Routing, Spectrum and Core Allocation in Flexgrid SDM Networks with ...

ONDM 2014, 19-22 May, Stockholm, Sweden

Routing, Spectrum and Core Allocation in Flexgrid SDM Networks with Multi-core Fibers Ajmal Muhammad1 , Georgios Zervas2 , Dimitra Simeonidou2 , Robert Forchheimer1 1

2

Link¨oping University, Link¨oping, Sweden, Email: {ajmal, robert}@isy.liu.se High-Performance Networks Group, University of Bristol, UK, Email: {georgios.zervas, dimitra.simeonidou}@bristol.ac.uk

Abstract—Space division multiplexing (SDM) over multi-core fiber (MCF) is advocated as a promising technology to overcome the capacity limit of the current single-core optical networks. However, employing the MCF for flexgrid networks necessitates the development of new concepts, such as routing, spectrum and core allocation (RSCA) for traffic demands. The introduction of MCF in the networks mitigates the spectrum continuity constraint of the routing and spectrum assignment (RSA) problem. In fact cores can be switched freely on different links during routing of the network traffic. Similarly, the route disjointness for demands with same allocated spectrum diminishes to core disjointness at the link level. On the other hand, some new issues such as the inter-core crosstalk should be taken into account while solving the RSCA problem. This paper formulates the RSCA network planning problem using the integer linear programming (ILP) formulation. The aim is to optimally minimize the maximum number of spectrum slices required on any core of MCF of a flexgrid SDM network. Furthermore, a scalable and effective heuristic is proposed for the same problem and its performance is compared with the optimal solution. The results show that the proposed algorithm is able to well approximate the optimal solution based on ILP model. Index Terms—Space division multiplexing (SDM), multi-core fiber (MCF), inter-core crosstalk, network planning, flexgrid networks.

I. I NTRODUCTION The emerging heterogeneous and bandwidth-intensive applications have characterized the capacity requirements of optical transport networks. To accommodate these applications effectively, the optical networks are evolving from rigid spectrum grid into flexgrid. The capability of flexgrid networks to allocate spectrum elastically enables these networks to handle traffic demands with requirements varying from subwavelength to super-wavelength. This leads to efficient utilization of spectrum resources [1]. Feasibility of flexgrid networks have been demonstrated by several experiments [2], [3], employing state of the art fibers and switching components [4]. To implement flexgrid networks, the available spectrum, for instance, C-band is split into slices of finer width compared to the current rigid grid of 50 GHz [5]. Proposals for the slice size in flexgrid networks are 25, 12.5, and even 6.25 GHz [6]. In order to assign spectrum slices in accordance to the traffic demands, the well known routing and wavelength assignment (RWA) problem is modified to the routing and spectrum allocation (RSA) problem [7] for flexgrid networks. The RSA problem is more challenging than the RWA problem as it has to incorporate routing and constraints, such as the spectrum

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contiguity and spectrum continuity. The spectrum contiguity ensures that the allocated spectrum resources/slices to a traffic demand have to be consecutive in spectrum domain. Similarly, the spectrum continuity imposes that the allocated slices must be the same on each link of the selected routing path. However, the users demand for bandwidth is expected to increase dramatically with time. On the other hand, there is a growing realization that the transmission capacity of the networks based on single-core optical fiber (SCF) are rapidly approaching their fundamental limit [8], [9]. In order to encompass this capacity limitation and attain far higher transmission throughput and spectral efficiency, research community has started to look at exploiting the only remaining unused dimension, i.e., space. The space division multiplexing (SDM) can be realized by using multimode fiber (MMF), multicore fiber (MCF), or few-mode multi-core fiber. MMF employs the propagation of few independent modes within a single core. The number of modes supported by a fiber depends on the core size and the refractive index of the fiber. On the other hand, MCF has several cores embedded in the fiber cladding where each core acts as a single-mode fiber (SMF). The capacity potential of SDM has been manifested in several transmission experiments [10]–[13], exceeding 1Pbps/fiber. The flexgrid networks with MCF necessitate the development of new concepts, for instance, the spectrum and core allocation for traffic demands. In flexgrid networks with SCF, different traffic demands with common spectrum slices cannot traverse through a network link due to spectrum non-overlapping constraint. However, in MCF case demands can be routed through the same link but different cores if they share some common spectrum slices as shown in Fig. 1. In addition, the spectrum continuity constraint of RSA problem is mitigated for MCF by switching demands from one core to another in the network nodes (Fig. 1). However, there are some challenges associated with MCF, namely, the inter-core crosstalk. The inter-core crosstalk incurs when optical signals using the same spectrum propagate through adjacent cores in MCF (Fig. 2). In other words, spectrum overlap among adjacent cores results in limiting the transmission performance of the network. However, the impact of inter-core crosstalk can be alleviated by properly assigning the core and spectrum resources to demands. This paper investigates the routing, spectrum and core allocation (RSCA) problem for flexgrid optical networks. Note that the RSCA problem is different from the RWA for multi-

