Spectrum-efficient multipath provisioning with content connectivity for the survivability of elastic optical datacenter networks

Optical Fiber Technology 36 (2017) 353–365

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Spectrum-efficient multipath provisioning with content connectivity for the survivability of elastic optical datacenter networks Tao Gao, Xin Li, Bingli Guo, Shan Yin, Wenzhe Li, Shanguo Huang ⇑ State Key Laboratory of Information Photonics and Optical Communication, Beijing University of Posts and Telecommunications (BUPT), Beijing 100876, China

a r t i c l e

i n f o

Article history: Received 26 December 2016 Revised 4 May 2017 Accepted 14 May 2017

Keywords: Survivability Elastic optical datacenter networks Content connectivity Multipath provisioning Distance adaptive modulation Dynamic content placement

a b s t r a c t Multipath provisioning is a survivable and resource efficient solution against increasing link failures caused by natural or man-made disasters in elastic optical datacenter networks (EODNs). Nevertheless, the conventional multipath provisioning scheme is designed only for connecting a specific node pair. Also, it is obvious that the number of node-disjoint paths between any two nodes is restricted to network connectivity, which has a fixed value for a given topology. Recently, the concept of content connectivity in EODNs has been proposed, which guarantees that a user can be served by any datacenter hosting the required content regardless of where it is located. From this new perspective, we propose a survivable multipath provisioning with content connectivity (MPCC) scheme, which is expected to improve the spectrum efficiency and the whole system survivability. We formulate the MPCC scheme with Integer Linear Program (ILP) in static traffic scenario and a heuristic approach is proposed for dynamic traffic scenario. Furthermore, to adapt MPCC to the variation of network state in dynamic traffic scenario, we propose a dynamic content placement (DCP) strategy in the MPCC scheme for detecting the variation of the distribution of user requests and adjusting the content location dynamically. Simulation results indicate that the MPCC scheme can reduce over 20% spectrum consumption than conventional multipath provisioning scheme in static traffic scenario. And in dynamic traffic scenario, the MPCC scheme can reduce over 20% spectrum consumption and over 50% blocking probability than conventional multipath provisioning scheme. Meanwhile, benefiting from the DCP strategy, the MPCC scheme has a good adaption to the variation of the distribution of user requests. Ó 2017 Elsevier Inc. All rights reserved.

1. Introduction Emerging applications such as cloud computing and online video game dramatically promote the increase of IP traffic and accelerate the development of advanced all-optical interconnection technology in datacenter networks. To achieve high spectrum efficiency, multi-carrier modulation techniques such as optically generated orthogonal frequency-division multiplexing (OFDM), Nyquist-WDM, and so on [1–3] are applied for next-generation optical networks, especially for the newly build optical interconnected datacenter networks, which is referred as elastic optical datacenter networks (EODNs). However, optical network is fragile and easy to be broken by natural or man-made disasters such as earthquake, hurricane, and weapons of mass destruction [4,5]. Especially when the capacity of one single fiber increase to Pb/s (for example by using low-crosstalk one-ring-structured 12-core fiber [6]), any fiber failure could cause a great loss of data and revenue. Consequently, improving the survivability of optical ⇑ Corresponding author. E-mail address: [email protected] (S. Huang). http://dx.doi.org/10.1016/j.yofte.2017.05.008 1068-5200/Ó 2017 Elsevier Inc. All rights reserved.

networks is crucially important and has been studied extensively [7–9]. Traditional single-path protection schemes reserve backup resource for an end-to-end connection so that the interrupted traffic can be switched over to the backup path when any failure occurs [10–12]. However, all these single-path protection schemes obviously deteriorate network spectrum efficiency due to large amount of backup spectrum resource reserving. Compared with the single-path protection, the multipath provisioning scheme has higher spectrum efficiency, in which traffic is transmitted through multiple node-disjoint paths. If a failure occurs on one path, the affected data stream can be transmitted through other paths and the service will not be interrupted. Multipath protection scheme for the end-to-end connection has been well studied in conventional wavelength-switched optical networks and elastic optical networks (EON). The authors in [13] developed an Integer Linear Program (ILP) model for optimally realizing static multipath routing and resource allocation while guaranteeing the required protection level. In [14], a dynamic multipath provisioning scheme supporting full and partial protection was proposed in elastic optical networks. In [15], a shared-protection multipath scheme was proposed to improve the survivability against multiple failures in

