Namaad, et al. / ACCEPTED MANUSCRIPT

14

specified possible SAL q along the route (corresponding to β qπ = 1 ) determines the required number of spatial paths (hqg) and spectrum width (wqg) based on the networking approach. After that, the “corner FS” determines the starting point of performing spectrum assignment; accordingly, the corner FS has the minimum possible f which can carry out the SAL (corresponding to χ δπ ,,fq = 1 ). The corner FS and used decision variables are depicted in Fig. 2 in order to allocate a connection demand with nd ,π = 4 in a GLS2-Ch switching network. This network has c=2 cores and m=3 modes in each core and accordingly θ=6 spatial paths at all. Equation (7) leads to set 2 Qd ,π = {(1, 4) , ( 2, 2)} with two SALs considering hmax=3 according to Table II. Considering the GLS d

d

RI PT

Ch switching and spectral guardband gw=1, set Q%d ,π will be created as Q%d ,π = {( 3,5) , ( 3,3)} based on (8), (9), and at last according to Table II. Fig. 2.a. shows the occupation status for candidate route π regarding to the route’s links occupation status. The link occupation status of a given link determines the occupancy of frequency slots of each spatial path in the link. Assume that this route has three links and the shaded squares ζ δe , f shows that this shaded FS is allocated in at least one of the mentioned links for another connection demand. Two filled squares χ δπ ,,fq demonstrate the two possible corner FSs for SALs. In one of these cases, the corner FS specifies the SAL in which hqg=3 spatial paths and wqg=5 are needed. The other corner FS specifies the layout with hqg=3 and wqg=3. Based on each SAL, the occupied γ δπ ,,fq are shaded. Assume that the first mentioned SAL is chosen based on the SA-RMLSSA objective. According to this assumption, decision variable of will be updated as shown in Fig. 2.b. which shows the used FS indexes over the network. Since the corner FS selection procedure is performed over the entire route, the space and spectrum continuities are ensured without constraints in our formulation. d

TE D

M AN U

SC

d

Fig. 2. (a) Route dependent decision variables χ δπ ,,fq ,

γ δπ ,,fq

and

ζ δe , f

,

EP

(b) the network dependent decision variable of for SA-RMLSSA.

AC C

The SA-RMLSSA is formulated with objective function u as (10) to minimize the summation of total number of utilized FS indexes from set F subject to constraints (11)-(19). An FS index is considered to be utilized if it is assigned to at least one connection demand in the network. SA –RMLSSA minimize u = ∑ of , f ∈F

(10)

Ygahubi-Namaad, et al./ ACCEPTED MANUSCRIPT

subject to: ∑ απ =1

15

, ∀d ∈ D .

(11)

π ∈Π d

∑

q∈Q%d ,πd

βqπ = απ

∑∑

δ ∈∆ f ∈ F

,∀d ∈ D , ∀π ∈Πd .

(12)

χ δπ ,,fq = β qπ , ∀ d ∈ D , ∀ π ∈ Π d , ∀ q ∈ Q% d ,π d

(13) (14)

χ iπ, ,fq = 0 , ∀ d ∈ D , ∀ π ∈ Π d , ∀ q ∈ Q%d ,π d , ∀ f ∈ F , ∀ i ∈ ∆ ex

(15)

χ iπ, n,q − γ πj ,,mq ≤ 0, ∀d ∈ D , ∀π ∈ Π d , ∀q ∈ Q%d ,π d , ∀i ∈ I con , ∀j ∈ J con , ∀n ∈ N con , ∀m ∈ M con .

e

e ∈ E δ ∈∆ π

π

,f

− E .θ . o f ≤ 0 , ∀ f ∈ F

 α , βq ∈ {0,1} ,  π ,q π ,q  χδ , f , γ δ , f ∈ {0,1},  e ζ δ , f ∈ {0,1}  o f ∈ {0,1}

(18)

∀ π ∈ Π , ∀ q ∈ Q%d ,π d ∀ π ∈ Π , ∀ q ∈ Q%d ,π d , ∀ δ ∈ ∆, ∀ f ∈ F ∀ δ ∈ ∆ , ∀f ∈ F , ∀e ∈ E ∀f ∈ F

(17)

SC

∑ ∑ζδ

γ δπ,,fq = ζ δe ,f , ∀e ∈ E , ∀δ ∈ ∆, ∀ f ∈ F

(16)

M AN U

∑ ∑

π ∈Ωe q ∈Q%d ,π d

RI PT

χ δπ ,,nq = 0 , ∀ d ∈ D , ∀ π ∈ Π d , ∀ q ∈ Q%d ,π d , ∀ δ ∈ ∆ , ∀ n ∈ Fex

(19)

EP

AC C

,q ,f

TE D

The first constraint is the route selection constraint for each connection demand d ϵ D ensured by (11) in which one and only one route is selected from the candidate routes of set Πd. The best modulation scheme is specified for each route in order to provide required OSNR regarding to the route length and used fiber. After that, the SAL selection procedure is ensured by (12) that one and only one SAL is selected among the possible SALs for the chosen candidate route. Moreover, (12) ensures no SAL selection for other routes of connection demand d. For each connection demand d, the existence of a corner FS in the selected route according to the chosen SAL is ensured by (13) as the corner FS selection constraint. To exclude such corner FS selection which has not enough frequency slot width, Eq. (14) forces χ δπ to be zero for this case. According to the value of wqg, set Fex determines the set of frequency slots that could not be chosen as corner FS as stated in Table IV. On the other hand, excluding the corner FS selections which have not enough spatial paths could be carried out similarly in spatial domain by (15). According to the values of hqg, set ∆ex determines the set of spatial paths that could not be chosen as corner FS. However, set ∆ex varies based on the networking approach and summarized in Table IV. This exclusion is not necessary for PS-Ch, where each spatial path is utilized separately as S-Ch. On the other hand, for MCFs with ring configuration of cores in which the spatial paths δ0 and δθ-1 are adjacent, this exclusion is not proper because of rotational property of spatial paths. Thus, this constraint will be disabled for PS-Ch and MCFs with ring configuration. However, for MCFs with ribbon configuration or other configurations that can provide spatial independency of the δ0 and δθ-1, the exclusion must be carried out similar to Fex. Moreover, as stated above and in Table II, all the modes of each core must be allocated to one connection demand and accordingly, hqg equals the number of modes in each core for LS2-Ch and GLS2-Ch. Accordingly, the space and spectrum assignment of both must be performed in the first spatial path of each core