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Figure 2.

Figure 1.

Network with multi-core fiber.

fiber networks [14]. Because, unlike RSCA which looks into flexgrid SDM networks, the study in [14] considers fixedgrid multi-fiber networks. Moreover, contrary to MCF there is no issue of inter-core crosstalk in multi-fiber networks. The RSCA problem is examined for the network planning case, i.e., all the traffic demands to be established in the network are known/given beforehand. The objective is to provision the demands through proper allocation of spectrum and core, while efficiently utilizing the spectrum resources. To achieve this objective, the problem is formalized as an integer linear programming (ILP) formulation. The optimal solution aims at evaluating the number of spectrum slices required to accommodate a given set of traffic demands and at the same time, fulfilling all the requisite constraints, such as inter-core crosstalk and spectrum overlapping (at the core level), etc. The ILP formulation cannot be solved efficiently for large networks, thus a sub-optimal but scalable heuristic algorithm that solves the planning RSCA problem is also presented. The rest of the paper is structured as follow. A brief overview of the crosstalk issue for networks with MCF is presented in section II. Section III describes the ILP formulation, whereas section IV presents the heuristic strategy for the RSCA problem. The planning strategy is evaluated in section V, and finally some concluding remarks are made in section VII. II. C ROSSTALK FOR F LEXGRID SDM N ETWORKS WITH MCF In the last couple of years, crosstalk suppression has been a prime concern in MCF research [15]–[19] for enabling high capacity and long distance transmissions. Most of these studies (i.e., [17]–[19],) reported the design and fabrication of MCF having low crosstalk and low attenuation, along with characterizing statistically the crosstalk of the MCF. Furthermore, the presented values for crosstalk are computed by considering single-link paths. However, the model for estimating crosstalk and the relation between crosstalk and fiber parameters (e.g.,

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Crosstalk between adjacent cores.

fiber length, bending radius, etc.) reported in [19] can be extended for transmission on multi-link paths. In such case, the crosstalk incurring in the switching ports should also be taken into consideration. The spectrum resource allocation for flexgrid networks with MCF has been addressed for a dynamic scenario in [20]. The proposed algorithm mitigates inter-core crosstalk by averting the spectrum overlaps in the adjacent core of the fiber while neglecting signal leakages in the switching ports. Similarly, for the dynamic scenario the wavelength and mode assignment problem for networks with MMF has been investigated in [21], without taking into account the crosstalk issue. To the best of the author’s knowledge, there is no prior work on ILP formulation of the RSCA planning problem. To incorporate the inter-core crosstalk in the ILP formulation two different approaches can be employed. The first approach is to set the avoidance of spectrum overlaps between adjacent cores (in the fiber links) as a constraint while allocating spectrum and core to different demands. In other words, same spectrum slices cannot be assigned to different demands that traversed through adjacent cores (in the fiber links), unless the crosstalk level at the receiver end is below a given threshold. The second approach is to pre-compute the crosstalk values for all the paths (for a given demand) and select a path with crosstalk value below a given threshold. For the precomputed values, all the possible leakages from the adjacent cores in all the links, and ports are incorporated. In other words, a worst-case interference scenario is considered. The first approach deprive the utilization of same spectrum slices at all cores of a given fiber link, whereas the second approach sacrifices candidate path space. Moreover, the first approach gives at least as good solutions as the second approach, but needs a higher number of variables and constraints and hence would be less scalable. This study adopts the second approach as it adds only one constraint in the ILP formulation. III. ILP M ODEL FOR THE O PTIMAL RSCA The optimization problem of RSCA for flexgrid SDM networks with MCF is formalized as an integer linear programming (ILP) problem. The objective is to optimally route and assign spectrum on different cores to requested demands so that the maximum index of the spectrum slices allocated among the provisioning demands is minimized. The ILP problem can be modeled as follows.

