The RBCMLSA problem on space division multiplexing elastic optical networks

Optical Fiber Technology 53 (2019) 102003

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The RBCMLSA problem on space division multiplexing elastic optical networks

T

Der-Rong Din , Zheng Jie Huang ⁎

Department of Computer Science and Information Engineering, National Changhua University of Education, No. 1, Jin De Road, Changhua 500, Taiwan, ROC

ARTICLE INFO

ABSTRACT

Keywords: RBCMLSA Space division multiplexing (SDM) Multi-core fibers (MCF) Elastic optical network (EON)

The introduction of space division multiplexing (SDM) is a promising solution to cope with ever-increasing Internet traffic. Multi-core fibers (MCFs) are a potential solution for the capacity crunch problem. In this article, the Routing, Baud rate, forward error correction (FEC) Coding, Modulation Level, and Spectrum Assignment (RBCMLSA) problem in elastic optical networks (EONs) employing MCFs and SDM is studied. An Integer Linear Program (ILP) model is used to define the studied problem and find the optimum solution in static traffic. Since the RBCMLSA problem is an NP-hard problem, for the dynamic traffic, the crosstalk-aware path routing algorithm (CAPRA) is proposed to solve this problem. Three core-selecting schemes, named Minimum Load (ML), Minimum Conflict (MC), and Minimum Weight (MW) are proposed. Simulation results show that the proposed algorithm can get lower blocking probability when compared to the algorithm for the existing simpler Routing, FEC Coding, Modulation Level, and Spectrum Assignment (RCMLSA) and Routing, Modulation Level, and Spectrum Assignment (RMLSA) problems.

1. Introduction The elastic optical network (EON) employs the optical-orthogonal frequency division multiplexing (O-OFDM) technology has attracted much attention since it utilizes the spectrum more efficient than the one that uses wavelength-division multiplexing (WDM) technology [1–5]. In EONs, the spectrum of fiber is divided into several frequency slots (FSs) and the key problem is the Routing and Spectrum Assignment (RSA) problem [1,2] for the service provisioning. In the RSA problem, for the given connection request, the goal is to find the routing lightpath and the assigned frequency spectrum for it. The transmitting distance between the source and destination of the request was not considered and the default modulation format (for example Binary Phase Shift Keying, BPSK) is used for all transmissions [1,6]. Several routing and spectrum assignment algorithms have been introduced in recent years [1,6]. In [7], authors have extended the RSA problem by considering the spectrum fragmentation and/or time fragmentation. The transparent reach (TR) or maximum transmitting distance of a single-core optical-amplified fiber can be limited by amplified spontaneous emission (ASE) noise and fiber nonlinearities [3]. Moreover, the distance of the source-destination pair and the modulation format of the lightpath may affect the number of required FSs of the request, in [3,8], the Routing, Modulation Level, and Spectrum Assignment (RMLSA)

⁎

problem was studied. They used the more efficient modulation format to reduce the number of the required FSs if the TR constraint can be satisfied. In [4], authors have proposed a hybrid single/multipath routing scheme to solve the RMLSA problem. In this scheme, multiple lightpaths were found to route a connection request if a single-path cannot be found to solve the RMLSA problem. In [5], authors have studied the multicast (one-to-many) routing problem in EONs, the goal is to reduce the blocking probability. In [9], based on the provided data rates, modulation formats, and different forward error correction (FEC) codes, the authors considered the Routing, Code, Modulation Level, and Spectrum Assignment (RCMLSA) problem. Different from the previous RMLSA problem, the FEC coding is considered together with the modulation format to extend transmitting distance between the source and destination nodes. To solve the RCMLSA problem, for a given connection request, not only the route and spectrum, but also the pair FEC code-modulation format best suited are selected to establish an optical connection in EONs. The authors proposed a heuristic algorithm to route the connection request to minimize the number of required FSs. Simulation results showed that the blocking probability of the RCMLSA problem is lower than that of the RSA and RMLSA problems. In [10], authors proposed a programmable controller on the Software Definition Network (SDN), several parameters (such as channel

Corresponding author. E-mail address: [email protected] (D.-R. Din).

https://doi.org/10.1016/j.yofte.2019.102003 Received 11 March 2019; Received in revised form 2 August 2019; Accepted 27 August 2019 1068-5200/ © 2019 Elsevier Inc. All rights reserved.

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D.-R. Din and Z.J. Huang

types, number of carries, transmitting rate, modulation format, central frequency, channel wide, FEC types, and number of FSs) can be dynamically determined to meet the connection request. In [11], authors introduced the idea of the plug and play auto-configuring transmitters of the optical network. In the proposed environment, the control plane should be capable of performing effective routing and spectrum assignment as well as the proper selection of the transmission parameters depending on the required TR. In the future EONs, the innovative optical transceivers enable the dynamic adaptation of the baud rate, modulation level, and FEC codes to the optical transmission properties; it will provide high levels of flexibility and allocate FSs efficiently. In [12,13], the Routing, Baud rate, FEC Coding, Modulation Level, and Spectrum Assignment (RBCMLSA) problem in single-core fiber (SCF) EONs was defined and studied. The RBCMLSA problem was extended from the RCMLSA problem by considering the baud rates of the transceivers. In the RBCMLSA problem, the parameters of transceivers (baud rate, FEC type, modulation format) can be determined and selected by the network controllers. In [12,13], both the single and multipath routing schemes were considered and several heuristic algorithms were proposed. An Integer Linear Programming (ILP) model was proposed to define the static routing problem [13]. Simulation results showed that the blocking performance of the algorithm for the RBCMLSA problem is better than that of the RCMLSA.

the available FSs and core allocation should be allocated and determined to the lightpath by considering XT. There is no core-switching function on the SDM-EON. In this paper, the RBCMLSA problem on SDM-EONs is formulated as an ILP and a heuristic algorithm is proposed to solve it. 1.3. Key contributions We first introduce a path-link-based ILP optimization model considering the XT. This problem is difficult to solve in acceptable execution time by the ILP method for large-scale problem instances. For this reason, we propose an XT-aware heuristic algorithm for achieving scalability. Three core-selecting schemes are proposed to determine the core-selecting order. To the best of our knowledge, our work is the first work that considers the XT-aware approach of the static RBCMLSA problem. The remainder of this paper is organized as follows. The related works are stated in Section II. The RBCMLSA problem on SDM-EON is formulated in Section III. The crosstalk-aware heuristic algorithm is presented in Section IV. We have presented a performance evaluation and explained the numerical results in Section V. Finally, in Section VI, we conclude the paper. 2. Related works

1.1. Multi-core fiber (MCF)

In this section, the related works are described. Firstly, the related results for studying the RSA problem in SDM-EONs are presented. Then, the RBCMLSA problem in single-core fiber (SCF) EON is described.