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flexible-grid optical networks. These studies improve the network survivability against single or multiple link failures and guarantee the flexible protection requirement of the traffic. Moreover, improving the spectrum efficiency is also an important issue in multipath protection scheme. The authors in [16] proposed a novel multipath routing and spectrum allocated (RSA) algorithm with distanceadaptive modulation format assignment in dynamic traffic scenario. In [17], to solve the problem of spectrum waste caused by the guard bandwidth in multipath protection scheme, a dynamic multipath routing algorithm with traffic grooming was proposed. By aggregating small-size connections originated from the same source node and sharing common fiber links, the scheme improves the spectrum efficiency and enhances the network throughout. To solve the spectrum fragmentation issue caused by spectrum contiguity and continuity constraints, the authors in [18] proposed a novel multipath de-fragmentation method, which aggregates spectrum fragments instead of reconfiguring existing spectrum paths. This scheme achieves high spectrum efficiency and reduces blocking probability in dynamic traffic conditions. A spectrum-efficient multipath routing scheme in elastic optical networks that supported simultaneously anycast and unicast traffic demands was proposed in [19]. However, multipath protection scheme for end-to-end connection relies on network connectivity, which has a fixed value for a given topology. In practical scenarios, sometimes it is hard to find sufficient node-disjoint paths for every source-destination node pair. Fortunately, most of services and data can be replicated and maintained in multiple datacenters such that any user can obtain the required content as long as one of these datacenters is reachable. Consequently, the spectrum efficiency and the survivability of EODNs can be further improved. In [20], the authors proposed a joint anycast and unicast routing scheme considering content distribution in elastic optical networks, which brought significant spectrum savings. From the perspective of network survivability, the authors in [21] first proposed the concept of content connectivity, which is defined as the reachability of every content from any point of an optical network. Considering content connectivity, the research for the survivability of EODNs has entered a new stage. In [22], the authors proposed the concept of k-node (edge) content connectivity and designed the k-node (edge) content connected optical datacenter networks against multiple failures, which had high spectrum efficiency. A novel perfect matching based sharing principle among multiple end-to-content paths was proposed to reduce the spectrum consumption while ensuring the survivability in [23]. The authors in [24] proposed a bandwidth-adaptive protection scheme where the backup path employed distance-adaptive modulation level in content connected EODNs. However, there are few researches jointly considering multipath provisioning and content connectivity. Meantime, all of above researches either focused on the static traffic scenario or focused on the dynamic traffic scenario without considering the practical network environment where network state such as disaster probability or the distribution of user requests is time-varying. To reduce the content loss caused by disasters of which probability changes as time passes in nature, the authors in [25,26] studied the dynamic content placement based on risk analysis in a cloud network. Nevertheless, compared with the changing frequency of disaster probability, the changing frequency of the distribution of user requests is higher [27,28]. Thus, dynamically readjusting the content placement among multiple datacenters according to the variation of user requests is meaningful to improve the spectrum efficiency. In this paper, we jointly consider multipath provisioning and content connectivity in EODNs. The impact of time-varying distribution of user requests is also taken into account. A novel survivable multipath provisioning with content connectivity (MPCC) scheme is proposed, which focuses on reducing the spectrum consumption as well as improving the survivability of EODNs.

Considering content connectivity, a user can be served by multiple datacenters, so that the number of node-disjoint end-to-content paths in the MPCC scheme will increase. Meantime, this scheme can achieve higher spectrum efficiency since the average length of end-to-content paths is shorter than that of end-to-end paths in the conventional multipath provisioning scheme. When addressing the routing, modulation level, and spectrum allocation (RMLSA) problem for each end-to-content path, the distance-adaptive spectrum allocation [29,30] is adopted by the MPCC scheme. Besides, since full replication of content where all content is replicated to each datacenter is not reasonable due to various cost such as storage cost and synchronization cost, there should be a trade-off between the spectrum efficiency and the cost of the content. In the MPCC scheme, under the limitation of the number of the content replicas, the spectrum consumption is minimized and the optimal content placement is achieved. We develop an ILP model for the MPCC scheme with the objective of minimizing the total spectrum consumption and optimizing content placement among multiple datacenters. We also design a heuristic algorithm for the MPCC scheme based on dynamic content placement (DCP) strategy in dynamic traffic scenario. In the DCP strategy, the distribution of user requests is periodically detected to determine whether the content placement algorithm is triggered or not. Simulation results indicate that the MPCC scheme can reduce the spectrum consumption and blocking probability dramatically compared with the full protection with content connectivity scheme (FPCC) and the multipath protection for end-to-end connection scheme (MPEE) in both static and dynamic traffic scenarios. The survivable provisioning scheme FPCC is based on the scheme proposed for anycast in content delivery networks in [20], and meanwhile, full protection is introduced. The MPEE scheme is a conventional multipath scheme [13,14], which is widely used for protecting end-to-end connections. The rest of this paper is organized as follows. In Section 2, the concept of content connectivity, the MPCC scheme, and the DCP strategy are stated. The ILP model and the heuristic algorithms are presented in Section 3 and Section 4 respectively. Section 5 presents the numeric results of our proposed MPCC scheme. Finally, Section 6 concludes this paper. 2. DCP based MPCC scheme In this section, we first introduce the concept of content connectivity. Then, the MPCC scheme is presented and compared with the traditional multipath provisioning scheme. Moreover, the DCP strategy, which readjusts the position of each content according to the current distribution of user requests, is also elaborated. 2.1. Content connectivity Content connectivity guarantees that the content is still available for users even if the disaster destroys the networks into multiple segregated parts. As presented in Fig. 1(a) and (b), the network has 8 optical nodes and 2 datacenters (node 2 and node 6). We assume that there are 5 user requests with different source nodes. In traditional datacenter networks as shown in Fig. 1(a), each content is only placed in one single datacenter (without content connectivity), and when two disasters destroy the networks into two segregated parts, requests r3 along light-path 4 ? 5 ? 6 and r4 along light-path 3 ? 6 are both interrupted. While in datacenter networks with content connectivity as shown in Fig. 1(b), the content is placed in multiple datacenters (Without loss of generality, we assume there is only one kind of content). In this case, even if the EODNs are disconnected, content placed in datacenter 2 and 6 is still available in both parts. In addition, the total spectrum consumption is reduced by serving the users through