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Input parameters • G(V, E, C): a directed graph where V is the set of vertices that represent the network nodes, E is the set of arcs that represent the network links, C is the set of cores on each link of the network; • D: set of traffic demands to be established in the network; • Ωd : number of slices requested by demand d ∈ D; d • π : set of candidate paths for d; • Hπ : set of links that are in the path π; • Ξ: inter-core crosstalk threshold; • Xtπ : inter-core crosstalk value for path π; • Υ: set of constants {K1 , K2 , . . . , K|Hπ | } with values such ˆ l−1 P that |C| · Kl < Kˆl , are used for core selection on l=1

•

different links of a chosen path; P M : large constant, e.g., M = Ωd ; d∈D

Variables ˆ d ∈ π d is utilized by d • xπ ˆ d ∈ {0, 1}- equal to 1 if path π and 0 otherwise; + • fd ∈ Z - denote the starting slice number for d; d • χc,uv ∈ {0, 1}- equal to 1 if d passed through core c on link (u, v) and 0 otherwise; ˆ (d,d) • fc,uv ∈ Z- indicate if d and/or dˆ is passing through c on link (u, v); ˆ (d,d) • δc,uv ∈ {0, 1}- equal to 0 if the starting slice number of d is greater than dˆ (i.e., fd > fdˆ) on c of link (u, v) and 1 otherwise; ˆ (d,d) • δc,uv ∈ {0, 1}- equal to 0 if the starting slice number of dˆ is greater than d (i.e., fdˆ > fd ) on c of link (u, v) and 1 otherwise; • MS - indicate the maximum allocated slice number among all the cores of the network links; Objective function M inimize : MS

(1)

ˆ ˆ ˆ d) (d,d) (d,d) ˆ f(d, c,uv ≤ 2 · δc,uv + 2 · δc,uv ∀(d, d) ∈ D, ∀c ∈ C, ∀(u, v) ∈ E (7) ˆ ˆ (d,d) ˆ ∈D fd − fdˆ + M ·(δc,uv + χdc,uv + χdc,uv ) ≤ 3·M − Ωd ∀(d, d) (8) ˆ ˆ (d,d) ˆ ∈D fdˆ − fd + M ·(δc,uv + χdc,uv + χdc,uv ) ≤ 3·M − Ωdˆ ∀(d, d) (9)

The objective (1) is the minimization of the maximum slice index among all the cores of all the network links, as defined in (2). Constraint (3) guarantees single path routing for each d. Constraint (4) picks a path for d with crosstalk value less than the set threshold level. Constraint (5) selects a core on each link of the chosen path for d. Constraints (6-9) ensure the spectrum continuity and non-overlapping spectrum allocation to different demands that share the same core on a given link. Note that the guardband to separate adjacent spectrum paths is not taken into account in this work, but they can be easily included by modifying constraints (2,8,9) accordingly, i.e., adopting the approach proposed in [22]. To elaborate on constraints (6-9), assume two different cases. First, when one (or both) of the demands (i.e., d and ˆ is not passing through core c on link (u, v), i.e., χd d) c,uv ˆ or/and χdc,uv equal to 0. In this case, constraints (8) and (9) are deactivated, i.e., they hold always regardless of fd and fdˆ values, due to the larger value on the right hand side of the constraints. Second, when both demands are traversing through ˆ core c on link (u, v), i.e., χdc,uv and χdc,uv are both equal to 1. For such case, one of the constraints (either (8) or (9)) ˆ ˆ (d,d) (d,d) is activated according to the values of δc,uv and δc,uv . For ˆ ˆ (d,d) (d,d) δc,uv =1 (i.e., when fdˆ > fd ) and δc,uv = 0, constraint (8) is actuated, which becomes fd +Ωd ≤ fdˆ, ensuring that the slices assigned to demands d and dˆ do not overlap. In addition, (9) is deactivated as it becomes fdˆ + Ωdˆ − fd ≤ M , which hold ˆ (d,d)

always irrespective of fd and fdˆ values. Similarly, for δc,uv =1 ˆ (d,d) δc,uv =