The development of multi-core fiber (MCF) technology has led to the adoption of space division multiplexing (SDM) in EONs. It uses several single-mode cores embedded in the fiber cladding and is a possible implementation of SDM-EON [14–17]. Moreover, it increases the capacity of the networks and has the advantages of lower crosstalk and core independence. In MCF EONs, the inter-core crosstalk (XT) affects the quality of transmission and reduces the availability of the spectrum for future allocations. The XT is a type of interference, which adjacent cores cause to another along with the same optical fiber link. Thus, to find a feasible lightpath for the demand in MCF EONs, the actual interference among super-channels with same frequencies and adjacent cores should be estimated [16]. In this paper, the XTs between two adjacent cores was considered (as the assumption of the RSCA problem [18–21]). That is, the XT occurs only when the same FSs are assigned to adjacent cores in a common fiber link to serve different transmission requests. To minimize the XT and achieve high-capacity and long-distance transmissions, how to suppress the XT has become a primary focus in MCF research [22–24]. Several researchers have studied the routing problem on the SDMEON with core-switching function, that is, the number of used cores of a lightpath may be greater than one. In [25], authors have considered the spectrum defragmentation by re-provisioning advance reservation (AR) requests in SDM-EONs with MCFs. In [26], authors have proposed a crosstalk-aware spectrum defragmentation (CASD) algorithm based on the spectrum compactness (SC). Simulation results showed that the proposed CASD algorithm can achieve better performance than a benchmark algorithm in terms of blocking probability and spectrum utilization.

2.1. SDM RSA problem In contrast to the RSA problem with SMF, which should satisfy the constraints of spectrum continuity, contiguity, and non-overlapping, the XT constraint should be taken into account in the RSA problem in SDM-EONs with MCFs when assigned the spectral resources. There are mainly three approaches [27] when considering the XT constraint.

• XT-avoid approach: is to avoid spectrum overlaps between adjacent • •

cores in the fiber links while allocating FSs and cores to different transmission requests [28]. XT-WC approach: is to consider the XT in a worst interference scenario [16,24]. XT-aware approach: is to compute the XT strictly depends on the interference of a core with other active adjacent cores that share the same FS and a link [18–21],

Both the XT-avoid and the XT-WC approaches can simplify the RSA problem and significantly reduce the complexity of the problem [27]. The XT-avoid approach can completely prevent the XT from occurring, the efficiency of the spectrum multiplexing of MCF will be decreased. In the XT-WC approach, for a given XT threshold, the maximum transmission reach will be bounded significantly, and it is shorter than what the optical signal can reach. This makes the XT-WC approach overconservative since the feasible lightpath space may become significantly small [27]. The RSA problem in SDM-EONs has been considered in [16,14] and several algorithms have been proposed. In [16], a Routing, Spectrum, and Core Allocation (RSCA) solution has been proposed for the SDMEON planning problem using an ILP formulation, as well as a heuristic algorithm. In [15], authors studied the RSA protection problem in SDMEONs by using the failure independent path protection (FIPP) p-cycles to protect primary paths. Since anycast communications are widely used, it is important to study the anycast planning problem in SDMEONs overlaid on MCFs. In [29], authors have studied the anycast RSA problem in SDM-EONs, referred to as anycast routing, spectrum, and core allocation (ARSCA) problem. In [30], authors have studied the

1.2. Studied problem In this paper, the RBCMLSA problem [12,13] in MCF SDM-EONs with flexible transmitters is studied. For a given EON and a sequence of connection requests, the goal is to establish a routing lightpath and assigned suitable channels to the lightpath of each request to meet the traffic requirement and the goal is to optimize the performance measure. For each request, the transmitting parameters (include baud rate, FEC coding type, and modulation format) of the lightpath should be determined according to the request and the network status. Moreover, 2

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lightpaths routing problem in SDM-EONs with considerations of the impairments and security vulnerabilities caused by inter-core crosstalk. The authors have proposed attack-aware RSCA (Aa-RSCA) algorithms that give priority to avoiding physical-layer security threats and then try to reduce the crosstalk-induced impairments. In [17] the RMLSA problem in SDM-EONs has been considered with optical signal-to-noise ratio (OSNR) margin, an ILP formulation and a heuristic method have been proposed. The XT-aware approach can always perform better than both the XT-avoid and the XT-WC approaches, and it leads to an optimal solution [31]. It strictly calculates the XT depending on the active adjacent cores that share the same FS on a common link along the lightpath. Therefore, for a strict XT threshold, the XT-aware approach can prevent the same FSs from being assigned to adjacent cores to ensure that the XT of the lightpath (for a given transmission request) is less than the XT threshold. To the best of our knowledge, no efficient method for XT calculation considering the XT-aware approach has been proposed in the previous literature for the static RCMLSA or RBCMLSA problem.

Table 1 The TR for the selected parameters [12,13].