Yaghubi-Namaad, et al. / ACCEPTED MANUSCRIPT

16

SC

RI PT

and other spatial paths should be excluded. The space and spectrum contiguities of allocated spatial paths and frequency slots are ensured by (16). If there is frequency slot n, selected as the FS index of corner FS for connection demand d, then wqg consecutive FSs should be assigned to this connection demand too. To provide spectrum contiguity in SA-RMLSSA formulation, two sets Ncon and Mcon are used. The same constraints should be considered for assigning hqg contiguous spatial paths to the connection demand according to the networking approach. To provide space contiguity in SA-RMLSSA formulation, two sets Icon and Jcon are used (see Table IV). The PS-Ch does not need the space contiguity as hqg=1 for connection demands. For the FS2-Ch switching, implemented by MCFs in ribbon configuration, the space contiguity could be implemented as such as spectral contiguity displayed in (16) and sets Icon and Jcon are defined accordingly. However, for ring configuration of MCFs and considering the adjacency of δ0 and δθ-1 and so on, and also importantly by considering the disabling of constraint (15), the definition of sets Icon and Jcon should be in a way to provide rotary for indexed spatial paths. This rotation of space contiguity could be enabled by remainder of spatial paths index at module θ. Finally, considering the definition of hqg for the LS2-Ch switching and GLS2-Ch switching that leads to the allocation of SALs in the first mode of each core, sets Icon and Jcon must be in harmony with this decision.

All

M AN U

TABLE IV Sets Fex, ∆ex, Ncon, Mcon, Icon and Jcon for each networking approach Networking ∆ex, Icon and Jcon sets approach Fex = {f k ∈ F |ψ − w qg + 2 ≤ k ≤ ψ }

N con = {f k ∈ F |1 ≤ k ≤ ψ −w qg + 2}

M con = {f k ∈ F | n ≤ k ≤ n + w qg − 1, f n ∈ N con } ∆ex = ∅ PS-Ch

I con = {δ i ∈ ∆ | 0 ≤ i ≤ θ − 1}

J con = {δ j ∈ ∆ | j = i , δ i ∈ I con } FS2-Ch (ribbon configuration)

∆ ex = {δ k ∈ ∆ |θ − hqg + 1 ≤ k ≤ θ − 1} I con = {δ i ∈ ∆ | 0 ≤ i < θ − hqg + 1}

J con = {δ j ∈ ∆ | j = i , i + 1,...., i + hqg − 1, δ i ∈ I con }

TE D

∆ex = ∅

FS2-Ch (ring configuration)

I con = {δ i ∈ ∆ | 0 ≤ i ≤ θ − 1}

J con = {δ j ∈ ∆ | j ∆ex = {δ k ∈ ∆ | k

LS2-Ch

modθ

= i , i + 1,...., i + h

qg

− 1, δ i ∈ I con }

mod hmax

≠ 0}

I con = {δ i ∈ ∆ | i = 0}

EP

J con = {δ j ∈ ∆ | j = i , i + 1,...., i + hqg − 1, δ i ∈ I con } ∆ex = {δ k ∈ ∆ | k

AC C

GLS2-Ch

I con = {δ i ∈ ∆ | i

mod hmax

≠ 0}

mod h max

= 0}

J con = {δ j ∈ ∆ | j = i , i + 1,...., i + hqg − 1, δ i ∈ I con }

Constraint (17) guarantees the non-overlapping constraint of spectrum allocation over the links. Accordingly, considering the definition of ζ ce, f ∈ {0,1} ensures that each FS in spatial paths of the

Ygahubi-Namaad, et al./ ACCEPTED MANUSCRIPT

17

M AN U

SC

RI PT

network links should be assigned to at most one connection demand. Constraint (18) forces decision variable of to be 1 if frequency slot index f is used in at least one spatial path of the network links. Total number of FSs with the same index is equal to the number of links multiplied by the number of spatial paths in each link. If one FS with index f is used, (18) forces of to be 1. On the other hand, if frequency slot index f is not used at all, the objective function (i.e., (10)) forces of to be 0. Moreover, (10) counts total number of used FSs in the network to serve all connection demands. Finally, (19) shows the range of decision variables for SA-RMLSSA. Note that decision variables χ δπ ,,fq , γ δπ ,,fq and ζ δe , f form the majority of applied decision variables, of which, finding the maximum number is necessary. For each connection demand, variables χ δπ ,,fq or γ δπ ,,fq are defined for each route, each possible SAL, each spatial path, and each FS index. The number of possible SALs for each connection demand and accordingly its maximum value among all the connection demands cannot be determined specifically without knowing the traffic matrix. However, as possible SALs are defined based on hmax, the maximum number of SALs is hmax in the worst case scenario. Thus, the decision variables χ δπ ,,fq and γ δπ ,,fq have the maximum number of k×hmax×θ×ψ for each connection demand. Decision variable ζ δe , f is defined for each link, each spatial path, and each FS index; therefore, total number of ζ δe , f is |E|×θ×ψ. To sum up, the network’s characteristics as the number of links, the number of spatial paths, and the number of FS indexes determine the number of decision variables. Clearly, for large networks, the huge number of decision variables leads to solve the problem in a time consuming manner. 4. Heuristic algorithm for resource allocation

TE D

The proposed SA-RMLSSA is not practical for large networks because of huge required decision variables. Consequently, the heuristic algorithm design to find near optimal solution in a suitable time is encouraging. Since the effect of sorting policies on the stepwise greedy algorithm performance is investigated in our previous work [39]. we focus on the switching adaptability of heuristic algorithm alongside with reducing computational complexity. Therefore, we modify the proposed SGA to support all types of fibers and switching solutions. Accordingly, the switching adaptable resource allocation algorithm is proposed. 4.1. Switching adaptable resource allocation algorithm