Constraints fd + Ωd − 1 ≤ MS X

∀d ∈ D

xπˆ d = 1 ∀d ∈ D

(2)

0 constraint (9) is triggered, whereas (i.e., fd > fdˆ) and constraint (8) is deactivated. Note that the proposed ILP model can be extended to multifibers networks (i.e., for routing, spectrum and fiber selection problem), by relaxing constraint (4) and replacing cores by

(3)

π ˆ d ∈π d

X

Xtπˆ d · xπˆ d ≤ Ξ

∀d ∈ D

(4)

π ˆ d ∈π d

X

X

˜ c∈C l:(u,v)∈Hπ ˆd

K˜l · χdc,uv −

X K˜l ·xπˆ d = 0 ∀ˆ π∈π ˆ d , ∀d ∈ D

˜ l:(u,v)∈Hπ ˆd

(5) ˆ

ˆ

d) ˆ χdc,uv + χdc,uv = f(d, c,uv ∀(d, d) ∈ D, ∀c ∈ C, ∀(u, v) ∈ E (6)

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Figure 3.

Shortest path with cumulative spectrum availability strategy.

ONDM 2014, 19-22 May, Stockholm, Sweden

Algorithm 1 Shortest path with Cumulative Spectrum Availability (SPSA) 1: G(V, E, C): network topology; 2: D: set of traffic demands to be provisioned; S 3: P : path matrix, P = d∈D π d ; 4: e S: initial set of available spectrum slices, e S= max{Ωd }; 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18:

Sort D in descending order of the Ωd ; while D 6= ∅ do for each demand d ∈ D do for each path π ˆ d ∈ π d do if Xtπˆ d ≤ Ξ then Let ωπˆ d be set of contiguous slices available on at least one core c ∈ C on each link of π ˆd if Ωd ≤ ωπˆ d then Provision d using the first available contiguous slices on shorter path, remove d from D; end if end if end for end for Increment e S by max{Ωd } of the remaining demands; end while

fibers (on a given link) in constraint (5). Furthermore, the RSCA optimization problem is an extension of the static spectrum allocation problem, which is known to be NPhard [23]. For this reason, a heuristic algorithm is proposed. IV. H EURISTIC A LGORITHM FOR THE RSCA P ROBLEM The proposed ILP model is tractable for small network topologies and low traffic demands. For topologies with high nodal degree and/or number of nodes, and high traffic demands practical solutions within reasonable time can be obtained by using heuristic algorithms. To attain the goal of minimizing the maximum spectrum slice number on a MCF, the following heuristic strategy is proposed. A. Shortest path with Cumulative Spectrum Availability (SPSA) SPSA strategy provisions a given set of D by starting from the ones with high Ωd requirement, and stepwise increment the available spectrum slices, e S, per link as illustrate in Fig. 3. For a given set of D, the algorithm first arranges demands in descending order according to their spectrum requirements (i.e, Ωd ). If two demands have the same spectrum requirement, then the one having smaller hop length value (i.e., |Hπ |) for its first (shortest) path in π ˆ d is given priority in ordering. Demand with larger spectrum requirement is given a high priority due to the fact that slices contiguity constraint makes it harder to seek available consecutive slices for such demand. Initially, the number of available spectrum slices on each core of the MCF link is set to the value equal to the maximum

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Figure 4.