2.2. RBCMLSA Problem In this section, the RBCMLSA problem [12,13] in SCF EON is presented. The connection request is represented by r = (s, d , BWr ) , where BWr is the required data transfer rate (Gb/s), and s and d is the source and destination node of the request, respectively. The transmitter provides several adaptive transmitting parameters, which include baud rates, modulation formats (Phase Modulation-Quadrature Phase-Shift Keying (PM-QPSK), PM-8Quadrature Amplitude Modulation (PM8QAM), PM-16QAM, PM-32QAM, PM-64QAM), and FEC types (Type 0 with no-FEC, Type 1 with Reed-Solomon [255,235], type 2 with ReedSolomon [255,239]–Bose-Chaudhuri-Hocquen-ghem [1023, 963] code, type 3 with Low-Density Parity-Check [416, 3431, 0.825] code, type 4 rate-adaptive code). Let B, F , and M be the set of baud rates, FEC types, and modulation formats of the transmitter, respectively. The OH [f ] is the required overhead of the FEC type f F and it is independent of b B and m M . The overhead of the FEC type f {0, 1, 2, 3, 4} is mapped to {0%, 6.69%, 13.34%, 21.20%, 66.66%} . The value of D [b , f , m] represents the TR of the transmitting parameters (b, f , m) , which can be obtained from Table 1 [12,13]. For example, if PM-QPSK is selected, the baud rate is set to 28, and type 4 FEC is used, then D[28, 4, PM-QPSK] is 2674 km. To find the routing path and assigned FSs for a connection request r = (s, d , BWr ) , in the proposed algorithm [12,13], first, a set Pr = {Pr1, Pr2 , …, Prk } of candidate paths is constructed by performing the kshortest path algorithm [32] on the given physical network. Let dist (Pri ) be the distance of the path Pri . Then, the set FM (Pri ) = {(b, f , m) dist (Pri ) D [b, f , m]} of feasible transmitting parameters (with in Table 1) of the request is constructed. For example, if the path Pri with distance 2,233 km is selected, then the set FM (Pri ) is {(28, 4, PM-QPSK), (30, 4, PM-QPSK), (32, 2, PM-QPSK), (32, 3, PM-QPSK), (32, 4, PMQPSK), (128, 4, PM-QPSK)}. For the selecting parameters (b, f , m ) of the path Pri , the number of required FSs (denoted as Nri ) of the request r can be computed by the formula [12,13]:

Nri =

BWr × (1 + OH [f ]) Cf × ML (m)

+ GB,

FEC Type f

D [ b , f , m] m

b

no-FEC

Type 1

Type 2

Type 3

Type 4

PM-QPSK

28 30 32

1674 1856 2084

1774 1956 2184

1874 2056 2284

1992 2174 2402

2674 2856 3084

PM-16QAM

28 30 32

1064 1134 1216

1164 1234 1316

1264 1334 1416

1382 1452 1534

2064 2134 2216

PM-QPSK

112 120 128

1122 1201 1292

1222 1301 1392

1322 1401 1492

1440 1519 1610

2122 2201 2292

PM-8QAM

75 80 85

1011 1075 1147

1111 1175 1247

1211 1275 1347

1329 1393 1465

2011 2075 2147

PM-16QAM

56 60 64

920 972 1031

1020 1072 1131

1120 1172 1231

1238 1290 1349

1920 1972 2031

PM-32QAM

45 48 51

844 888 937

944 988 1037

1044 1088 1137

1162 1206 1255

1844 1888 1937

PM-64QAM

37 40 43

765 801 840

865 901 940

965 1001 1040

1083 1119 1158

1765 1801 1840

PM-32QAM

112 120 128

724 756 791

824 856 891

924 956 991

1042 1074 1109

1724 1756 1791

PM-64QAM

93 105 117

665 692 722

765 792 822

865 892 922

983 1010 1040

1665 1692 1722

Fig. 1. Nri of selecting parameters in FM (Pri ) of candidate path Pri .

Nri =

100 × (1 + 66.66 %) 12.5 × 2

+ 1 = 8. For the other transmitting parameters in

FM (Pri ),

the computation of Nri is described in Fig. 1. Four constraints are considered in the RBCMLSA problem [12,13], they are spectrum continuity constraint, subcarrier consecutiveness constraint, non-overlapping spectrum constraint, and TR constraint. The definition of these constraints can be found in [1,14].

(1)

where Cf is the data transfer rate (Gb/s) provided by each FS (e.g. 12.5 Gb/s), ML (m ) is the modulation level of the modulation format m M (e.g. ML(PM-QPSK) = 2, ML(PM-8QAM) = 3, ML(PM16QAM) = 4, ML(PM-32QAM) = 5, and ML(PM-64QAM) = 6). The GB is the frequency guard band between in term of FSs and it is set to 1. For example, if the required date rate BWr is 100 Gb/s and the parameters (28, 4, PM-QPSK) are selected, then we have OH[4] = 66.66%, ML(PMQPSK) = 2, and the actual number of required FSs is

3. Problem definition In this section, definitions, notations, constraints of the studied problem are given. Section 3.1 the computation of crosstalk on MCF EON is described. The ILP model for the RBCMLSA problem in MCF EON is defined in Section 3.2.

3

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3.1. Crosstalk on MCF-SDM EON

request r, and equals 0 otherwise;

• b {0, 1} : equals 1, if core c on link e is utilized to accommodate traffic of the request r, and equals 0 otherwise; {0, 1} : equals 1, if the FS w on core c of link e is occupied to •x accommodate the request r, and equals 0 otherwise; • y {0, 1} : equals 1, if the FS w of link e is utilized to accommodate traffic of the request r, and equals 0 otherwise; w {1, 2, …, W } : denotes the index of starting FS index of traffic • of the request r. • Fmax: denotes the maximum index of allocated FSs in all cores of rec

The crosstalk (XT) of a particular core is the ratio of power created from the rest of fiber cores with the power that spread out from that specific core, thus the unit of the XT is dB. The XT threshold usually is used to constrain the transmission in MCF-SDM EON. In this paper, we make the same realistic assumptions assumed in [31,33]. For the weakly coupled MCF with cores organized in a hexagonal array. The C ) on a link e, crosstalk between two adjacent cores (c C and c utilized on the same FS (denoted as XTec, c ) can be computed by the following formulae [31,33]:

XTec, c =

h=2

1 exp( 2 × h × L (e )) , 1 + exp( 2 × h × L (e ))

(coc ) 2 br

.

wrec

wre 0 r

MCFs employed in the network.

