Manycast routing, modulation level and spectrum assignment over elastic optical networks

Optical Fiber Technology 36 (2017) 317–326

Contents lists available at ScienceDirect

Optical Fiber Technology www.elsevier.com/locate/yofte

Regular Articles

Manycast routing, modulation level and spectrum assignment over elastic optical networks Xiao Luo a,⇑, Yang Zhao a, Xue Chen a, Lei Wang a, Min Zhang a, Jie Zhang a, Yuefeng Ji a, Huitao Wang b, Taili Wang b a State Key Lab of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), P.O. Box 128, #10 XiTuCheng Road, HaiDian District, Beijing 100876, China b ZTE Corporation, HaiDian District, Beijing 100191, China

a r t i c l e

i n f o

Article history: Received 1 December 2016 Revised 6 May 2017 Accepted 8 May 2017

Keywords: Manycast Routing, modulation level and spectrum assignment (RMLSA) Integer linear programming (ILP) Elastic optical network (EON)

a b s t r a c t Manycast is a point to multi-point transmission framework that requires a subset of destination nodes successfully reached. It is particularly applicable for dealing with large amounts of data simultaneously in bandwidth-hungry, dynamic and cloud-based applications. As rapid increasing of traffics in these applications, the elastic optical networks (EONs) may be relied on to achieve high throughput manycast. In terms of finer spectrum granularity, the EONs could reach flexible accessing to network spectrum and efficient providing exact spectrum resource to demands. In this paper, we focus on the manycast routing, modulation level and spectrum assignment (MA-RMLSA) problem in EONs. Both EONs planning with static manycast traffic and EONs provisioning with dynamic manycast traffic are investigated. An integer linear programming (ILP) model is formulated to derive MA-RMLSA problem in static manycast scenario. Then corresponding heuristic algorithm called manycast routing, modulation level and spectrum assignment genetic algorithm (MA-RMLSA-GA) is proposed to adapt for both static and dynamic manycast scenarios. The MA-RMLSA-GA optimizes MA-RMLSA problem in destination nodes selection, routing lighttree constitution, modulation level allocation and spectrum resource assignment jointly, to achieve an effective improvement in network performance. Simulation results reveal that MA-RMLSA strategies offered by MA-RMLSA-GA have slightly disparity from the optimal solutions provided by ILP model in static scenario. Moreover, the results demonstrate that MA-RMLSA-GA realizes a highly efficient MA-RMLSA strategy with the lowest blocking probability in dynamic scenario compared with benchmark algorithms. Ó 2017 Elsevier Inc. All rights reserved.

1. Introduction With the dramatic growth of high-speed network traffics in various modulation formats and diverse bitrates, the future optical network tends to be dynamic, heterogeneous and unpredictable. This trend calls for innovations in optical communication systems, i.e., rising optical switching and transmission technologies to satisfy multi-granularity, cost-efficiency and bitrate flexibility demands. To address this issue, the elastic optical networks (EONs) [1,2] are proposed to realize flexible and efficient spectrum allocation with much finer spectrum granularity (e.g. 6.25 GHz or 12.5 GHz). Specially, EONs provide just-enough bandwidth for arriving traffic demands dynamically, which leads to the better

⇑ Corresponding author. E-mail address: [email protected] (X. Luo). http://dx.doi.org/10.1016/j.yofte.2017.05.005 1068-5200/Ó 2017 Elsevier Inc. All rights reserved.

spectrum assignment flexibility and the higher network resource utilization than traditional wavelength-division multiplexing (WDM) optical networks followed the ITU-I fixed frequency-grid standard [3]. In EONs, one of the fundamental networking problems is routing and spectrum assignment (RSA) [4]. Considering the trade-off between spectral efficiency and transmission reach by dynamic adjusting modulation formats so that network infrastructure can be optimally used, the RSA problem in EONs is extended to a routing, modulation level and spectrum assignment (RMLSA) problem [5]. As an upgrade of the routing and wavelength assignment (RWA) in traditional WDM networks, the RSA/RMLSA in EONs should keep spectrum contiguity constraint which states the allocated frequency slots (FS’s) on one optical fiber stay contiguously on frequency axis. Moreover, without wavelength conversion, light path must use the same FS’s in each fiber link along the entire route which is regarded as spectrum continuity constraint. This

318

X. Luo et al. / Optical Fiber Technology 36 (2017) 317–326

constraint is the same as that applied to WDM networks. As the feature of flexible bandwidth adjustment with a fine granularity and newly spectrum contiguity constraint, the existing RWA algorithms cannot be implemented to RMLSA problems directly. RMLSA problem is known as NP-complete [6] and usually considered in two types, which are static scenario and dynamic scenario. Static scenario is network planning with a set of requests given ahead of time, nevertheless, dynamic scenario is network provisioning along with requests arriving continuously. At present, a large number of literatures have addressed both static and dynamic RSA/RMLSA problems in EONs [5–10]. However, most of them did not consider point-to-multipoint communication which has become a necessary communication scheme to efficiently support emerging services and applications in EONs. It is known that multicast is a typical communication scheme where a single source transmits data to a number of destinations [3]. In this paper, we investigate a newly communication paradigm called manycast [11,12] in EONs, which can be treated as a pointto-multipoint communication between source node and a subset of destination nodes. By contrast to multicast, manycast has freedom to choose different destination nodes depending on the current state of network, resulting in the better demand performance and the higher network resource utilization. Since the feature of high flexibility in destination nodes selection, the manycast transmission scheme has become an essential communication framework to support the newly network services and applications emerging in cloud/grid computing and e-Science [13]. As a specific example for application of manycast, we refer to inter datacenter distributed backup scenario. There is a large amount of data stored in each datacenter locally so that can be timely accessed by users or servers. Inter datacenter distributed backup happens in a period of time, to against losses from natural disaster, optical fiber damage and network failure. When data backup among multiple datacenters begins, we can utilize manycast communication scheme to construct a manycast light-tree by choosing a subset of destination datacenters to complete data transmission simultaneously. Selection metrics of destination datacenters can depend on backup demands, which may be the shortest physical transmission distance, the lowest transmission cost, the highest network resource utilization and etc. For this type of inter datacenter backup, all candidate destination datacenters can be employed to run the same backup operations and once a specified quantity of them have stored backup data successfully, the inter datacenter backup is complete. Although multicast communication scheme can adapt to this scenario as well, multicast cannot select destination datacenters flexibly based on the current network status and there is no need to store backup data to all candidate destination datacenters. The plenty of network flows may be occupied to data backup transmission which reduces network efficiency and substantial backup data stored in every destination datacenter consumes massive storage resources. Therefore, manycast is a necessary and efficient communication paradigm under this inter datacenter distributed backup scenario with high efficiency transmission. Previously, numerous literatures have investigated multicast RMLSA problem and proposed various approaches to solve it with different optimization objectives in EONs [3,14–16]. Specifically, static multicast RMLSA problem in EONs was solved in [17] with two ILP models and an effective heuristic, where multicast candidate tree model has a better performance in spectrum usage and applicability. For dynamic multicast RMLSA problem, the impairment- and splitting-aware [18,19] and the fragmentationaware [20] multicast RMLSA approaches were proposed and obtained excellent performances with each special objective.