AC C

EP

SARA serves ordered connection demands in sequence with the objective of achieving near optimal solution (see Algorithm I). In each iteration, SARA greedily tries to accommodate one connection demand in a way that the used FS index all over the network is minimum. Accordingly, SARA is executed in initialization phase with traffic matrix, pre-determined routes, and highest attainable modulation level for each route as inputs. Then, parameter nd ,π is determined based on (5), for each candidate route π of each connection π demand d according to M max . After that, different possible SALs to assign the required nd ,π FSs are investigated regarded to the networking approaches and set Q% is generated (see Lines 2-8). The d

d

d ,π d

sorting of connection demands is performed in Line 9, by two sorting policies: (1) descending FS

Yaghubi-Namaad, et al. / ACCEPTED MANUSCRIPT

18

number (DFN) that serves connection demands with large nd ,π first and (2) ascending SAL number (ASN) that serves connection demands with small SAL number first. These two policies have provided the best performance in [39]. At the end of initialization phase, links occupation status are initialized to be empty. The second phase of SARA, the resource allocation, receives sorted connection demands as input. The algorithm starts at the top of sorted list and finds the best solution of SALs for every candidate route (see Lines 11-15). To do so, the adaptive SAL selection for a networking approach (ASNA) algorithm is executed to determine the best SAL of each route which determines the relevant π π π parameters f max , δ max , h qgπ and w qg (see Algorithm II). Thus, ASNA chooses the best SAL for each route of a connection demand. Then, the candidate routes are compared with each other in Line 16. Accordingly, the algorithm decides which route with proper modulation level and which SAL must be chosen. After choosing the route and modulation level, the space and spectrum assignment of connection demand d is performed at the chosen route according to the chosen SAL from ASNA. Finally, the links occupation status of the route is updated (see Lines 17-19).

RI PT

d

SC

Algorithm I: Switching Adaptable Resource Allocation (SARA) Heuristic Algorithm for Specified Networking Approach Phase 1: Initialization Inputs: traffic matrix, predetermined candidate routes and M π 1 For a given traffic matrix and predetermined candidate routes, calculate the relevant parameters. 2 For each connection demand d 3 For each pre-candidate route πd 4 Calculate corresponding number of FSs n π to accommodate the connection demand according to the highest attainable modulation level M π 5 Investigate different possible SALs regarding to the networking approach and generate set Q%

M AN U

max

d,

d ,πd

6 7

End FOR Save nd ,π and

Q%d ,π

of each route.

d

max

TE D

d

d

8 9 10

AC C

EP

End FOR Sort the connection demands based on sorting policy. Initialize the links occupation status to be empty on every spatial paths and frequency slots Phase 2: resource allocation 11 While there is a connection demand d(sd, td, Rd) in the sorted connection demand set do 12 Select one connection demand from the top 13 For each candidate route π ∈Πd . 14 Find the relevant parameters f π , δ π , h π and w π with algorithm ASNA 15 End For 16 Set f = min{f π | ∀π ∈ Π } and determine the relevant parameters δ π , h π ,w π . 17 Assign the space and spectrum based on {f , δ , h ,w } 18 Update the links occupation status according for the chosen route’s links. d max

max

max

max

qg

qg

d

max

d max

d max

d qg

d qg

qg

qg

Ygahubi-Namaad, et al./ ACCEPTED MANUSCRIPT

19

19

End While

The ASNA algorithm tries to find the best SAL pursuant to the problem objective for each candidate route as detailed in the following (see Algorithm II). To add greedy manner to this algorithm, the first frequency fit policy is used to decrease the used frequency slot index in every step of SARA. In the FS2-Ch switching, using the route’s links occupation status, the ASNA finds the best “corner FS” for each SAL q from set Q% . The best corner FS is the one that could d ,π d

accommodate the examined SAL q with lower maximum FS index. Hence, each SAL leads to the π ,q π ,q π ,q , hqgπ ,q and w qg specified maximum FS index f max and relevant parameters δ max as shown in Fig. 2 (see

SC

RI PT

π π ,q π , hqgπ and Lines 1-5). Then, ASNA selects f max as the minimum f max of every SAL and determines δ max w qgπ in Line 6. For the PS-Ch, LS2-Ch, and GLS2-Ch switchings, because all of the SALs have the same hqg, this function selects the SAL with minimum wqg that provides the lowest increase for the used FS indexes. Then, ASNA finds the best corner FS based on the links occupation status. Finally, ASNA π π π , hqgπ and w qg determines parameter f max and determines the relevant parameters δmax (see Lines 8-12).

Algorithm II: Adaptive SAL selection for a Networking Approach (ASNA) Inputs: given route, route’s links occupation status and Q% d ,π d

2

If networking approach is FS -Ch For each SAL q from set Q%

3

Considering the first frequency fit policy, find the best corner FS based on links occupation status. π ,q Determine f max and the relevant parameters π ,q π ,q π δ max , hqg and w End For π π ,q = min{f max | ∀q ∈Q%d ,π } and determine the Select f max π , hqgπ and w π relevant parameters δmax End If If networking approach is PS-Ch, LS2-Ch, or GLS2-Ch The SAL with minimum wqg is selected. According to the first frequency fit policy, find the best corner FS based on links occupation status. π Determine f max and the relevant parameters π π π δ max , hqg and w End If

M AN U

1 2

d ,π d

4

,q qg

5 6

d

qg

TE D

7 8 9 10

EP

11

qg

12

AC C

4.2. Complexity analysis

The computational complexity for SARA is equal to O(| D | ×k × O( ASNA) | and varies based on the networking approach. The number of connection demands is |D|. The computational complexity of

Yaghubi-Namaad, et al. / ACCEPTED MANUSCRIPT

20

ASNA, in the FS2-Ch switching is bounded by O (hmax × θ ×ψ × | E |) . Recall that the number of SALs for each route is less than hmax and its variety depends on the connection demands. Note that θ ×ψ × | E | corresponds to the worst case complexity of finding the corner FS to allocate the connection demand over the route’s links. For the PS-Ch, LS2-Ch, and GLS2-Ch switchings, the computational complexity of ASNA is bounded by O (θ ×ψ × | E |) . Consequently, these networking approaches have less complexity than FS2Ch because first the best SAL is decided and then the corner FS finding is performed.