Let nrp Z+ denote the minimal number of FSs that have to be allocated on path p Pr to support the request r RQ by using the best transmitting parameter with a distance constraint. Similar in [35], we consider that an adequate mapping of the traffic volume BWr to the number of required FSs nrp (includes GB). This can be done in the algorithm preprocessing step taking into account the length of the p Pr and all transmitting parameters (includes the modulation formats, FEC types, and baud rates) that can be used on the path p with greater spectral efficiency. Consider the request r with request BWr = 780 Gb/s and the set of candidate paths Pr ={Pr1 (with distance 0.39 km), Pr2 (with distance 0.43 km), and Pr3 (with distance 0.91 km), then nrp for these paths are mapped to {12, 12, 13}. The computation of nrp (or Nri ) is illustrated in Fig. 2. Several constants are defined here:

(2) (3)

In (2) and (3), h is crosstalk increase per unit length, br is the bending radius of fiber 0.05 m, coc is the coupling coefficient 4 × 10 4 , is the core-pitch (distance between cores) 4.0 × 10 5 m, is the constant 4 × 10 6 m, and L (e ) is the length of the fiber e E [31,33]. Then, the total crosstalk on an FS is calculated as the aggregation of the crosstalk caused by all the interfering cores (denoted as AD (c ) ) of core c as follows:

XTec, c

XT (e ) = c

AD (c )

(4)

• : equals 1 if path p for request r contains link e, otherwise it is 0; • XT : denotes the crosstalk between two adjacent cores c C and c C on link e E . • cr : is the crosstalk value of the request r RQ on link e E ; • : denotes the crosstalk of request r RQ, if path p P is chosen to accommodate it. • : shows the crosstalk threshold of request r RQ. • MN: is a great positive integer. • N : denotes the number of FSs required for accommodating traffic of

Consequently, the end-to-end crosstalk on a path p is obtained by adding the crosstalk of all its links (e p ) as follows:

XT (p) =

XT (e) e p

rpe

c, c e

(5)

re

rp

The end-to-end crosstalk for all the FSs allocated to a request must be less than its threshold. It is enough to assure that the crosstalk on the most affected FS allocated to a request is less than its threshold [34]

max XT w W

XTth ,

r

r

(6)

r

RQ .

request r

where W = {1, 2, …, W } is the set of FSs of each core of fiber and is the XTth be the threshold limit of the XT.

minimize Fmax

3.2. ILP formulation

p Pr

srp = 1,

In this subsection, we formulate an ILP (alternate to the one presented in [13] for the SCF EON RBCMLSA problem and the one presented in [31] for SDM-EON Routing, Modulation, Core and Spectrum Assignment (RCMSA) problem) for the static routing problem. In this formulation, both the baud rate, modulation levels, and FEC codes are incorporated into the model for the single path routing. Similarly, as in [13,31], the path-link approach is used for the network flow representation of the SDM-EON RBCMLSA problem. In such a formulation, a set of predefined paths between the source and destination nodes of each request is constructed. The physical topology of the network is represented by G (V , E , C ) , where V is the set of nodes, E is the set of links, and C is the set of cores. Each link in E is characterized by two parameters, that is the set of cores C and the set of FSs W. Let RQ be the set of requests and Pr be the set of predefined candidate paths for request r = (s, d , BWr ) RQ . Each set Pr comprises paths that have the origin s and the destination d. In the following, r shows the request indices, w is the FS indices. Besides, p , e and c are the indices of candidate paths for each request, network links, and fiber cores, respectively. The variables of the ILP formulation are defined as follows:

r

(7)

RQ,

(8)

srp × nrp = Nr ,

r

RQ,

srp ×

rp

=

r,

r

RQ ,

srp ×

rpe

= are ,

r

RQ,

r

RQ,

(9)

p Pr

(10)

p Pr

e

E

(11)

p Pr

brec = are ,

e

E,

(12)

c C

x wrec

MN × brec ,

r , c, e ,

(13)

w

brec

x wrec ,

r , c, e,

(14)

w

MN × (ywre

1)

w

MN × (ywre

1)

wr0 + Nr

x wrec w

• s {0, 1} : equals 1, if path p is chosen to accommodate the request r, and equals 0 otherwise; • a {0, 1} : equals 1, if link e is used to accommodate traffic of the

Nr

c

4

(1

c

x wrec = ywre ,

rp

re

wr0,

r , e , w,

(15)

r , e , w, 1

w,

are) × MN ,

r , e , w,

r , e,

(16) (17) (18)

Optical Fiber Technology 53 (2019) 102003

D.-R. Din and Z.J. Huang

Fig. 2. (a) COST239 network, (b) nrp (or Nri ) of candidate paths Pr1, Pr2 , and Pr3 .

XTwec = c

crre

r

XTwec

crre

(1 r,

x wr ec × XTec, c ,

e , c, w,

x wrec ) × MN ,

r , e , c, w,

RQ

r,

+ Nr

Fmax ,

(20) (21)

e E

wr0

by 1. The core with the minimum cost is selected as the next core for examining. If all cores are examined (COST (ci ) = , ci C ), the costs of cores are reset to zero for the next request. This core-selecting scheme has the following drawbacks: First, the current loads of cores are not considered in the core-selecting process. Second, for each request, the required bandwidth (or number of FSs) and actual length (or hops) of lightpath are not considered precise. Simply, in this scheme, the load of request is treated as the same. Moreover, the possible crosstalk causing by the adjacent cores are not considered precise. Simply, it assumes the possible crosstalk of each adjacent core is 1. The actual amount of the load of the core and the actual possible crosstalk causing by all adjacent cores should be considered precise. In the article, three new core-selecting schemes are considered, they are Minimum Load (ML) First, Minimum Conflict (MC) First, and Minimum Weight (MW) First. Together with the simple two schemes First-Fit (FF) and Random-Fit (RF), these schemes are described in the follows.