Moreover, multicast transmission in EONs with multicastincapable switches was studied in [21] and corresponding heuristic algorithm was proposed to improve spectrum efficiency. In [22], M. Zeng et al. optimized multicast RSA and virtual network function (VNF) jointly in an inter-datacenter EON with less cost and they further considered control plane in inter datacenter EONs with dynamic multicast sessions in [23]. The proposed multicast-tree rearrangement algorithms can reduce request blocking probability effectively with the least light path rerouting. Nevertheless, all mentioned multicast ILP models and heuristic algorithms for multicast RMLSA under different scenarios cannot be applied to manycast communication scheme compatibly due to extra destination nodes selection constraint in manycast. Different destination nodes combinations obviously influence the manycast routing, modulation level and spectrum assignment (MA-RMLSA) solutions and make MA-RMLSA problem more complicated. The concept of manycast was first proposed in [12] which used to detect potential access conflicts and prevent both processes from updating data simultaneously in distributed database system. Manycasting over optical burst-switched (OBS) networks has been studied in [24–26], with main challenge of providing reliability despite random contentions [13]. These literatures focus on distributed routing or unicast routing algorithms with dynamic traffic to provide reliable manycast. As different network properties between OBS networks and EONs, MA-RMLSA in EONs mainly considers about efficient network resource utilization and request blocking probability reduction. In addition, manycast routing and wavelength assignment (MA-RWA) problem has been investigated already [27,28]. The literature [13] was the first paper to investigate MA-RWA problem in WDM networks. The proposed heuristics observably improved network performance in required wavelengths reduction over realistic networks. However, the MA-RWA scheme in [13] has some inadequacies to implement in EONs, such as lacking of modulation level selection and spectrum assignment constraints. Owing to unique spectrum flexibility in EONs, supporting manycast communication scheme has essential difference compared with above manycast scenarios and captures research interests recently. So far, there are few studies about MA-RMLSA problem in EONs. The energy-efficiency MA-RMLSA strategy was proposed by green-energy aware destination nodes selection in [29]. While the authors poured more attention to network energy conservation, there is still room for improvement in spectrum resource utilization. In this paper, we focus on MA-RMLSA in EONs considering high network resource utilization. The main contributions of this paper are as follows. First, an ILP model is designed to achieve the optimal solution to MA-RMLSA problem in static EONs planning. Second, since ILP model has high computation complexity and lacks of scalability, a heuristic algorithm called manycast routing, modulation level and spectrum assignment genetic algorithm (MA-RMLSA-GA) is proposed to apply for large scale networks. Particularly, destination nodes selection, routing light-tree constitution, modulation level allocation and spectrum resource assignment are considered integrally in MA-RMLSA-GA to reach a joint optimization. Third, we perform extensive numerical experiments to compare ILP model and MA-RMLSA-GA in static EONs planning, as well as to evaluate the performance of MA-RMLSA-GA in dynamic EONs provisioning. To the best of our knowledge, this is the first paper that focuses on MA-RMLSA problem solving by genetic algorithm (GA) based heuristic algorithm in EONs. The rest of this paper is organized as follows. Section 2 defines MA-RMLSA problem. In Section 3, we describe our ILP formulation. Then, the proposed MA-RMLSA-GA is discussed in Section 4. And in

319

X. Luo et al. / Optical Fiber Technology 36 (2017) 317–326

Section 5, performance evaluations with numerical simulations are presented. Finally, Section 6 summarizes the paper. 2. Problem description 2.1. Network model assumptions

Optical Amplifier

...

BV WSS

Coupler

Splitter

BV WSS

Optical Amplifier Input Fiber 2

Coupler

...

Input Fiber 1

Splitter

The physical network topology is structured as a graph G(V, E) in EONs, where V denotes node set and E denotes fiber link set, respectively. Every two adjacent nodes a and b are connected by two directed links in opposite directions, denoted by (a, b) for one from node a to node b and (b, a) for the one from node b to node a. The total number of FS’s in one fiber link is denoted as F. For each manycast request, we assume it is routed by light-tree [30] without spectrum conversion that starts at source node and arrives at all of selected destination nodes. And all nodes in EONs are able to split an input optical signal to any number of output ports which achieved by multicast-capable optical cross connect (MC-OXC). We illustrate switch architecture of the MC-OXC we use in Fig. 1, which is adapted from [19]. The input manycast optical signals are switched in bandwidth variable wavelength selective switch (BV-WSS). Then manycast optical signals are split by splitters while unicast optical signals can directly pass through. Replicas of input signals are switched from optical switch where wavelengths destined to their corresponding fiber are passed while the rest are blocked, to couplers where all optical signals are combined to destined fibers.

Optical Switch

Output Fiber 1

Output Fiber 2

Coupler

...