RI PT

5. Performance evaluation

sumof required FS . MUFSI ×θ× | E |

TE D

DUR =

M AN U

SC

In this section, the performance of the proposed ILP and heuristic algorithm with two different sorting policies (i.e. ASN and DFN) are investigated through static and dynamic experiments for all networking approaches. The implementation of the SA-RMLSAA is performed by IBM ILOG CPLEX. The implementation of SARA is carried out by Matlab for static traffic and by OPNET for dynamic traffic. The Maximum utilized frequency slot index (MUFSI) is the minimum FS number that could serve all the connection demands without any blocking. The optimal value of MUFSI will be determined by SA-RMLSSA, but SARA leads to a near-optimal value of MUFSI. This optimal and nearoptimal MUFSIs, and difference between them –known as optimality gap- are used as the metric to show how accurately a heuristic algorithm tends to find near-optimal solution for each networking approach. Moreover, to investigate the networking approaches’ performance, another metric called demand utilization ratio (DUR) is used. The DUR is defined in (20) as the all connection demands’ required FSs (when BPSK modulation is used) proportional to all available spectral resources in regard to the MUFSI. Therefore, the DUR determines that how a networking approach utilizes the available spectral resource in all spatial paths of links to allocate the normalized traffic matrix. Finally, bandwidth blocking rate (BBR) is used to investigate the network performance in the dynamic scenario. (20)

AC C

EP

The fiber with three cores and three modes in each core is considered for GLS2-Ch networking approach. The MMF with ten modes is used to implement the LS2-Ch. For PS-Ch, the 12-SMF bundle is considered. Finally, the MCF with twelve cores is considered to implement FS2-Ch in both ring and ribbon configurations. The fibers are chosen to have spatial path numbers near to each other and based on available commercial fibers [16, 19]. Even though, the value of ψ must be calculated according to (6), but to reduce the space dimension of problem, we considered ψ=384 as actual number of 12.5 GHz FSs in 4.8 THz C-band. Then, k=3 pre-determined routes are considered along the network for each source-destination pair. Because of spatial diversity, the more number of spatial paths brings more capacity available. Therefore, increasing the number of spatial paths leads to reduction of MUFSI, while traffic matrix is fixed. Moreover, it is obvious for a fixed number of spatial paths that increasing the traffic load needs more MUFSI. Thus, we use normalized traffic in both static and dynamic evaluations in regard to the number of spatial paths to make the simulations more realistic. This normalization is

Ygahubi-Namaad, et al./ ACCEPTED MANUSCRIPT

21

carried out to the interval of data rates in the static scenario. For static traffic, traffic matrices are generated for each possible pair of network nodes as even integer number of FSs in interval [nfmin, nfmax] with uniform distribution and average equal to nf ave = ( nf max − nf min ) / 2 . Accordingly, each

SC

RI PT

traffic matrix has (| V | −1)2 non-zero entities. Choosing the different values for nfmin and nfmax represents different network traffic loads. Accordingly, the minimum and maximum data rate of connection demands are between [nfmin×Rfs, nfmax× Rfs], and each traffic matrix supports total traffic 2 equal to T =(| V | −1) ×nfave × Rfs in average, where Rfs is the base frequency slot capacity as defined in Section 3.1. Note that each traffic matrix is created for GLS2-Ch (9 spatial paths) for all possible pair of nodes. Then, this traffic matrix is scaled up based on spatial paths proportion for the networking approach under study. Moreover, the normalized load per spatial path and normalized interval of connection demands are used for dynamic traffic. For example, normalized 100 Erlang traffic load for GLS2-Ch means 900 Erlang, and accordingly means 1200 Erlang for FS2-Ch. Moreover, the connection demand FS request has the uniform distribution between [3, 13] per spatial path. Therefore, the connection demands of LS2-Ch has the FS request between [30, 130] according to the 10-mode used MMF. 5.1. Small network experiment

TE D

M AN U

To investigate SARA’s capability to achieve near-optimal solution of the SA-RMLSSA problem, the small network with six nodes and nine bidirectional links is considered as shown in Fig. 3.a. The results for small network, for two different traffic loads considering four different network approach are obtained. The modulation adaptivity for this network is considered based on the number of hops and same for all networking approaches to eliminate fiber PLI’s influence. The parameters of simulations, i.e., the value of guardbands are summarized in Table V.

1

3

2

EP

4

5

a) b) Fig. 3. (a) Small network with six nodes and nine bidirectional links. (b) European Cost239 network. Numbers shows the length in km.

AC C

6

Yaghubi-Namaad, et al. / ACCEPTED MANUSCRIPT

22

TABLE V. SIMULATION PARAMETERS AND THEIR VALUES FOR SMALL NETWORK

Networking approach No. of Spatial path hmax Traffic load low high Modulation level

LS2-Ch PS-Ch FS2-Ch 10 12 12 10 1 12 [22,44] [26,54] [26,54] [44,60] [54,8]) [54,82] No. of Hops 1 2 3 4 2 1 spectral gw=1 spatial gs=1

RI PT

Guardband

GLS2-Ch 9 3 [20,40] [40,60]

EP

b) Fig. 4. The MUFSI of networking approaches in small network under (a) low load and (b) high load.

AC C

a)

TE D

M AN U

SC

The MUFSI of SARA and SA-RMLSSA and the optimality gaps between them are shown respectively in Fig. 4 and Fig. 5 for different networking approaches. The results are averaged over 50 different randomly created traffic matrices with 95% confidence interval, with less than 5% error for each displayed point of diagram. The results shows the ability of SARA to find near optimal solution. The ASN policy tends to prepare better near-optimal solution for each networking approach for both low and high traffic.

Ygahubi-Namaad, et al./ ACCEPTED MANUSCRIPT

RI PT

23

a) b) Fig. 5. The optimality gap of networking approaches in small network under (a) low load and (b) high load.