(19)

r;

(22)

Eq. (7) shows the objective function of ILP, which minimizes the utilized resources by minimizing the maximum index of allocated FS in all the cores of employed MCFs. Eq. (8) assures that exactly one path is employed for each request. Eq. (9) determines the number of necessary FSs to accommodate each traffic demand, according to the employed path. Eq. (10) determines the crosstalk according to the employed path. Eq. (11) specifies the links of the employed path for each request. Eq. (12) assures that exactly one core is utilized to accommodate the request r on each link of its employed path. Eqs. (13) and (14) specify the utilized core to accommodate the request r on each link of its employed path. Eqs. (15)–(18) allocate the required frequency spectrum. Eq. (19) determines the crosstalk on each FS. Eqs. (20) and (21) assure that the end-to-end crosstalk of each request is less than the corresponding threshold [31]. Eqs. (20) and (21) are written by because only one core on fiber is utilized to accommodate a traffic demand and also the fact that the total crosstalk among the FSs should be considered [31,36].

• FF: • •

4. Crosstalk-Aware Path Routing Algorithm (CAPRA) In this subsection, the details of the proposed Crosstalk-Aware Path Routing Algorithm (denoted as CAPRA) are described. In Section 4.1 several core-selecting schemes are described and then the main algorithm is described in Section 4.2. 4.1. Core-selecting schemes

•

In the previous study [18], Tode et al. have considered the crosstalk between cores (named as Tode method) on SDM EON. They proposed a pre-defined priority of core selection and design a crosstalk-aware routing algorithm to solve the RSA problem on SDM-EON. In the proposed scheme [18], firstly, all the costs COST (ci ), ci C of cores are initialized by zero. If core ci is selected as the first prioritized core, the cost of ci is set to , and the costs of adjacent cores of ci are incremented 5

In FF, the core is selected according to the fixed order 1 3 5 4 6 2 7 . The core 1 is selected first and then the non-adjacent core 3 is selected and examined next (shown in Fig. 3 (a)). RF: In RF, the next core selected to examine is determined randomly. ML: For the request r, the whop (r ) is the actual allocated weighted hop distance of the request. That is, whop (r ) = Nri × hop (Pri ) , if path Pri is selected as the routing path and hop (Pri) is the hop number of the path Pri . For each core (ci ), the load L (ci ) of core ci is the summation of total weighted hop distance of all lightpaths allocated to the core. Load of the core is updated when a request is allocated or released dynamically. In the ML scheme, the core is ordered according to a load of cores in increasing order. The core with the minimum load is selected as the next core for examining. Consider the status of the cores shown in Fig. 3 (b), the core-selecting order of the ML scheme is 4 → 5 → 2 → 6 → 7 → 3 → 1. MC: The conflict Conflict (ci ) of core ci is the total load of the adjacent cores of core ci . For example, cores c2, c6, and c7 are adjacent cores of core c1 (shown in Fig. 3 (a)). Consider the status of the cores (shown in Fig. 3 (b)), Conflict (c1) = L (c2 )+ L (c6) + L (c7 ) = 3 + 4 + 5 = 12. The load and conflict of the core are updated when the request is allocated or released dynamically. For the MC scheme, the core is ordered according to the conflicts of cores in increasing

Optical Fiber Technology 53 (2019) 102003

D.-R. Din and Z.J. Huang

Fig. 3. Example for core selecting schemes: (a) FF, (b) status of cores.

Fig. 4. Flowchart of the proposed algorithm.

Fig. 5. (a) NSFNet network, (b) TR for RCMLSA.

order. The core with the minimum conflict is selected as the next core for examining. Consider the status of the cores (shown in Fig. 3 (b)), the core selecting order of the MC scheme is 3 → 5 → 1 → 6 → 2 → 4 → 7. If the conflicts of the two cores are the same, then the

next core is selected randomly.

• MW: For each core (c ), the weighted function W (c ) of core c

i i i is × L (ci) + (1 ) × Conflict (ci) , where [0, 1]. defined as Consider the status of the cores (shown in Fig. 3 (b)), if = 0.3, then

6

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4.2. Main algorithm

Table 2 Simulation results for ILP and heuristic algorithm on the COST239 network. RQ

FF

RF

Tode

9 11 21

10 12 15

10 12 15

10 11 13

MC Fmax value 8 8 9

ML

MW(0.1)

ILP

10 12 14

9 9 10

7 7 7

The flowchart of the CAPRA is shown in Fig. 4 and the details of the CAPRA are shown in Algorithm 1. For the connection request r = (s, d , BWr ) , the set of candidate paths Pr is found by performing the k-shortest path algorithm. This set of paths also can be found in the preprocessing step to speed up the computing. Then, all candidate paths in Pr are examined and the respective best-transmitting parameters are found. For the selected path Pri, 1 i k , the following steps are performed:

Table 3 Simulation results for ILP and heuristic algorithm on the NSFNET network. RQ

FF

RF

Tode

10 15 20

22 24 25

26 31 33

25 27 32

MC Fmax value 21 23 24

ML

MW(0.1)

ILP

25 28 33

21 23 25

20 22 23

• The set FM (P ), which contains all feasible transmitting parameters (b, f , m) , is obtained from Table 1. • If the set FM (P ) is empty, then the path P cannot be used as the routing path. • If the set FM (P ) has at least one element, the best parameter (dei r

i r

i r

•

the weighted function of each core is shown in Fig. 3 (b) and the core selecting order of the MW scheme is 5 → 3 → 1 → 6 → 2 → 4 → 7.

noted as (bi , fi , mi ) ) which uses the minimal number of FSs (Nri computed by applying the formula (1)) is selected. The path Pri and the associated best-transmitting parameters (bi , fi , mi ) are added to the priority queue (PQ) of paths with increasing order according to the weight hop (Pri) × Nri , where hop (Pri) is the number of hops of the path Pri . This is an improvement of the previous algorithm proposed in [12] which only selects the shortest path as the routing path.

Fig. 6. Effect of k (a) FF, (b) RF, (c) Tode, (d) ML, (e) MC, and (f) MW. 7

i r

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Fig. 7. Effect of XTth : (a) FF, (b) RF, (c) Tode, (d) ML, (e) MC, and (f) MW.