Input Fiber 3

Splitter

Optical Amplifier

BV WSS

Output Fiber 3

2.2. Manycast routing, modulation level and spectrum assignment procedures 1) Manycast destination node selection and routing light-tree constitution We define a manycast request as MaRi ¼ fsi ; Di ; ki ; C i g, where integer i is manycast request ID. si is source node of MaRi , and Di ¼ fdi;1 ; di;2 ; . . . ; di;jDi j g is candidate destination nodes set of MaRi where di;j 2 Di , j = 1, 2, . . . |Di|. ki (ki 6 jDi j) is the number of destination nodes must be connected to source node and C i denotes requested capability. The example of manycast routing scheme depends on light-tree is shown in Fig. 2. In this six nodes network topology, there are three manycast requests that they all have three candidate destination nodes and should reach two of them arbitrarily. The Fig. 2 illustrates several possible manycast light-trees combinations for request 1, 2 and 3 in three different colors. Considering different manycast destination nodes combinations for these three requests, each request has 3 possible destination nodes combinations that leads to 27 possible transmission schemes in total. With the increment of network scale, the number of candidate routing light-trees for each manycast request is significantly rising that brings on a great deal of available MA-RMLSA schemes with different network performances. Hence, it’s necessary and important to ensure the optimal destination nodes combination is selected in manycast transmission to achieve efficient network performance. 2) Modulation assignment

...

...

BV WSS ...

...

... Client Signals

Data Rate/Bandwidth Variable Transponder

Fig. 1. Multicast-capable optical cross connect based on the non broadcast and select architecture.

allocation

and

spectrum

resource

After manycast light-tree construction, we allocate modulation level and spectrum resource for each manycast request. We assume the main impairments in MA-RMLSA are caused by transmission and we consider distance-adaptive modulation level allocation in EONs which depends on distance of the longest light branch in manycast light-tree. In addition, to reach the highest spectral efficiency, we always allocate the highest modulation level for manycast light-tree as long as transmission distance permits [19]. There are four available modulation formats, which are binary phase-shifted keying (BPSK), quadrature phase shift keying (QPSK), 8 quadrature amplitude modulation (8-QAM) and 16-QAM. We assume modulation level mi = 1, 2, 3 and 4 represents for BPSK, QPSK, 8-QAM and 16-QAM, respectively. The mapping relationships between modulation format and the maximum transmission distance are revealed in Table 1 [31]. Besides, we suppose that bandwidth of each FS stays the same and provides a capacity of C BPSK when using BPSK as modulation format. The capacity of each FS under different modulation formats is mi  C BPSK . As a consequence, the number of continuous FS’s assigned to manycast light-tree can be calculated as follows.


Ni ¼

Coupler

level

Ci mi  C BPSK

 ð1Þ

where Ni is the number of FS’s assigned to MaRi . For instance, an incoming MaRi demands capacity Ci = 45 Gbits/s and the longest transmission reach in routing light-tree of MaRi equals 3400 km. The highest modulation level can be assigned to request is mi = 2 (QPSK) since transmission reach of QPSK exceeds 3400 km and that of 8-QAM less than 3400 km which refers to Table 1. Accordingly, the number of required FS’s is two, i.e., N i ¼ 2, calculated by Eq. (1). 3. ILP formulation In this section, we formulate an ILP model to solve static MARMLSA problem in EONs which is constructed by sub-problems

320

X. Luo et al. / Optical Fiber Technology 36 (2017) 317–326

Fig. 2. The example of different manycast light-tree combination schemes.

Table 1 The relationship between modulation format and transmission reach. Modulation format

Transmission reach

BPSK QPSK 8-QAM 16-QAM

10,000 km 5000 km 2500 km 1250 km

max

 lmi : Integer variable that represents the maximum transmission distance under modulation level mi .  N mi : Integer variable that represents the number of FS’s allocated to light-tree of manycast request MaRi under modulation level mi . Objective: i

Minimize n ¼ maxi2I f w of destination nodes selection, routing light-tree constitution, modulation level allocation and spectrum resource assignment. Notations:  G(V, E): Network topology, where V and E are sets of nodes and links in network, respectively.  MaRi: The manycast request with ID i.si: The source node of manycast request MaRi .  Di: The candidate destination nodes set of manycast request MaRi .  ki: The number of destination nodes should be reached by manycast request MaRi .  Ci: The capacity of manycast request MaRi .  di,j: The jth destination node of manycast request MaRi , where j = 1, 2, . . .,jDi j.  F: The total number of FS’s in a fiber link.  I: The set of all manycast requests.  l(a,b): The length of link (a, b) in kilometers, where (a, b) 2 E.

The objective of ILP model is to minimize the maximum FS index number n after serving all manycast requests in EONs. The smaller n means the less number of FS’s are used to serve the same number of manycast requests and also leads to a more balanced spectrum resource allocation for the whole network. Subject to the following constraints: 1) Destination nodes selection constraint:

X di;j 2Di

Hidi;j ¼ ki ; 8i 2 I; j ¼ 1; 2; . . . ; jDi j:

2) Routing light-tree constitution constraints:

X i X i /ðsi ;aÞ  /ða;si Þ P 1; 8i 2 I; X i X i /ðb;aÞ  /ða;bÞ P 0; 8b 2 V; b–si ; b–di;j ; 8i 2 I;

Hidi;j :

a2V

Boolean variable that equals 1 if the di;j is selected as a des-



/iða;bÞ :

Boolean variable that equals 1 if link (a, b) is used by

manycast request MaRi , and 0 otherwise.  ui,t: Boolean variable that equals 1 if manycast request MaRi and manycast request MaRt use the same fiber link, and 0 otherwise.  wi,t: Boolean variable that equals 1 if the first FS index number of manycast request MaRi is lower than the first FS index number of manycast request MaRt , and 0 otherwise. d

i;j : Boolean variable that equals 1 if link (a, b) is used to serve  dða;bÞ

the path to destination node di;j of manycast request MaRi , and 0 otherwise.  mi: Integer variable that represents modulation level allocated to manycast request MaRi . i f z:



Integer variable that represents index number of the first FS used by manycast request MaRi .



i f w:

Integer variable that represents index number of the last FS i

used by manycast request MaRi .lmax : Integer variable that represents length of the longest branch in light-tree of manycast request MaRi .

ð4Þ

a2V

Variables:

tination node for manycast request MaRi , and 0 otherwise.