AC C

EP

TE D

M AN U

SC

From another viewpoint, the PS-Ch needs more spectral resource to support the same normalized traffic load. The lack of flexibility for SAL in PS-Ch leads to have more MUFSI which is increased as the connection demand size arises. However, the optimality gap is zero for PS-Ch. The LS2-Ch shows the next most MUFSI because of more resource wastage. The resource wastage could be because of spectral and spatial guardbands or because of allocation of all the modes to only one connection demand even when that connection demand is not going to use all the modes. Moreover, the optimality gap between the algorithm solution and optimal solution for this networking approach is the most, i.e., around 6 frequency slots with DFN for low traffic load. As Fig.4 and Fig. 5 shows, the use of spatial guardband for FS2-Ch has a little influence on the MUFSI for the ASN policy. But, the spatial guardband affects the MUFSI of DFN policy and leads to approximately one more FS for low-load and two more FSs for high load in contrast with when spatial guardband is not used. Consequently, it can be concluded that spatial guardband provides crosstalk management without penalty on the MUFSI. Note that for the small network experiment, the results for FS2-Ch in either ring or ribbon configurations are approximately the same. Accordingly, only the results of ring configuration are shown in Fig.4 and Fig. 5. Finally, the GLS2-Ch achieves the least MUFSI among all networking approaches. Note that even FS2-Ch has more flexibility in choosing the best SAL for allocating connection demands, GLS2-Ch obtains the least MUFSI. Having more MUFSI of FS2-Ch, in contrast with GLS2-Ch, is outcome of the need to use more spectral guardband for S2Chs regarded to more spatial paths. This wastage of resources and having higher connection demands leads to more MUFSI of FS2-Ch in Fig. 4. However, under the realistic network experiment in Section 5.2., when the fiber PLI’s effect is considered, the FS2-Ch obtains the least MUFSI. Moreover, both the ASN and DFN of SARA tend to achieve near optimal solution accurately with small optimality gap in GLS2-Ch. Fig.6 shows the demand utilization ratio of each networking approach achieved from each sorting policy. It demonstrates that DFN utilizes the same demands in a worst manner in contrast with ASN. When traffic load is high, the better DUR can be achieved. For both policies, PS-Ch has the worst and GLS2-Ch has the best performance of allocating connection demands with a smaller

Yaghubi-Namaad, et al. / ACCEPTED MANUSCRIPT

24

RI PT

spectral resources.

SC

a) b) Fig. 6. The DUR of networking approaches in small network under different loads with (a) ASN policy and (b) DFN policy.

M AN U

Table VI shows the running times of SARA and ILP solver when a computer with an Intel Xeon E5, 2.20 GHz CPU and 32 GB RAM is used to carry out simulations. The average running time of heuristic algorithm is at most 0.464 seconds for different traffic loads. The ILP solver has much higher running time which is around few thousand seconds for different networking approaches. Table VI shows the best case and the worst case of running time for the heuristic algorithm and ILP, too. Even the best case of the ILP solver has much higher running time than the worst case of heuristic algorithm. TABLE VI.

RUNNING TIME (IN SECONDS)

Traffic

high

EP

5.2. Realistic network experiment

ASN DFN ILP ASN DFN ILP

average

0.334 0.322 4032 0.464 0.402 5472

TE D

low

algorithm

min

0.039 0.039 643 0.035 0.035 812

max

0.972 0.992 186624 1.723 1.474 235782

AC C

To have more realistic assumptions about the modulation adaptivity regarded to the routes length, the COST239 network (see Fig. 3.b.) is simulated. The results are averaged over 30 randomly generated traffic matrices. The number of spatial paths for each networking approach is the same as the small network experiment. The transmission reach versus different spectral granularities has been carried out in [31] for SMF bundles. But they did not take into account the energy coupling of modes for MMFs and inter-core crosstalk for MCFs. The inter-core crosstalk effect for PS-Ch is investigated in [38] that showed smaller transmission reach is attainable in contrast with the work

Ygahubi-Namaad, et al./ ACCEPTED MANUSCRIPT

25

performed in [31]. For MMFs, the Gaussian noise model is used to model nonlinear PLIs in [53] without networking considerations. But to the best of our knowledge, till now there is no work to model OSNR coupled MCFs in FS2-Chs. Considering all works performed in this subject, we use the modulation adaptivity according to the route length summarized in Table VII for networking approaches. The spectral guardband wg=2 and spatial guardband sg= 1 is considered for FS2-Ch. The FS requests of connection demands are generated uniformly based on the normalized traffic load (ρ) interval used differently for each networking approach as [ρ×2×θ, (ρ+1)×2×θ]. TABLE VII Networking approach

l<500

500
1000
l>2000

6 4 8 8

4 2 6 6

2 1 4 4

1 1 2 2

Traffic load interval 18 20 24 24

SC

GLS2-Ch LS2-Ch PS-Ch FS2-Ch

Route length l (km)

RI PT

SIMULATION PARAMETERS AND THEIR VALUES FOR REALISTIC NETWORK

AC C

EP

TE D

M AN U

Fig. 7 shows the MUFSI of each networking approach for each sorting policy of the heuristic algorithm versus normalized load that determines different traffic loads of network. Like before, the ASN achieves lower values of MUFSI than DFN. When traffic load increases, the value of MUFSI for each networking approach arises. The networking approaches forced to allocate all the modes to one connection demand and to use lower modulation level for the same route length (such as LS2Ch and GLS2-Ch) would achieve higher values of MUFSI. Accordingly, the LS2-Ch switching requires the most and the GLS2-Ch has the second high value for MUFSI (unlike the small network experiment). The ASN sorting policy of SARA obtains the near MUFSI values for PS-Ch and FS2Ch (with or without spatial guardband) with a difference around one FS at most. It shows that the modulation level plays an important role for networking approaches. Note that FS2-Ch with ribbon and ring configurations have obtained approximately the same results in both policies (with maximum difference of 0.3 FS). Consequently, the results are only abstracted to FS2-Ch ring configuration with sg=1 and FS2-Ch ribbon configuration with sg=0 to prevent confusion in Fig. 7. The effect of spatial guardband is clearer in DFN where using the spatial guardband leads to more MUFSI for the FS2-Ch with ring configuration. Recall the performance of heuristic algorithm based on each sorting policy depends on the network topology, connectivity degrees of nodes, number of spatial paths, traffic load, and used modulation adaptivity.