Network topology.

spectrum requirement of any demand in D. For each demand d, the set of pre-computed candidate paths π d is used to find spectrum resources on all the cores of the feasible paths (i.e., paths with crosstalk values less than threshold level). If spectrum slices (on same or different cores of the path links) satisfying the contiguity and continuity constraints are available on the very first (shortest) feasible path, then d is established in the network. Otherwise, the next demand in D is considered for provisioning. The remaining demands in D that are not accommodated in the current iteration are re-considered for the value of spectrum resources (i.e., e S) incremented by max{Ωd } of the remaining (after the current iteration) demands. The process terminates when all demands are provisioned in the network. Finally, the computational complexity of Algorithm 1 is O[|D2 ||π d ||V||C|]. V. O PTIMAL D ESIGN A SSESSMENT The planning strategy is evaluated for both the optimal (i.e., ILP formulation) and sub-optimal (i.e., heuristic) solutions for flexgrid SDM networks with MCF. The ILP formulation is solved by running a commercially available ILP solver, i.e., CPLEX [24]. For the ILP formulation, all the possible routes for all d are computed, by setting the value of π d to its maximum value, whereas it is set to 3 for the heuristic strategy. Furthermore, the paths are computed by using Yen algorithm [25]. For the assessment of the proposed strategy, a sample topology (Fig. 4) with 6 nodes and 18 unidirectional links is considered. It is assumed that the number of cores (|C|) per link is equal to 3. Given a fixed number of traffic demands, a set of demands is generated by uniformly selecting the source and destination nodes. The value of Ωd for each demand is selected uniformly from the set {2, 4, 6, 8} spectrum slices. It has been reported in [6] that the spectrum per channel must be symmetrical around a center frequency and that each channel must have an even number of slices. This is the reason for choosing the even number of slices per demand in this study. The crosstalk for a particular core is the ratio of power in that specific core originating from the rest of fiber cores to the power emanates from that specific core. For fiber with |C|=3, the inter-core crosstalk per link for any core can be calculated by using the formula (i.e., eq. (27)) reported in [19].

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Table I PARAMETERS AND THEIR VALUES Value 1550 nm 0.01 m 107 1/m 3.16 x 10−5 4.5 x 10−5 m -50 dB -30 dB

Resource utilization per core (%)

Parameter Wavelength (λ) Bending radius (R) Propagation constant (β) Coupling coefficient (κ) Core pitch (Λ) Port isolation Crosstalk threshold (Ξ)

Core 1

Core 2

Core 3

80

70

60

50

40

30

2

2 − 2exp(−3 · 2 κβ 1 + 2exp(−3 · 2

R Λ L) R β Λ L)

κ2

(30, 150)

Table I presents the list of physical parameters and their values used for crosstalk calculation, while L denotes the length of the fiber link. More details about these values and crosstalk computation can be found in [18], [19], [26], [27]. Fig. 5 shows the average number of spectrum slices as a function of the number of demands (with total required slices) to be provisioned in the network. Different observations can be made from the results shown in Fig. 5. Firstly, the proposed heuristic is able to well approximate the optimal solution, i.e., average error is less than 6%. Secondly, improvement in the number of spectrum slices specially at high loads (for optimal case) can be achieved by relaxing the crosstalk constraint (i.e., constraint (10)), compared to the case with crosstalk constraint. This can be envisaged as a gain brought by the future multi-cores fibers with negligible inter-core crosstalk. Fig. 6 exhibits resource utilization for different cores of the network using the heuristic strategy. It can be seen from the figure that for low loads most of the demands are accommodated at core 1. However, as the network traffic grows the utilization level of resources of the other cores also start to elevate. Heuristic ILP: with crosstalk constraint ILP: without crosstalk constraint

Avg. number of spectrum slices

35

30

25

20

15

10

(30, 150)

(60, 299)

(90, 449)

(120, 598)

(150, 745)

(180, 899)

Number of traffic demands with required slices Figure 5.

Avg. number of spectrum slices per core vs. traffic demands.

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20

(10)

(60, 299)

(90, 449) (120, 598) (150, 745) (180, 899)

Number of traffic demands with required slices Figure 6.

Resource utilization per core vs. traffic demands.

0.08 0.075 Core 1

Core 2

Core 3

0.07

Utilization entropy

XtL =

0.065 0.06 0.055 0.05 0.045 0.04 0.035 0.03

(30, 150)

(60, 299)

(90, 449) (120, 598) (150, 745) (180, 899)

Number of traffic demands with required slices Figure 7.

Utilization entropy vs. traffic demands.