ð3Þ

Eq. (3) ensures that ki out of Di destination nodes are selected for each manycast request.

a2V



ð2Þ

ð5Þ

a2V

X i X i /ðdi;j ;aÞ  /ða;di;j Þ P 1; 8i 2 I: a2V

ð6Þ

a2V

Eq. (4) is flow constraint for source node in each manycast light-tree which stipulates there should be output flow(s) and no incoming flow. Eq. (5) ensures if there is an incoming flow to the intermediate node in each manycast light-tree, there should be output flow(s) from this node. And Eq. (6) ensures there is only one incoming flow to each destination node in each manycast light-tree. d

i;j /iða;bÞ P dða;bÞ ; 8ða; bÞ 2 E; 8di;j 2 Di ; 8i 2 I;

ð7Þ

uði;tÞ P /iða;bÞ þ /tða;bÞ  1; 8ða; bÞ 2 E; 8i; t 2 I:

ð8Þ

Eq. (7) ensures the common links that shared by light paths to different destination nodes in one manycast light-tree are aggregated into one link. Eq. (8) ensures all common links between two manycast light-trees are handled. 3) Modulation level allocation constraints:

321

X. Luo et al. / Optical Fiber Technology 36 (2017) 317–326

X

d

i

i;j dða;bÞ  lða;bÞ 6 lmax ; 8i 2 I; 8di;j 2 Di ;

ð9Þ

ða;bÞ2E

i

max

lmax 6 lmi ; 8i 2 I;

ð10Þ

X Nmi  /iða;bÞ 6 F; 8ða; bÞ 2 E:

ð11Þ

i2I

Eq. (9) ensures the distance of all branches in each manycast lighttree is no longer than distance of the longest branch. And Eq. (10) ensures all branches in each manycast light-tree can be reached under selected modulation level. Eq. (11) ensures there is enough spectrum resource (FS’s) on the selected links for each manycast light-tree under modulation level mi . 4) Spectrum resource assignment constraints i

i

f w  f z þ 1 P N mi ; 8i 2 I;

ð12Þ

wi;t þ wt;i ¼ 1; 8i; t 2 I; i–t;

ð13Þ

t

i

ð14Þ

i

t

ð15Þ

f w  f z þ 1 6 F  ð1 þ wi;t  uði;tÞ Þ; 8i; t 2 I; i–t; f w  f z þ 1 6 F  ð2  wi;t  uði;tÞ Þ; 8i; t 2 I; i–t; i

i

0 < f z 6 f w 6 F; 8i 2 I:

ð16Þ

Eq. (12) ensures the number of FS’s assigned to each manycast request can satisfy the capacity of it. Eqs. (13), (14) and (15) ensure that the common link(s) of two different light-trees for manycast requests MaRi and MaRt do not have overlapped spectrum resource. And Eq. (16) ensures index number of the first and the last FS used by manycast request within range of the total number of FS’s in each fiber link. 4. Heuristic approach It is known that ILP model is inefficient to solve out an optimum solution timely under large and scalable problems. In this section, we propose a MA-RMLSA-GA to improve spectrum resource utilization and network traffic load balance. The flowchart of MARMLSA-GA is demonstrated in Fig. 3, and the detailed operation descriptions are in the following sub-sections. The GA is a search heuristic that mimics natural evolution in real world [32]. It splits problem into a set of sub-problems which is similar to a chromosome contains a set of genes and finds a feasible solution for each of them. The general GA operations are given in five steps as shown in Fig. 3, i.e., population generation, fitness value calculation, chromosome selection, gene crossover and gene mutation. The first step generates a set of chromosomes (candidate solutions for problem) as an initial population. Then fitness value of each chromosome is calculated by fitness function, the fittest chromosomes are selected that based on fitness value to update the population. The fourth and fifth steps are gene level operations, which randomly occur on some/all genes in selected chromosomes. At last, GA repeats above five steps until the population reaches termination condition. 4.1. Gene encoding for manycast request Gene encoding procedures are presented in Algorithm1, Phase1.   ki For each manycast request MaRi , we decompose it into jDi j   ki combinations for all canmulticast requests since there are jDi j didate destination nodes. Multicast requests are denoted as

Fig. 3. The flowchart of MA-RMLSA-GA.



 ki , where Di;g sel represents jDi j the gth candidate destination nodes combination for manycast request MaRi . Then we decompose each multicast MuRi;g into ki unicast requests, which are denoted as

MuRi;g ¼ fsi ; Di;g sel ; C i g, g ¼ 1; 2; . . . ;

UnRqi;g ¼ fsi ; di;j ; C i ; di;j 2 Di;g sel g; q ¼ 1; 2; . . . ; ki .

After

manycast

request decomposition, we randomly assign a routing light path PLp si ;di;j for each si - di;j pair which is indentified by a light path index LpIndex. Note that we calculate all possible light paths between each node pair in network beforehand and assign each path a unique index number. Candidate modulation level mqi;g is selected by the transmission distance of unicast light path. In order to follow spectrum continuity constraint, the final modulation level mi for all unicast requests should be unified and selected from all candidate modulation level mqi;g to guarantee transmission of all unicast requests. The number of contiguous FS’s for each unicast request UnRqi;g is determined by Eq. (1), where we define a contini

i

uous FS’s set Bðf z ; f w Þ to denote specific spectrum resource allocated to each unicast request. The detailed modulation level selection and spectrum resource assignment regulations are described in Section 2.2. Finally, an encoded gene is formed as i

i

geneqi;g ¼ fLpIndex; mi ; Bðf z ; f w Þg. Encoding all arriving manycast requests as a set of genes, we call it a chromosome, denoted as chr. By changing unicast light paths randomly in some or all genes, we can constitute tremendous different chromosomes. And the set of chromosomes is regarded as a population Pop in GA.