Fig. 8. Simulation results of RBCMLSA for XTth =-28 (a) BR, (b) average SUR, and (c) SD of SURs.

8

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Fig. 9. The SURs of cores for all schemes with Erlang 16000 and XTth =

Fig. 10. Simulation results for RMLSA model with XTth =

Fig. 11. Simulation results for RCMLSA model with XTth =

9

28.

28 (a) BR, (b) average SUR, and (c) SD. of SURs.

28 (a) BR, (b) average SUR, and (c) SD. of SURs.

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D.-R. Din and Z.J. Huang

Fig. 12. Comparisons of BR for RBCMLSA, RCMLSA, and RMLSA problems: (a) FF, (b) RF, (c) Tode, (d) MC, (e) ML, and (f) MW.

Table 4 The reduce of BR for heuristic algorithms on the NSFNET network. Model

FF

RF

Tode

MC

ML

MW(0.1)

average

RCMLSA

reduce BR ratio

2.26% 11.95%

2.04% 7.97%

2.14% 8.41%

2.96% 15.93%

2.15% 8.40%

2.03% 10.56%

2.26% 10.54%

RBCMLSA

reduce BR ratio

2.71% 14.32%

2.77% 10.86%

2.68% 10.52%

3.70% 19.94%

2.55% 9.96%

2.66% 13.86%

2.85% 13.25%

The steps are shown in Steps 3–11 of Algorithm 1. All paths and respective transmitting parameters in PQ are selected in order and examined one-by-one; first, based upon the core-selecting scheme, a core c is selected. Then, the first-fit spectrum allocation method is applied to allocate the required FSs along with the path on the selected core c if possible. If the spectrum allocation algorithm return successfully and the XT constraint can be satisfied, then the found resources are allocated for the request. Otherwise, the next core is

selected (according to the core-selecting scheme) and examined for the same path and the same transmitting parameters. In the same core, the available frequency spectrum is examined in a first-fit manner. If all cores have been examined for the selecting path, but there is no free resource can be found along with the path, then the next candidate path (and the associated transmitting parameters) in PQ is selected and examined. If all paths in PQ are examined and there is no free resource can be allocated for these paths, then the request r is blocked. The steps

10

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are shown in Steps 13–33 of Algorithm 1. The time complexity of the CAPRA is O ( E + V log V + k B F M + k C W V ) .

from the interval [50, 150] for the NSFNET network and [50, 400] for the COST239 network, respectively. In these simulations, the number of FSs ( W ) is set to 40 and the number of candidate paths (k) is set to 3. For a larger value of k {4, 5} , it increases computation time dramatically, but the objective value cannot be reduced. These parameters are set due to the maximum numbers of variables and constraints that the solver can be applied. The XTth is set to −28 dB. For the same sets of requests, the proposed heuristic algorithm together with six core-selecting schemes is also simulated and compared. Table 2 and Table 3 show the results for the COST239 and NSFNET networks, respectively. These results show that the Fmax of the ILP method is better than other methods and heuristic algorithms. For the computation time, the ILP model takes 26,936 s to solve 20 requests on NSFNET network, it is so time-consuming and not an efficient way to solve a larger problem. On the other hand, for these sets of simulations, the proposed heuristic algorithms take less than 1 s to solve, it is more efficient than the ILP methods. Moreover, in these simulations, the MC scheme can find better values than that of the other schemes, and very close to the values of respective ILPs.

Algorithm 1 CAPRA 1: Input: G (V , E , C ), r = (s, d, BWr ) , core-selecting scheme; 2: Output: lightpaths p, parameters (b, f , m ), core c, and FS index; 3: perform k-shortest path algorithm on G to find the set Pr = {Pr1, Pr2, …, Prk } of candidate paths; 4: construct an empty priority queue PQ; 5: for (Pri

Pr ) do

6:

construct the set FM (Pri) of feasible parameters of path Pri ;

7:

if (FM (Pri)

8:

) then

select the best triple (bi , fi , mi) in FM (Pri) with the minimum number Nri of required FSs which is computed by the formula (3);

9: add path Pri (with parameters (bi , fi , mi) and weight Nri × hop (Pri )) to PQ; 10: end if 11: end for 12:// find crosstalk-satisfying allocable FSs on all possible cores

13: sort all paths in PQ in increasing order according to the weight Nri × hop (Pri) ; 14: while (PQ ) do 15: { 16: 17: 18: 19: 20:

21: 22: 23:

24: 25:

26:

5.2. Dynamic traffic

select and remove a path Pri with parameters (bi , fi , mi) from PQ; let C be the set of cores; while (C ) do select and remove a core c from C according to the core-selecting scheme; // for all possible FS blocks find free resources for the request for (z = 1, 2, …, W {

In these simulations for dynamic traffic, the arrival of requests to the network follows the Poisson distribution with connection requests per unit time and the connection-holding time obeys negative exponential distribution with a mean value of 1/ µ = 10 , the average number of required FSs of the request is f. In these simulations, the connection request is randomly generated uniformly for different pairs of nodes. The load in Erlang is defined as f × × µ and 2000 connection requests are randomly generated. These connections are simulated for each algorithm for eight different network loads. The network load is given as Erlang in {2000, 4000, 6000, 8000, 10000, 12000, 14000, 16000}. For each set of requests, 10 simulations are performed and the average results are used for comparisons. For each simulation, the number (k) of candidate paths is 3. Three performance criteria are considered in these simulations, they are: (1) Blocking Ratio (BR) which is defined as the ratio of the number of blocked connections versus the total number of requests, (2) average Spectrum Utilization Ratio (average SUR) that is the average ratio of used resources to that of the total resources of all cores, and (3) Standard Deviation (SD) of SURs. In these simulations, only the result of the NSFNET network is given since the result of the COST239 network is quite similar.