Furthermore, to analyze the level of resource fragmentation for the heuristic strategy the utilization entropy metric [28] is employed. The utilization entropy for the network is computed by measuring the changes in the usage status of all the spectrum slices on all the network links. The measured value is then divided by the product of the total network links and the number of available slices per links reduced by 1 (i.e., e S-1). The value of utilization entropy varies from 0 to 1, and a low value indicates that the slices are utilized in an ordered form with minor gaps and hence low fragmentation. Fig. 7 displays the utilization entropy for different cores at different traffic demands. The figure manifests that the strategy to stepwise increment the available spectrum slices (e S) results in minimizing the slice fragmentation, i.e., the highest utilization entropy value is far less than 1. Furthermore, core 1 which has high resource utilization level (Fig. 6) attains the minimum utilization entropy value, and similarly core 3 with lower resource utilization level exhibits high utilization entropy.

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VI. C ONCLUSION The paper presents a planning strategy for flexgrid networks with multi-core fibers (MCF). The strategy exploits the flexibility offered by MCF in the form of switching cores on different links during provisioning of traffic demands. At the same time, the strategy takes into account the inter-core crosstalk stems from the multi-cores embedded in the fiber cladding. The design strategy is defined through an integer linear programming formulation and is solved for a real case scenario. To overcome the scalability limitation by the optimal solution based on integer linear programming formulation, a scalable and efficient heuristic algorithm is proposed. The heuristic strategy sorts the traffic demands based on their spectrum requirements and path lengths. The spectrum resources are gradually incremented after each iteration (for establishing demands), till all the demands are provisioned in the network. The results indicate that the proposed heuristic is able to generate close to optimal solution in polynomial time. The proposed strategy for RSCA problem can be exploited for efficient switching of traffic at diverse granularities, e.g., core, waveband and wavelength. Synthetic MCF-based SDM Networks with scalable nodes for supporting a wide range of granularities can be designed by extending the proposed strategy to programmable ROADMs. ACKNOWLEDGMENT This work is supported by the EPSRC grant EP/I01196X: The Photonics Hyperhighway, the EC FP7 grant no. 317999, IDEALIST, and ”Security in All-optical networks” funded by VINNOVA (The Swedish Governmental Agency for Innovation Systems). R EFERENCES [1] B. Kozicki, H. Takara, Y. Sone, A. Watanabe, and M. Jinno, “Distanceadaptive spectrum allocation in elastic optical path network (SLICE) with bit per symbol adjustment,” in Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2010, pp. 1–3. [2] D. Qian, M.-F. Huang, E. Ip, Y.-K. Huang, Y. Shao, J. Hu, and T. Wang, “101.7-Tb/s (370x294-Gb/s) PDM-128 QAM-OFDM transmission over 3x55-km SSMF using pilot-based phase noise mitigation,” in Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011, pp. 1–3. [3] J. Oliveira, M. Siqueira, G. Curiel, A. Hirata, F. van’t Hooft, D. Macedo, M. Colazza, and C. Rothenberg, “Experimental testbed of reconfigurable flexgrid optical network with virtualized GMPLS control plane and autonomic controls towards SDN,” in International Microwave Optoelectronics Conference (IMOC), 2013, pp. 1–5. [4] WaveShaper S-series product brief. [Online]. Available: http://www. finisar.com/optical instrumentation [5] ITU-T G.694.1, “Spectral grids for WDM applications: DWDM frequency grid.” 2002. [6] Y. Li, F. Zhang, and R. Casellas, “Flexible grid label format in wavelength switched optical network,” in IETF RFC Draft, 2012. [7] M. Jinno, H. Takara, and B. Kozicki, “Dynamic optical mesh networks: drivers, challenges, and solutions for the future,” in 35th European Conference and Exhibition on Optical Communication (ECOC), 2009, pp. 1–3. [8] R. Essiambre, G. Kramer, P. Winzer, G. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” Journal of Lightwave Technology, vol. 28, no. 4, pp. 662–701, 2010. [9] R. Essiambre and R. Tkach, “Capacity trends and limits of optical communication networks,” Proceedings of the IEEE, vol. 100, no. 5, pp. 1035–1055, 2012.

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