322

X. Luo et al. / Optical Fiber Technology 36 (2017) 317–326

4.3. Genetic operations Algorithm 1 phase 2 demonstrates operations of MA-RMLSA-GA in chromosomes selection, gene crossover and mutation during population evolution. We design selection operation with roulette wheel algorithm [33] to get all chromosomes we need which randomly selects chromosomes from population Pop. Particularly, each chromosome has its selected probability according to fitness value. After chromosomes selection, crossover operation initiates. We design the crossover as a multi-points gene level operation to chromosome pairs with crossover rate tc . At crossover points in each chromosome pairs, genes randomly exchange. Furthermore, mutation operation modifies genes in selected chromosomes according to mutation rate tm . It randomly changes the original routing path to another available routing path in genes while modulation level and occupied spectrum resource are re-calculated after routing path changing. In Algorithm 1, the iteration of population constitution in phase 1 with the complexity of OðjIj2 Þ, where I is the total number of manycast requests. In phase 2, the iteration of population evolution with the complexity of OðlogjchrjÞ where jchrj denotes the total number of genes in one chromosome. For the worst case, the loop at line 17 will be run U times, where U implies the maximum iteration number. Thus, the computational complexity of Algorithm 1 is OðjIj2 þ UlogjchrjÞ. 4.4. GA convergence condition To evaluate convergence performance of GA, we utilize the algorithm diversity to reflect GA convergence degree which is formulated as follows [31]: 4.2. Fitness function

Div Pop ¼

The fitness value is an evaluation criterion for superiorityinferiority of a candidate GA solution. To optimize MA-RMLSAGA evolution process, the fitness function is a safeguard for right evolution direction. Different fitness functions make GA suit for different scenarios. In this paper, we involve two types of fitness function which are used under EONs with static manycast traffic and with dynamic manycast traffic, respectively. Under static manycast traffic scenario, we define that fitness function is the same objective as ILP model to improve spectrum resource utilization and traffic load balance in EONs, which is to minimize the maximum index number of used FS’s on links after serving all manycast requests. The fitness function can be expressed as follows.

F fitness ¼ n

ð17Þ

The smaller FS index number leads to a more efficient MARMLSA solution under static scenario. Thus, we assume that the lower fitness value causes the higher survival rate for each chromosome in MA-RMLSA-GA. Under dynamic manycast traffic scenario, network performance is closely associated with the number of blocked requests. Hence, the fitness function is defined as follows.

F fitness ¼ n þ Q  nblocked þ nblocked

ð18Þ

The Eq. (18) is adapted from [31], where n is defined in Eq. (2). Q is a constant larger than the total number of FS’s in one fiber link, and nblocked is the number of blocked manycast requests in one time interval. When requests blocked, the weight of nblocked increases that changes the aim of fitness function to mainly reduce the number of blocked requests, otherwise, fitness function is the same as the static one to focus on efficient spectrum allocation with no request blocked.

jPopj1 jPopj X X 2 jPopjðjPopj  1Þ chr ¼1 chr ¼chr 1

2

1 þ1

dðchr1 ; chr2 Þ jchrj

ð19Þ

where dðchr1 ; chr2 Þ is a function that can return the number of different genes between chromosomes chr1 and chr2 . And we can obtain a threshold value by simulating GA in a large number of generations. In this paper, we assume MA-RMLSA-GA is convergence if Div Pop is lower than threshold value with a certain times. 5. Performance evaluation In this section, we evaluate the proposed MA-RMLSA-GA in both static and dynamic manycast traffic scenarios. Firstly, MARMLSA-GA and benchmark algorithms are compared with ILP model under small scale static scenario measured by spectrum resource utilization. Then MA-RMLSA-GA and benchmark algorithms are compared under large scale static scenario to further evaluate efficiency of MA-RMLSA-GA. In addition, we evaluate performance of MA-RMLSA-GA under dynamic scenario, which mainly concerns about request blocking probability. Request blocking probabilities are appraised as well to demonstrate influences of the parameters in manycast request under dynamic scenario. 5.1. Benchmark algorithms To obtain a distinct and convictive simulation results, we design two general MA-RMLSA algorithms as benchmarks, which are based on the shortest path tree (SPT) algorithm [34] and the minimal spanning tree (MST) algorithm [35], respectively. As the variation of fundamental SPT algorithm, the manycast shortest path tree and first fit [36] spectrum assignment algorithm (MA-SPTFFSA) essentially has similar operation mechanism, which treats a manycast request as multicast one and only chooses the closest

X. Luo et al. / Optical Fiber Technology 36 (2017) 317–326

k nodes out of all candidate destination nodes to constitute the shortest path manycast light-tree. Modulation level is adaptively selected by transmission distance with the highest spectral efficiency and just-enough continuous FS’s are assigned by first fit mechanism. The manycast minimal spanning tree and first fit spectrum assignment algorithm (MA-MST-FFSA) is to select the minimum cost (hop counts) manycast light tree by searching all candidate destination nodes combinations, and the following procedures are the same as MA-SPT-FFSA. Moreover, we implement a MA-RMLSA algorithm with layered MST (MA-RMLSA-LMST), based on integrated multicast-capable RSA algorithm with layered MST (MC-RSA-LMST) [37]. Algorithm procedure of MA-RMLSA-LMST is to utilize the rules of layered auxiliary graph proposed in [37] to layer network topology as a number of sub-network topologies. And all candidate manycast light-trees are calculated by MST algorithm for different destination nodes combinations. The modulation level and the number of FS’s are calculated for each candidate manycast light-tree which follows the rules mentioned in Section 2.2. Search for all candidate light-trees under each sub-network topology until satisfactory FS’s are allocated to one of candidate light-trees. 5.2. EON planning with static manycast traffic To evaluate MA-RMLSA-GA with static manycast traffic, we firstly compare it with ILP model and three benchmark algorithms in 8-node network topology as shown in [29]. We also simulate MA-RMLSA-GA and three benchmark algorithms in 14-node NSFNET network topology [31] to evaluate algorithm performance in more complex and realistic environment. The aim of this static scenario is to optimize all manycast requests in an acceptable time period to reach a better balanced network resource allocation. Hence, the main significant parameters are the maximum FS index number n and the algorithm running time T measured in seconds. We use IBM ILOG CPLEX optimizer [38] to simulate ILP model, meanwhile, MA-RMLSA-GA and three benchmark algorithms are simulated by C++ programming to construct network scenario directly. The configuration of simulation computer is 3.30 GHz Inter Core, i5-4590 CPU with 4.00 GB RAM. To get a more realistic simulation condition, we assume that network is at C waveband which means there is almost 4.45THz spectrum resource on each optical fiber, i.e., there are about 356 FS’s while capacity of each FS is 12.5 GHz. Furthermore, all manycast requests have five candidate destination nodes, of which two, three, four and five destination nodes should be reached, respectively (i.e., jDi j ¼ 5, ki = 2, 3, 4, 5). Table 2 shows simulation parameters for static manycast traffic scenario. Table 3 shows simulation results in 8-node network topology with known |I| = 5. We run simulation twenty times to get average value, with randomly constructing manycast requests at each time. The results indicate ILP model can obtain the smallest n which means it can provide the most efficient MA-RMLSA solutions. Nonetheless, the drawback of highly operation complexity induces tremendous running time (T) consumption. As Table 3 shown, MARMLSA-GA provides excellent MA-RMLSA solutions (i.e., the values of n are slightly disparity with solutions solved by ILP model and better than values offered by three benchmark algorithms). Although three benchmark algorithms have deficient performance by contrast in network resource load balance with the larger n values, primitive computational complexity brings on the less running time. The Fig. 4 shows convergence performance of MA-RMLSA-GA under |I| = 50, |Di| = 5, ki = 2. The value of algorithm diversity is calculated by Eq. (19) mentioned in Section 4.4. We can observe that MA-RMLSA-GA has converged within 30 evolution iterations. It is demonstrated that high efficiency of MA-RMLSA-GA in solving static MA-RMLSA problem.