Nri + 1 ) do

if (there are Nri free FSs block [z , z + Nri core c) then

1] along with the path Pri on

compute XT of the path Pri by using formula (5) on the current network; if ( XT XTth ) then allocate resources to the path Pri on core c;

27: return path Pri with parameter (bi , fi , mi) , core c, and z; 28: end if 29: else 30: z++; 31: end if 32: } 33: end for 34: end while 35: } 36: end while 37: return block;

5. Simulation results The proposed algorithm was coded by using the Java programming language and an ad hoc simulator was constructed for the simulation. All simulations were run on a personal computer with 3.4 GHz Intel Core i7-2600 CPU, 16 GB RAM and with Windows 7 pro 64-bit operating system. The COST239 (shown in Fig. 2)) and NSFNET (shown in Fig. 5(a)) networks were used for simulations. In Fig. 5(a)) and Fig. 5(a), the number nears the link is the length (km) of the fiber. We used k = 3, C = 7 , and W = 120 as the default parameters of the network. In these simulations, the static and dynamic traffic is simulated.

5.2.1. Effect of k To know the effect of the number (k) of pre-computed paths, simulations are performed for different values of k {1, 2, 3, 4, 5, 6} and all core-selecting schemes. In these simulations, the value of XTth is set to −28. For different values of k (1 k 6), the results of BR for all core-selecting schemes are shown in Fig. 6. The results show that using greater k can get lower BR, for all core-selecting schemes. But for the cases k > 4 the BR cannot be reduced for most of the core-selecting schemes. Thus, k = 3 is the best trade-off between BR performance and computing time. The results in Fig. 6 also show that the BR increases as the network load increases.

5.1. Static traffic

5.2.2. Effect of XTth To know the effect of the crosstalk threshold, simulations are performed for different values of XTth { 18, 20, 22, 24, 26, 28} and all core-selecting schemes. In these simulations, the value of k is set to 3. The BR results of all core-selecting schemes are shown in Fig. 7. Fig. 7 shows that the case with XTth = 28 is the most rigorous and it gets the highest BR. As the value of XTth increase, the BR decreases. For the cases with XTth greater than −22, the BR cannot be reduced, this may be the reason that requests may be blocked due to lack of resource and/or violation of some resource constraints on EONs.

In this subsection, we present and discuss the results we obtained by performing the ILP optimization exploiting path-link formulation on the NSFNET and COST239 networks. To solve the ILP problems we used the software tool AMPL [37] with the IBM ILOG CPLEX Optimization Studio version 12.4 based on the branch-and-bound method [38]. For three sets with different numbers (10, 15, and 20) of static connection requests, the computation time and objective value Fmax are examined. The connection request is randomly generated uniformly for all possible pairs of nodes and the required bandwidth (Gb/s) is randomly selected 11

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D.-R. Din and Z.J. Huang

5.2.3. Effect of core-selecting schemes To know the effect of core-selecting schemes, several simulations are performed. In these simulations, the number of candidate paths for a request is k = 3, W = 120 FSs are provided for each fiber, and the value of XTth is set to −28. For the MW scheme, the cases with {0.2, 0.4, 0.6, 0.8} are examined. For different core-selecting schemes, the simulations are shown in Fig. 8. In Fig. 8(a), for the MW scheme with different values of , smaller can get lower BR. The MC and ML scheme is the special case of MW with = 0 and = 1, respectively. The results show that the MC scheme can get a lower BR than that of the ML scheme. The results also show that the MC scheme can get the lowest BR. The BR of the RF scheme can be reduced by 8.85% if the MC scheme is applied. Fig. 8(b) shows the average SURs of all cores for these core-selecting schemes. Fig. 8(b) shows that MW(0.8) can get the largest average SUR for most of the cases, and the average SURs of these schemes are very close. Fig. 8(c) shows the SD of SURs of all core-selecting schemes. The ML scheme can get the smallest SD of SURs since the load of the core is the major factor for core-selecting. The Tode and RF schemes have smaller SDs of SURs, that is, load balance can be made by these schemes, but the BR of these schemes is higher than other schemes. The MC, FF, and MW with ( = 0.2, 0.4, 0.6 ) schemes can get larger SDs of SURs. Moreover, the SD of SURs reaches a stable value as the load increases for most of the cases. The SUR of each core for all core-selecting schemes with the load 16000 and XTth = 28 is shown in Fig. 9. For the RF, Tode and ML schemes, the SUR values of cores are quite balanced. For the FF scheme, the SUR values of cores decrease according to the core-selecting order (for example, 1 → 3 → 5 → 4 → 6) and the SUR value of core 7 is almost 0. For the MC, FF and MW scheme, cores 1, 3 and 5 have higher SUR. Moreover, core 7 has the lowest SUR, due to it may cause conflict to all cores.