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Fig. 1. Comparison between traditional datacenter networks and content connected EODNs under disasters (a) traditional datacenter networks (b) content connected EODNs.

shorter end-to-content paths than through end-to-end paths in traditional networks.

Table 1 Parameters for different modulation levels.

2.2. The MPCC scheme

Modulation level

Bits per symbol

Data rate per subcarrier (Gbps)

Transmission reach (km)

When a link failure occurs, a user can tolerate the reduced capacity as long as the essential service is guaranteed. Therefore, a request usually has a flexible protection level. In the MPCC scheme, a request is defined as r(s,c,b,p), where s denotes the source node, c denotes the required content, b denotes the bandwidth demand, and p denotes the protection level ð0 < p 6 1Þ. The required content is transmitted through multiple nodedisjoint end-to-content paths from multiple datacenters to the source node. If a link along one end-to-content path fails, the data stream transmitted on other end-to-content paths will not be interrupted and the bandwidth capacity bp can be guaranteed. The MPCC scheme needs to address the RMLSA problem for each end-to-content path, which can be divided into three parts. Firstly, the MPCC scheme calculates K ðK P 2Þ node-disjoint end-tocontent paths between multiple datacenters that host the required content and the source node. Thus, any two end-to-content paths will not break down at the same time under random single link failure. Secondly, each end-to-content path selects the modulation level according to its transmission distance. Generally, the optical signals with higher modulation level will have shorter transmission reach. In this paper, we consider several mainstream modulation levels such as Polarization Division Multiplexing Binary Phase Shift Keying (PDM-BPSK), Polarization Division Multiplexing Quadrature Phase-Shift Keying (PDM-QPSK), Polarization Division Multiplexing 8-Quadrature Amplitude Modulation (PDM-8QAM), Polarization Division Multiplexing 16-Quadrature Amplitude Modulation (PDM-16QAM), etc. The transmission rate of all these modulation

PDM-BPSK PDM-QPSK PDM-8QAM PDM-16QAM

1 2 3 4

50 100 150 200

6000 3000 1500 750

levels are referred to [2] and the transmission distance is determined by using the half distance law [20,31], as shown in Table 1. Finally, the spectrum allocated to each end-to-content path must satisfy spectrum contiguity constraint and spectrum continuity requirements [32]. In the MPCC scheme, the allocated spectrum of each end-to-content path is jointly determined by parameter K and parameter p. If K P 1=ð1  pÞ, at least b=K bandwidth demand needs to be allocated on each end-to-content path and b  p=ðK  1Þ bandwidth demand is allocated otherwise. Considering the different modulation level adopted, the number of the spectrum slots (FSs) allocated to different end-to-content paths for a request may not be identical. In more detail, we assume that X denotes the basic capacity of a FS with modulation level PDM-BPSK, m denotes the adopted modulation level, and Cr denotes the bandwidth demand needed to be allocated on each end-to-content path. As a result, the number of FSs allocated on each path n ¼ dC r =ðm  XÞe þ GB, where GB is the number of FSs for guard bandwidth. Compared with the traditional multipath protection scheme which searches multiple end-to-end paths for each coming request, the MPCC scheme improved the survivability and the spectrum efficiency dramatically. On the one hand, each end-to-

Fig. 2. Multipath provisioning (a) in traditional networks (b) in content connected EODNs.