323

Table 2 Simulation parameters for MA-RMLSA-GA in static scenario. C i , capability range of each manycast request CBPSK , the smallest capability of FS Threshold for GA convergence judgment Crossover rate tc Mutation rate t m

10-100Gbits/s 12.5Gbits/s 0.12 0.5 0.05

Fig. 5(a) and (b) depict simulation results on the maximum FS index number n in 14-node NSFNET by accordingly comparing small and large number of arriving manycast requests (jDi j ¼ 5, ki ¼ 3). As presented in Fig. 5 (a) and (b), MA-RMLSA-GA can provide the best MA-RMLSA solutions with the minimum n values which reduces the maximum FS index number in 10.45%–23.45% and 1.9%–9.69% compared with solutions provided by MARMLSA-LMST under small and large request scales, respectively. In Fig. 5(a), optimization capability of MA-RMLSA-GA increases with the increment of request number. It is reflected that MARMLSA-GA is high efficiency when network resource is sufficient. And in Fig. 5(b), on account of available network resource decreases rapidly with request number increasing, MA-RMLSA solutions of these four algorithms approaching along with the growth of request number. Furthermore, we evaluate performance of MA-RMLSA-GA under low and high manycast request capacity (jDi j ¼ 5, ki ¼ 3), as presented in Fig. 6(a) and (b). MA-RMLSA-GA can provide the best MA-RMLSA solutions under both low and high request capacity which decreases the maximum FS index number in 16.87%–23.06% and 14.24%–23.89% compared with solutions provided by MA-RMLSA-LMST, respectively. By contrasting simulation results in Fig. 6(a) and (b), the optimal performance of MARMLSA-GA becomes more obvious with request capacity increasing. So it is clear that MA-RMLSA-GA is more suitable for solving network planning with high request capacity compared to benchmark algorithms. 5.3. EON provisioning with dynamic manycast traffic In this scenario, we evaluate performance of MA-RMLSA-GA under 14-node NSFNET network topology and 28-node US Backbone network topology [14] with dynamic manycast traffics. Manycast requests are formed a Poisson process with average arrival rate k and service time of each request is formed a exponential distribution with mean value l. Traffic load for the whole network can be denoted as k=l Erlangs. We set traffic load varies between 150–600 Erlangs by changing service time from 5 up to 50. The number of candidate destination nodes is four, of which three should be reached (i.e., jDi j ¼ 4, ki ¼ 3). Furthermore, the rest of simulation parameters are the same values as shown in Table 2. As results shown in Fig. 7(a) and (b), it’s obvious that MARMLSA-GA reaches the lowest request blocking probabilities under all simulation traffic loads. This is because MA-RMLSA-GA optimizes MA-RMLSA solutions in destination nodes selection, routing light-tree constitution, modulation level allocation and spectrum resource assignment jointly by selecting chromosomes with the smallest fitness value. Although MA-RMLSA-LMST solves MARMLSA problem in an integrated way as well, the searching scale of manycast light-trees is limited in set of candidate MSTs which causes performance variation. For MA-MST-FFSA and MA-SPTFFSA, only destination nodes and routing light-tree selection can be optimized by shorten light-tree, resulting in higher request blocking probabilities. The request blocking probability reductions of MA-RMLSA-GA are 59.69%–83.75%, 49.82%–78.89% and 13.33%–45.14%, compared to MA-MST-FFSA, MA-SPT-FFSA and MA-RMLSA-LMST under NSFNET network, respectively. And the similar comparison results under US Backbone network are

324

X. Luo et al. / Optical Fiber Technology 36 (2017) 317–326

Table 3 Simulation results under static scenario. k 2 3 4 5

n T n T n T n T

ILP

MA-RMLSA-GA

MA-MST-FFSA

MA-SPT-FFSA

MA-RMLSA-LMST

6.267 976.108 6.548 1625.641 7.040 3092.263 7.851 5418.057

7.307 0.021 7.961 0.025 8.733 0.030 10.415 0.033

11.258 0.0032 12.901 0.0043 14.534 0.0050 15.805 0.0057

11.090 0.0023 12.769 0.0031 14.378 0.0035 15.714 0.0052

9.725 0.0056 10.881 0.0072 12.211 0.0084 13.902 0.0093

Fig. 4. Convergence performance of MA-RMLSA-GA.