Yaghubi-Namaad, et al. / ACCEPTED MANUSCRIPT

RI PT

26

a) b) Fig. 7. The MUFSI of networking approaches versus normalized load in COST239 with (a) ASN, (b) DFN

a)

EP

TE D

M AN U

SC

The demand utilization ratios of networking approaches are shown in Fig. 8 for each sorting policy. The ASN policy achieves more DUR than DFN for all networking approaches except PS-Ch that has the same DUR. Fig. 8 illustrates the effect of resource wastage in the performance of each networking approach. Consequently, LS2-Ch and GLS2-Ch enhance the lower value of DUR. Since the number of unused modes could be more for LS2-Ch, it has the lowest DUR. The guardband wastage effect is obvious in the DFN sorting policy, in which, using the spatial guardband for FS2Ch ring configuration reduces the DUR compared with the FS2-Ch ribbon configuration. However, the spatial guardband effect could be compensated if the influence of SAL flexibility is considered for sorting connection demands as achieved for the ASN policy.

b) Fig. 8. The DUR of networking approaches versus normalized load in COST239 with (a) ASN, (b) DFN.

AC C

5.3. Dynamic traffic experiment

To investigate the effect of resource wastage, networking approaches, and configuration of cores for FS2-Ch, the SARA’s performance is studied for dynamic traffic by the OPNET simulator. The SARA’s resource allocation phase is used as a dynamic heuristic RMLSSA algorithm. The holding

Ygahubi-Namaad, et al./ ACCEPTED MANUSCRIPT

27

M AN U

SC

RI PT

time of each connection demand has a uniform distribution between [1, 11] seconds. The interarrival time of connection demands follows the exponential distribution. Moreover, traffic of each networking approach is normalized based on the number of spatial paths. Figure 9 shows the bandwidth blocking rate of each networking approach versus the normalized load per core. The LS2-Ch shows the worst performance because of resource wastage. Accordingly, PS-Ch depicts the least BBR because of using only spectral guardband. However, implementation of PS-Ch requires the SMF bundles or MCFs without any coupling between cores. The spatial guardband effect is more observable in dynamic traffic, where FS2-Ch with spatial guardband leads to more BBR even more than GLS2-Ch. Interestingly, the ring configuration of FS2-Ch shows slightly more BBR than its ribbon configuration.

Fig. 9. BBR versus normalized load per core in COST239.

6. Conclusion

TE D

Therefore, the simulation results altogether indicate that (1) for static traffic, the connection demands requirement, network topology, and connectivity have the most effect on the MUFSI (e.g., the performance of PS-Ch), (2) the modulation adaptivity requirement (regarded to the required OSNR) affects the MUFSI and DUR in network planning phase intensively (e.g., compare the performance of GLS2-Ch in two experiments), (3) resource wastage plays an important role in both static and dynamic traffic performance, especially for multimode fibers, (4) the ring or ribbon configuration of cores in the FS2-Ch networking approach shows approximately the same performance for the static and dynamic experiments.

AC C

EP

We have resolved the switching adaptable routing, modulation level, space, and spectrum assignment (SA-RMLSSA) problem with different networking approaches defined based on fiber type and switching solutions for SDM-EON. We have discussed the forced constraints from networking approaches to the resource allocation and translate them to all inclusive ones. Based on these comprehensive constraints, generic SA-RMLSSA ILP formulation has been presented with generality to support all SDM fibers, switching solution, and networking approaches to provision all connection demands. Moreover, SARA has been introduced as a heuristic algorithm for resource allocation of large and complex networks with a feasible complexity. We have investigated the

Yaghubi-Namaad, et al. / ACCEPTED MANUSCRIPT

28

SARA performance to achieve near-optimal solution of different networking approaches for static traffic. For realistic network experiment, we have also investigated the effect of each networking approach, fiber-specified modulation adaptivity, cores configurations and spatial guardbands necessity for MCFs through simulations for both static and dynamic traffic. References

[6] [7] [8]

[9]

[10]

[11] [12]

[13]

[14]

[15]

RI PT

SC

[5]

M AN U

[4]

TE D

[3]

EP

[2]

M. Jinno, H. Takara, B. Kozicki, Y. Tsukishima, Y. Sone, and S. Matsuoka, "Spectrum-efficient and scalable elastic optical path network: architecture, benefits, and enabling technologies," IEEE Communications Magazine, vol. 47, 2009. O. Gerstel, M. Jinno, A. Lord, and S. B. Yoo, "Elastic optical networking: A new dawn for the optical layer?," IEEE Communications Magazine, vol. 50, 2012. M. Jinno, "Elastic Optical Networking: Roles and Benefits in Beyond 100-Gb/s Era," Journal of Lightwave Technology, vol. 35, pp. 1116-1124, 2017. G. Zhang, M. De Leenheer, A. Morea, and B. Mukherjee, "A survey on OFDM-based elastic core optical networking," IEEE Communications Surveys & Tutorials, vol. 15, pp. 65-87, 2013. M. Jinno, B. Kozicki, H. Takara, A. Watanabe, Y. Sone, T. Tanaka, and A. Hirano, "Distanceadaptive spectrum resource allocation in spectrum-sliced elastic optical path network " IEEE Communications Magazine, vol. 48, 2010. W. Shieh, H. Bao, and Y. Tang, "Coherent optical OFDM: theory and design," Optics express, vol. 16, pp. 841-859, 2008. W. Shieh, "OFDM for flexible high-speed optical networks," journal of lightwave technology, vol. 29, pp. 1560-1577, 2011. S. Frisken, G. Baxter, D. Abakoumov, H. Zhou, I. Clarke, and S. Poole, "Flexible and grid-less wavelength selective switch using LCOS technology," in Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011 and the National Fiber Optic Engineers Conference, 2011, pp. 1-3. H. Beyranvand and J. A. Salehi, "A quality-of-transmission aware dynamic routing and spectrum assignment scheme for future elastic optical networks," Journal of Lightwave Technology, vol. 31, pp. 3043-3054, 2013. M. Koubàa, M. Bakri, A. Bouallègue, and M. Gagnaire, "QoT-aware elastic bandwidth allocation and spare capacity assignment in flexible island-based optical transport networks under shared risk link group constraints," Computer Networks, vol. 116, pp. 111-140, 2017. T. J. Xia, H. Fevrier, T. Wang, and T. Morioka, "Introduction of spectrally and spatially flexible optical networks," IEEE Communications Magazine, vol. 53, pp. 24-33, 2015. D. Klonidis, F. Cugini, O. Gerstel, M. Jinno,V. Lopez, E. Palkopoulou, M. Sekiya, D. Siracusa, G. Thouénon, and C. Betoule, "Spectrally and spatially flexible optical network planning and operations," IEEE Communications Magazine, vol. 53, pp. 69-78, 2015. W. Klaus, B. J. Puttnam, R. Luis, J. Sakaguchi, J. Mendinueta, Y. Awaji and N.Wada, "Advanced space division multiplexing technologies for optical networks," Journal of Optical Communications and Networking, vol. 9, pp. C1-C11, 2017. G. M. Saridis, D. Alexandropoulos, G. Zervas, and D. Simeonidou, "Survey and evaluation of space division multiplexing: From technologies to optical networks," IEEE Communications Surveys & Tutorials, vol. 17, pp. 2136-2156, 2015. M. Klinkowski, P. Lechowicz, and K. Walkowiak, "Survey of resource allocation schemes and algorithms in spectrally-spatially flexible optical networking," Optical Switching and Networking, 2017.