RCMLSA, and RMLSA problems are shown in Fig. 12. The results show that the BR of the BRCMLSA is lower than that of the RCMLSA and RMLSA. By comparing BR of the RMLSA problem, the average reduced RB and the average reduced ratio of RCMLSA and RBCMLSA problems are summarized in Table 4. The results show that the MC can get the best performance. For the RCMLSA and RBCMLSA problem, the BR can be reduced by 2.26% and 2.85%, respectively. By comparing to the BR of the RMLSA problem, for the RCMLSA and RBCMLSA problem, the reduced ratio is about 10.54% and 13.25%, respectively. 6. Conclusions In this paper, the RBCMLSA problem in MCF SDM-EONs has been defined and studied. For serving the transmission in SDM-EONs, a crosstalk-aware path routing algorithm and an ILP model have been proposed. Three core-selecting schemes are proposed in the proposed algorithm. The proposed algorithm has been examined through simulations and the results showed that the proposed algorithm could achieve a lower blocking probability than the simpler RCMLSA and RMLSA problems. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, athttps://doi.org/10.1016/j.yofte.2019.102003. References [1] G. Zhang, M.D. Leenheer, A. Morea, A survey on OFDM-based elastic core optical networking, IEEE Commun. Surv. Tut. 15 (2012) 65–87, https://doi.org/10.1109/ SURV.2012.010912.00123. [2] M. Klinkowski, K. Walkowiak, Routing and spectrum assignment in spectrum sliced elastic optical path network, IEEE Commun. Lett. 15 (2011) 884–886, https://doi. org/10.1109/LCOMM.2011.060811.110281. [3] L. Gong, X. Zhou, W. Lu, Z. Zhu, A two-population based evolutionary approach for optimizing routing, modulation and spectrum assignments (RMSA) in O-OFDM networks, IEEE Commun. Lett. 16 (2012) 1520–1523, https://doi.org/10.1109/ LCOMM.2012.070512.120740. [4] Z. Zhu, W. Lu, L. Zhang, N. Ansari, Dynamic service provisioning in elastic optical networks with hybrid single-/multi-path routing, J. Lightw. Technol. 31 (2013) 15–22, https://doi.org/10.1109/JLT.2012.2227683. [5] L. Gong, X. Zhou, X. Liu, W. Zhao, W. Lu, Z. Zhu, Efficient resource allocation for all-optical multicasting over spectrum-sliced elastic optical networks, J. Opt. Commun. Netw. 5 (2013) 836–847, https://doi.org/10.1364/JOCN.5.000836. [6] J. Yuan, Y. Fu, R. Zhu, X. Li, Q. Zhang, J. Zhang, A. Samuel, A constrained-lowerindexed-block spectrum assignment policy in elastic optical networks, Opt. Switching Networking 33 (2019) 25–33. [7] R. Zhu, Y. Zhao, H. Yang, X. Yu, J. Zhang, A. Yousefpour, N. Wang, J.P. Jue, Dynamic time and spectrum fragmentation-aware service provisioning in elastic optical networks with multi-path routing, Opt. Fiber Technol. 32 (2016) 13–22. [8] J. Yuana, Z. Rena, R. Zhub, Q. Zhanga, X. Lic, Y. Fua, A RMSA algorithm for elastic optical network with a tradeoff between consumed resources and distance to boundary, Opt. Fiber Technol. 46 (2018) 238–247. [9] D. Garrido, A. Leiva, A. Beghelli, R. Ahumada, R. Olivares, Routing, code, modulation level and spectrum assignment (RCMLSA) algorithm for elastic optical networks, in Proc. 18th IEEE Int. Conf. on Transp. Opt. Netw. (ICTON), Italy, Trento, July 2016, pp. Tu.B3.4. [10] N. Sambo, G. Meloni, F. Paolucci, F. Cugini, M. Secondini, F. Fresi, L. Pot, P. Castoldi, Programmable transponder, code and differentiated filter configuration in elastic optical networks, J. Lightw. Technol. 32 (2014) 2079–2086, https://doi. org/10.1109/JLT.2014.2319859. [11] F. Cugini, F. Paolucci, F. Fresi, N. Sambo, L. Potí, A. D’Errico, P. Castoldi, Toward plug-and-play software-defined elastic optical networks, J. Lightw. Technol. 34 (2016) 1494–1500, https://doi.org/10.1109/JLT.2015.2511802. [12] D.R. Din, M.X. Zhan, The RBCMLSA problem on EONs with flexible transceivers, in: Proc. 14th Adva. Int. Conf. on Telec. (AICT 2018), Spain, Barcelona, July 2018, pp. 14–21. [13] D.R. Din, M.X. Zhan, The RBCMLSA problem on EONs with flexible transceivers, Photon Netw. Commun. 38 (2019) 62–74. [14] M. Klinkowski, P. Lechowicz, K. Walkowiak, Survey of resource allocation schemes and algorithms in spectrally-spatially flexible optical networking, Opt. Switch. Netw. 27 (2018) 58–78, https://doi.org/10.1016/j.osn.2017.08.003. [15] H.M.N.S. Oliveira, N.L.S. da Fonseca, Routing, spectrum and core assignment algorithms for protection of space division multiplexing elastic optical networks, J. Netw. Comput. Appl. 128 (2019) 78–89, https://doi.org/10.1016/j.jnca.2018.12. 009. [16] A. Muhammad, G. Zervas, D. Simeonidou, R. Forchheimer, Routing, spectrum and

5.2.4. Comparisons with RCMLSA and RMLSA Two previous RCMLSA [9] and RMLSA [3] problems are also implemented for comparison. The transmitting parameters of the RCMLSA problem are shown in Fig. 5(b), which are the same as the best parameters of the RBCMLSA problem (selected from the central part of the Table 1) but without considering baud rates. The TR (denoted as D [f , m]) is completely determined by the f and m in this problem. The transmitting parameters of the RMLSA problem are the same as the best parameters for RCMLSA (shown in the first and second columns of Fig. 5(b)) but without FEC overhead. The TR is completely determined by the modulation format and limited by 1,292 km. For those connections whose distances of the selected paths are greater than the maximum TR, the modulation format is assumed to be BPSK and the modulation level is set to 1, i.e., ML (BPSK ) = 1. The proposed algorithm CAPRA was modified to solve the RCMLSA and RMLSA problems in SDM-EON with the proposed core-selecting schemes. The simulation results for the RMLSA and RCMLSA problem are shown in Fig. 10 and Fig. 11, respectively. In the RMLSA problem on SDM-EON, Fig. 10(a) shows that the MC scheme can get the lowest BR in light load (2000–10000) and the FF and MW schemes can get the lowest BR in heavy load. The behavior the RF, Tode, and ML schemes are quite similar and close. By comparing to the BR of the RF scheme, the FF and MW schemes can reduce BR about 5.84%. The results in Fig. 10(b) show that there is no significant difference between these schemes for average SURs. The average SUR of the MC scheme is greater than that of the other schemes in heavy load. The results in Fig. 10(c) show the SD of SURs of six core-selecting schemes. The values of MC, FF, and MW are greater than those of the other schemes. The FF scheme can get greatest SD of SURs and the ML scheme can get the lowest SD of SURs. In the RCMLSA problem on SDMEON, the simulation results are shown in Fig. 11. The results are quite similar to that of the RMLSA problem. For each core-selecting scheme, the results of BR for the RBCMLSA, 12

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