16.43%–62.88%, 21.58%–72.99% and 12.26%–43.84%. Notably, the simulation results trends of MA-MST-FFSA and MA-SPT-FFSA as illustrated in Fig. 7(a) and (b) have changed. It can be analyzed from the difference of network topologies and essence of two algorithms. The feature of 14-node NSFNET topology is less nodes with longer transmission distance while 28-node US Backbone topology is just in opposite. Light-tree constitution with the shortest paths and the minimum hop counts are essences of MA-SPT-FFSA and

MA-MST-FFSA, respectively. Hence, the feature of 14-node NSFNET network topology makes MA-SPT-FFSA can set up a SPT more efficient and bring on a better network performance. The similar reasons can be obtained for MA-MST-FFSA in US Backbone network topology. In dynamic scenario, we also simulate MA-RMLSA-GA in different numbers of destination node k (D = 5, k = 2, 3, 4, 5) and different numbers of candidate destination nodes D (k = 3, D = 3, 4, 5, 6) to evaluate impact of these two parameters. We compare MARMLSA-GA with MA-RMLSA-LMST under 28-node US Backbone network topology due to MA-RMLSA-LMST has a better performance than the other two benchmark algorithms. We can observe that, with the rise of k, request blocking probability presents an upward trend as shown in Fig. 8(a). This is because the increase of k leads to decrease of candidate nodes selection diversity and finally influences MA-RMLSA solution optimization. And results also indicate that disparity of request blocking probability between two algorithms goes into greater with the increase of k and this tendency is increasingly apparent with the increase of traffic load. It is demonstrated that MA-RMLSA-GA is less affected by value of k than MA-RMLSA-LMST. In Fig. 8(b), results show that request blocking probability decreases with the increment of D clearly. This is because the lager D can make more candidate destination nodes combination schemes to be chosen by algorithms. Moreover, the disparity of request blocking probability between MA-RMLSA-GA and MA-RMLSA-LMST becomes smaller with traffic load increasing as presented in Fig. 8(b). It means increasing value of D can weaken the impact of algorithm difference. Consider about the impact of k and D for MA-RMLSA in EONs, MA-RMLSA-GA is more stable to provide a better MA-RMLSA solution under network with various kinds of manycast traffic requests.

Fig. 5. The maximum FS index number n on (a) small scale and (b) large scale manycast request set.

X. Luo et al. / Optical Fiber Technology 36 (2017) 317–326

325

Fig. 6. The maximum FS index number n under (a) low and (b) high manycast request capacity.

Fig. 7. The request blocking probability of proposed MA-RMLSA-GA, and benchmark algorithms with jDi j ¼ 4, ki ¼ 3 scheme under (a) 14-node NSFNET topology and (b) 28node US Backbone, respectively.

Fig. 8. The impact of (a) different k and (b) different D in dynamic MA-RMLSA scenario.

6. Conclusion In this paper, we have investigated MA-RMLSA problem in EONs and decomposed it into four sub-problems: destination nodes selection, routing light-tree constitution, modulation level alloca-

tion and spectrum resource assignment. We first formulated MARMLSA problem into an ILP model. Then, we introduced the heuristic called MA-RMLSA-GA for solving MA-RMLSA problem in EONs. The proposed MA-RMLSA-GA was evaluated by numerical simulations in both static and dynamic manycast traffic scenarios. Simu-

326

X. Luo et al. / Optical Fiber Technology 36 (2017) 317–326

lation results in static scenario indicated that MA-RMLSA-GA can provide highly efficient MA-RMLSA solutions which has slightly disparity with the optimum solutions offered by ILP model. We also observed that MA-RMLSA-GA is suitable for solving MARMLSA problem with different request numbers and request capacities. In dynamic scenario, we observed that MA-RMLSA-GA achieved the maximum request blocking probability reduction which is 72.99% compared with benchmark algorithms. Moreover, the impact of manycast parameters has been evaluated as well by considering different numbers of candidate destination nodes and destination nodes. The simulation results demonstrated that MARMLSA-GA is applicable for solving dynamic MA-RMLSA problem with a variety of manycast requests which achieves stable improvement in network performance. Acknowledgement This study is supported by National Natural Science Foundation of China (No. 61571061). References [1] J. Armstrong, OFDM for optical communications, J. Lightwave Technol. 27 (3) (2009) 189–204. [2] Y. Ji, J. Zhang, Y. Zhao, X. Yu, J. Zhang, X. Chen, Prospects and research issues in multi-dimensional all optical networks, Sci. China Inf. Sci. 59 (10) (2016) 101301:1–101301:14. [3] A. Cai, J. Guo, R. Lin, G. Shen, M. Zukerman, Multicast routing and distanceadaptive spectrum allocation in elastic optical networks with shared protection, J. Lightwave Technol. 34 (17) (2016) 4076–4088. [4] Y. Wang, X. Cao, Y. Pan, A Study of the Routing and Spectrum Allocation in Spectrum-Sliced Elastic Optical Path Networks, in Proceedings of INFOCOM, 2011, pp. 1503–1511. [5] A. Pagès, J. Perelló, S. Spadaro, J. Comellas, Optimal route, spectrum, and modulation level assignment in split-spectrum-enabled dynamic elastic optical networks, J. Opt. Commun. Networking 6 (2) (2014) 114–126. [6] K. Christodoulopoulos, I. Tomkos, E.A. Varvarigos, Elastic bandwidth allocation in flexible OFDM-based optical networks, J. Lightwave Technol. 29 (9) (2011) 1354–1366. [7] N. Wang, J.P. Jue, Holding-time-aware routing, modulation, and spectrum assignment for elastic optical networks, in: Proceedings of Global Communications Conference (GLOBECOM), 2014, pp. 2180–2185. [8] Y. Qiu, Z. Fan, C. Chan, Efficient routing and spectrum assignment in elastic optical networks with time scheduled traffic, Opt. Fiber Technol. 30 (2016) 116–124. [9] C. Wang, G. Shen, S.K. Bose, Distance adaptive dynamic routing and spectrum allocation in elastic optical networks with shared backup path protection, J. Lightwave Technol. 33 (14) (2015) 2955–2964. [10] E. Archambault, N. Alloune, M. Furdek, Z. Xu, C. Tremblay, A. Muhammad, J. Chen, L. Wosinska, P. Littlewood, M.P. Belanger, Routing and spectrum assignment in elastic filterless optical networks, IEEE/ACM Trans. Networking 24 (6) (2016) 3578–3592. [11] C. Carter, S. Yi, P. Ratanchandani, R. Kravets, Manycast: exploring the space between anycast and multicast in AD Hoc Networks, in: Proceedings of International Conference on Mobile Computing and Networking (MobiCom), 2003, pp. 273–285. [12] C.P. Low, Optimal quorumcast routing, in: Proceedings of Global Telecommunications Conference, 1998, pp. 3013–3016. [13] N. Charbonneau, V.M. Vokkarane, Routing and wavelength assignment of static manycast demands over all-optical wavelength-routed WDM networks, J. Opt. Commun. Networking 2 (7) (2010) 442–455. [14] W. Kmiecik, R. Gos´cien´, K. Walkowiak, M. Klinkowski, Two-layer optimization of survivable overlay multicasting in elastic optical networks, Opt. Switching Networking 14 (4) (2014) 164–178. [15] Q. Wang, L.K. Chen, Performance analysis of multicast traffic over spectrum elastic optical networks, in: Proceedings of OFC/NFOEC, 2012, Paper. OTh3B.7.