AC C

[1]

Ygahubi-Namaad, et al./ ACCEPTED MANUSCRIPT

[22] [23]

[24]

[25] [26] [27] [28]

[29]

[30]

[31]

[32]

RI PT

[21]

SC

[20]

M AN U

[19]

TE D

[18]

EP

[17]

K. Nakajima, P. Sillard, D. Richardson, M.-J. Li, R.-J. Essiambre, and S. Matsuo, "Transmission media for an SDM-based optical communication system," IEEE Communications Magazine, vol. 53, pp. 44-51, 2015. J. H. Chang, S. Bae, H. Kim, and Y. C. Chung, "Heterogeneous 12-Core 4-LP-Mode Fiber Based on Trench-Assisted Graded-Index Profile," IEEE Photonics Journal, vol. 9, pp. 1-10, 2017. T. Mizuno and Y. Miyamoto, "High-capacity dense space division multiplexing transmission," Optical Fiber Technology, vol. 35, pp. 108-117, 2017. T. Mizuno, K. Shibahara, F. Ye, Y. Sasaki, Y. Amma, K. Takenaga, Y. Jung, K. Pulverer,H Ono, Y. Abe, and M. Yamada, "Long-Haul Dense Space-Division Multiplexed Transmission Over LowCrosstalk Heterogeneous 32-Core Transmission Line Using a Partial Recirculating Loop System," Journal of Lightwave Technology, vol. 35, pp. 488-498, 2017. S. Talebi, F. Alam, I. Katib, M. Khamis, R. Salama, and G. N. Rouskas, "Spectrum management techniques for elastic optical networks: A survey," Optical Switching and Networking, vol. 13, pp. 34-48, 2014. F. S. Abkenar and A. G. Rahbar, "Study and analysis of routing and spectrum allocation (RSA) and routing, modulation and spectrum allocation (RMSA) algorithms in elastic optical networks (EONs)," Optical Switching and Networking, vol. 23, pp. 5-39, 2017. R. W. Alaskar, I. Ahmad, and A. Alyatama, "Offline routing and spectrum allocation algorithms for elastic optical networks," Optical Switching and Networking, vol. 21, pp. 79-92, 2016. K. Walkowiak, M. Klinkowski, B. Rabiega, and R. Goścień, "Routing and spectrum allocation algorithms for elastic optical networks with dedicated path protection," Optical Switching and Networking, vol. 13, pp. 63-75, 2014. A. Pagès, J. Perelló, S. Spadaro, and G. Junyent, "Split spectrum-enabled route and spectrum assignment in elastic optical networks," Optical Switching and Networking, vol. 13, pp. 148-157, 2014. K. Christodoulopoulos, I. Tomkos, and E. Varvarigos, "Elastic bandwidth allocation in flexible OFDM-based optical networks," Journal of Lightwave Technology, vol. 29, pp. 1354-1366, 2011. M. Klinkowski and K. Walkowiak, "Routing and spectrum assignment in spectrum sliced elastic optical path network," IEEE Communications Letters, vol. 15, pp. 884-886, 2011. D. M. Marom and M. Blau, "Switching solutions for WDM-SDM optical networks," IEEE Communications Magazine, vol. 53, pp. 60-68, 2015. D. Siracusa, F. Pederzolli, D. Klonidisz, V. Lopezy, and E. Salvadori, "Resource allocation policies in SDM optical networks," in Optical Network Design and Modeling (ONDM), 2015 International Conference on, 2015, pp. 168-173. B. Shariati, P. S. Khodashenas, J. M. Rivas-Moscoso, S. Ben-Ezra, D. Klonidis, F. Jiménez, L. Velasco, and I. Tomkos, "Evaluation of the impact of different SDM switching strategies in a network planning scenario," in Optical Fiber Communications Conference and Exhibition (OFC), 2016, 2016, pp. 1-3. D. Siracusa, F. Pederzolli, P. Khodashenas, J. Rivas-Moscoso, D. Klonidis, E. Salvadori, and I. Tomkos, "Spectral vs. spatial super-channel allocation in SDM networks under independent and joint switching paradigms," in Optical Communication (ECOC), 2015 European Conference on, 2015, pp. 1-3. P. S. Khodashenas, J. M. Rivas-Moscoso, D. Siracusa, F. Pederzolli, B. Shariati, D. Klonidis, E. Salvadori, and I. Tomkos, "Comparison of spectral and spatial super-channel allocation schemes for SDM networks," Journal of Lightwave Technology, vol. 34, pp. 2710-2716, 2016. B. Shariati, J. M. Rivas-Moscoso, D. M. Marom, S. Ben-Ezra, D. Klonidis, L. Velasco, and I. Tomkos, "Impact of spatial and spectral granularity on the performance of SDM networks based on spatial superchannel switching," Journal of Lightwave Technology, vol. 35, pp. 2559-2568, 2017.