[16] Z. Fan, Y. Li, G. Shen, C.C.K. Chan, Dynamic resource allocation for all-optical multicast based on sub-tree scheme in elastic optical networks, in: Proceedings of Optical Fiber Communication Conference and Exhibition (OFC), 2016, Paper. W2A.50. [17] K. Walkowiak, R. Goscien, M. Klinkowski, M. Woz´niak, Optimization of multicast traffic in elastic optical networks with distance-adaptive transmission, IEEE Commun. Lett. 18 (12) (2014) 2117–2120. [18] L. Yang, L. Gong, F. Zhou, B. Cousin, M. Molnár, Z. Zhu, Leveraging light-forest with rateless network coding to design efficient all-optical multicast schemes for elastic optical networks, J. Lightwave Technol. 33 (18) (2015) 3945–3955. [19] Z. Zhu, X. Liu, Y. Wang, W. Lu, L. Gong, S. Yu, N. Ansari, Impairment- and splitting-aware cloud-ready multicast provisioning in elastic optical networks, IEEE/ACM Trans. Networking (2017) (in Press). [20] S. Li, W. Lu, X. Liu, Z. Zhu, Fragmentation-aware service provisioning for advance reservation multicast in SD-EONs, Opt. Express 23 (20) (2015) 25804– 25813. [21] X. Liu, L. Gong, Z. Zhu, On the spectrum-efficient overlay multicast in elastic optical networks built with multicast-incapable switches, IEEE Commun. Lett. 17 (9) (2013) 1860–1863. [22] M. Zeng, W. Fang, Z. Zhu, Orchestrating tree-type VNF forwarding graphs in inter-dc elastic optical networks, J. Lightwave Technol. 34 (14) (2016) 3330– 3341. [23] M. Zeng, Y. Li, W. Fang, W. Lu, X. Liu, H. Yu, Z. Zhu, Control plane innovations to realize dynamic formulation of multicast sessions in inter-DC softwaredefined elastic optical networks, Opt. Switching Networking 23 (3) (2017) 259–269. [24] B.G. Bathula, V.M. Vokkarane, QoS-based manycasting over optical burstswitched (OBS) networks, IEEE/ACM Trans. Networking 18 (1) (2010) 271– 283. [25] X. Huang, Q, She, V.M. Vokkarane, J.P. Jue, Manycasting over optical burstswitched networks, in: Proceedings of IEEE International Conference on Communications (ICC), 2007, pp. 2353–2358. [26] B.G. Bathula, R.R.C. Bikram, V.M. Vokkarane, S. Talabattula, Impairment-aware manycast algorithms over optical burst-switched networks, in: Proceedings of International Conference on Computer Communications and Networks (ICCCN), 2008, pp. 1–6. [27] N. Charbonneau, V.M. Vokkarane, Tabu search meta-heuristic for static manycast routing and wavelength assignment over wavelength-routed optical WDM networks, in: Proceedings of IEEE International Conference on Communications (ICC), 2010, pp. 1–5. [28] A. Zakouni, J. Luo, F. Kharroubi, Random optimization algorithm for solving the static manycast RWA problem in optical WDM Networks, in: Proceedings of International Conference on Information and Communication Technology Convergence (ICTC), 2016, pp. 640–645. [29] A. Fallahpour, H. Beyranvand, J.A. Salehi, Energy-efficient manycast routing and spectrum assignment in elastic optical networks for cloud computing environment, J. Lightwave Technol. 33 (19) (2015) 4008–4018. [30] L.H. Sahasrabuddhe, B. Mukherjee, Light Trees: optical multicasting for improved performance in wavelength routed networks, IEEE Commun. Mag. 37 (2) (1999) 67–73. [31] L. Gong, X. Zhou, X. Liu, W. Zhao, W. Liu, Z. Zhu, Efficient resource allocation for all-optical multicasting over spectrum-sliced elastic optical networks, J. Opt. Commun. Networking 5 (8) (2013) 836–847. [32] X. Zhou, W. Lu, L. Gong, Z. Zhu, Dynamic RMSA in elastic optical networks with an adaptive genetic algorithm, in: Proceedings of Global Communications Conference (GLOBECOM), 2012, pp. 2912–2917. [33] A. Lipowski, D. Lipowska, Roulette-wheel selection via stochastic acceptance, Physica A 391 (6) (2012) 2193–2196. [34] R. Wang, Y. Yi, Research on shortest path tree algorithm for multicast routing, in: Proceedings of International Conference on Computational & Information Sciences (ICCIS), 2013, pp. 1445–1448. [35] M.R.S. Aghaei, Z.A. Zukarnain, A. Mamat, H. Zainuddin, A quantum algorithm for minimal spanning tree, in: Proceedings of International Symposium on Information Technology, 2008, pp. 1–6. [36] X. Sun, Y. Li, I. Lambadaris, Y.Q. Zhao, Performance analysis of first-fit wavelength assignment algorithm in optical networks, in: Proceedings of International Conference on Telecommunications, 2003, pp. 403–409. [37] X. Liu, L. Gong, Z. Zhu, Design integrated RSA for multicast in elastic optical networks with a layered approach, in: Proceedings of Global Communications Conference (GLOBECOM), 2013, pp. 2346–2351. [38] International Business Machines Corp, IBM ILOG CPLEX Optimizer 12.3, , 2012. Last Accessed on August 6, 2012.