AC C

[16]

29

Yaghubi-Namaad, et al. / ACCEPTED MANUSCRIPT

30

[39]

[40]

[41]

[42] [43] [44]

[45]

[46]

[47]

RI PT

[38]

SC

[37]

M AN U

[36]

TE D

[35]

EP

[34]

B. Shariati, D. Klonidis, D. Siracusa, F. Pederzolli, J. Rivas-Moscoso, L. Velasco, and I. Tomkos, "Impact of traffic profile on the performance of spatial superchannel switching in SDM networks," in ECOC 2016; 42nd European Conference on Optical Communication; Proceedings of, 2016, pp. 1-3. F. Pederzolli, D. Siracusa, J. M. Rivas-Moscoso, B. Shariati, E. Salvadori, and I. Tomkos, "Spatial group sharing for SDM optical networks with joint switching," in Optical Network Design and Modeling (ONDM), 2016 International Conference on, 2016, pp. 1-6. F. Pederzolli, D. Siracusa, B. Shariati, J. M. Rivas-Moscoso, E. Salvadori, and I. Tomkos, "Improving performance of spatially joint-switched space division multiplexing optical networks via spatial group sharing," IEEE/OSA Journal of Optical Communications and Networking, vol. 9, pp. B1-B11, 2017. A. Muhammad, G. Zervas, D. Simeonidou, and R. Forchheimer, "Routing, spectrum and core allocation in flexgrid SDM networks with multi-core fibers," in Optical Network Design and Modeling, 2014 International Conference on, 2014, pp. 192-197. R. Rumipamba-Zambrano, F. Moreno-Muro, P. Pavón-Marino, J. Perelló, S. Spadaro, and J. SoléPareta, "Assessment of flex-grid/MCF optical networks with ROADM limited core switching capability," in Optical Network Design and Modeling (ONDM), 2017 International Conference on, 2017, pp. 1-6. F.-J. Moreno-Muro, R. Rumipamba-Zambrano, P. Pavón-Marino, J. Perelló, J. Gené, and S. Spadaro, "Evaluation of core-continuity-constrained ROADMs for flex-grid/MCF optical networks," Journal of Optical Communications and Networking, vol. 9, pp. 1041-1050, 2017. M. Yaghubi-Namaad, A. G. Rahbar, and B. Alizadeh, "Adaptive Modulation and Flexible Resource Allocation in Space-Division-Multiplexed Elastic Optical Networks," Journal of Optical Communications and Networking, vol. 10, pp. 240-251, 2018. K. Walkowiak, P. Lechowicz, M. Klinkowski, and A. Sen, "ILP modeling of flexgrid SDM optical networks," in Telecommunications Network Strategy and Planning Symposium (Networks), 2016 17th International, 2016, pp. 121-126. P. Lechowicz, K. Walkowiak, and M. Klinkowski, "Selection of spectral-spatial channels in SDM flexgrid optical networks," in Optical Network Design and Modeling (ONDM), 2017 International Conference on, 2017, pp. 1-6. P. Lechowicz, K. Walkowiak, and M. Klinkowski, "Spectrum usage for various SDM scenarios," in Transparent Optical Networks (ICTON), 2017 19th International Conference on, 2017, pp. 1-4. S. Chandrasekhar and X. Liu, "OFDM based superchannel transmission technology," Journal of lightwave technology, vol. 30, pp. 3816-3823, 2012. L. Nelson, M. Feuer, K. Abedin, X. Zhou, T. Taunay, J. Fini, B. Zhu, R. Isaac, R. Harel, G. Cohen, and D. Marom, "Spatial superchannel routing in a two-span ROADM system for space division multiplexing," Journal of Lightwave Technology, vol. 32, pp. 783-789, 2014. S. Fujii, Y. Hirota, H. Tode, and K. Murakami, "On-demand spectrum and core allocation for reducing crosstalk in multicore fibers in elastic optical networks," Journal of Optical Communications and Networking, vol. 6, pp. 1059-1071, 2014. R. Ryf, R. Essiambre, S. Randel, A. Gnauck, P. Winzer, T. Hayashi, T. Taru, and T. Sasaki, "MIMOBased Crosstalk Suppression in Spatially Multiplexed 3×56-Gb/s PDM-QPSK Signals for Strongly Coupled Three-Core Fiber," IEEE Photonics Technology Letters, vol. 23, pp. 1469-1471, 2011. D. M. Marom, P. D. Colbourne, A. D’errico, N. K. Fontaine, Y. Ikuma, R. Proietti, L. Zong, J. Rivas-Moscoso, and I. Tomkos, "Survey of photonic switching architectures and technologies in support of spatially and spectrally flexible optical networking," Journal of Optical Communications and Networking, vol. 9, pp. 1-26, 2017.

AC C

[33]

Ygahubi-Namaad, et al./ ACCEPTED MANUSCRIPT

[54]

RI PT

[53]

SC

[52]

M AN U

[51]

TE D

[50]

EP

[49]

A. Muhammad, G. Zervas, and R. Forchheimer, "Resource allocation for space-division multiplexing: optical white box versus optical black box networking," Journal of Lightwave Technology, vol. 33, pp. 4928-4941, 2015. A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, "Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links," Journal of Lightwave Technology, vol. 30, pp. 1524-1539, 2012. R. Pastorelli, G. Bosco, S. Piciaccia, and F. Forghieri, "Network planning strategies for nextgeneration flexible optical networks," IEEE/OSA Journal of Optical Communications and Networking, vol. 7, pp. A511-A525, 2015. G. Rademacher and K. Petermann, "Nonlinear Gaussian noise model for multimode fibers with space-division multiplexing," Journal of Lightwave Technology, vol. 34, pp. 2280-2287, 2016. G. Rademacher, S. Warm, and K. Petermann, "Analytical description of cross-modal nonlinear interaction in mode multiplexed multimode fibers," IEEE Photonics Technology Letters, vol. 24, pp. 1929-1932, 2012. G. Rademacher, R. Ryf, N. K. Fontaine, H. Chen, R.-J. Essiambre, B. J. Puttnam, R.S. Luís, Y. Awaji, N. Wada, S. Gross, and N. Riesen, "Long-Haul Transmission Over Few-Mode Fibers With Space-Division Multiplexing," Journal of Lightwave Technology, vol. 36, pp. 1382-1388, 2018. B. Puttnam, R. Luis, T. Eriksson, W. Klaus, J.-M. D. Mendinueta, Y. Awaji, and N. Wada, "Impact of intercore crosstalk on the transmission distance of QAM formats in multicore fibers," IEEE Photonics Journal, vol. 8, pp. 1-9, 2016.

AC C

[48]

31