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T. Gao et al. / Optical Fiber Technology 36 (2017) 353–365

content path in the MPCC scheme will have a shorter transmission distance than the end-to-end path in the traditional multipath protection scheme. On the other hand, the maximum number of the end-to-end paths between any two nodes, which is limited by network connectivity, is much smaller than the maximum number of the end-to-content paths in the MPCC scheme. For example in the 6-node topology as shown in Fig. 2(a), in traditional multipath protection scheme, there are only two node-disjoint paths for the request r(b,d,400,0.8) (d is the destination node here). For these two end-to-end paths, the numbers of allocated FSs are 4 and 7 with modulation level PDM-QPSK and modulation level PDMBPSK respectively. Hence, the total number of occupied FSs is 4  2 + 7  2 = 22. For the same request with full protection, i.e., q = 1, the number of occupied FSs is 4  2 + 8  2 = 24. While in Fig. 2(b), content C1 is hosted in both datacenter a and datacenter d. The number of node-disjoint paths for request r(b,C1,400,0.8) is set to 3 (there are four node-disjoint end-to-content paths at most in fact). In the MPCC scheme, the total number of occupied FSs for request r is 1 + 2  1 + 2  2 = 7, which is less than 22 in the traditional multipath provisioning scheme and 24 in the full protection scheme. From this example we can find that, the MPCC scheme has higher spectrum efficiency than traditional protection schemes while satisfying the specified survivability requirements. 2.3. The DCP strategy In EODNs, the distribution of user requests is varying with time passing by. Accordingly, the content placement should consider the current network state to reduce the resource consumption and blocking probability or achieve other goals. Here, we propose a DCP strategy for the MPCC scheme, which can choose and readjust the position of each content according to the ever-changing distribution of user requests. Fig. 3 shows the case where the distribution of user requests varies as time passes in NSFNET (link length in km). In Stage I, the users in Zone 1 request content C1 intensively, hence content C1 should be placed in datacenter D3 that is closest to the users in Zone 1 (shown in Fig. 3(a)). With time passing by, in Stage II, more users in Zone 2 begin to request content C1. On this occasion, if content C1 is still merely placed in datacenter D3, the users in Zone 2 will be served through long light paths. Then the spectrum consumption of overall network will increase dramatically. Hence, the content placement should be dynamically readjusted according to the variation of the distribution of user requests. As shown in Fig. 3(b), content C1 is placed in datacenter D1 nearer to the users in Zone 2, which can reduce the spectrum consumption for all user requests. Based on the DCP strategy, the MPCC scheme can adapt to the variation of the distribution of user requests. The method to precisely evaluate the variation degree of the distribution of user requests and content placement algorithm are elaborated in Section 4.3.

modulation level PDM-BPSK can be adopted for all end-tocontent paths. The ILP model is detailed as follows. G={V,D,E}

R

M Tm

X

pc cc cd L(i,j) u Z GB K

r;k;m

f ði;jÞ

nr;k;m ði;jÞ

ur;k;m d

r;k;m

lði;jÞ 2 f0; 1g

0

0

0

0

;k ;m 2 f0; 1g orr;k;m;ði;jÞ 0

;k ;m arr;k;m;ði;jÞ 2 f0; 1g 0

3. ILP formulation for the MPCC scheme In this Section, an ILP model with the objective of minimizing the total spectrum resource consumption for the given user requests is developed for the MPCC scheme in EODNs. In static traffic scenario, all user requests are generated off-line in advance. Besides solving the RMLSA problem for each request, the ILP model simultaneously considers the optimal placement of content according to the attributes of user requests, which also helps to minimize the spectrum resource consumption of overall EODNs. To compare the performance of the MPCC scheme adopting distance-adaptive spectrum allocation with the scheme adopting the lowest modulation level (i.e. PDM-BPSK) based spectrum allocation, we also conduct the ILP model in which only the lowest

xr;k;m 2 f0; 1g d

yr;k m 2 f0; 1g

qdc 2 f0; 1g

The EODNs, where V denotes the set of optical nodes, D denotes the set of datacenters, E denotes the set of fiber links, ði; jÞ 2 E. Set of user requests. r 2 R, r = (s,c,b,p), where s denotes the source node, c denotes the required content, b denotes the bandwidth demand, and p denotes the protection level. Set of optional modulations levels, m 2 M. The maximum transmission reach of modulation level m. Base capacity of a FS with modulation level PDM-BPSK. The maximum number of replicas of content c. The size of content c. The storage capacity of datacenter d. The length of link (i,j). The number of FSs on each fiber link. A large integer constant. The number of FSs for guard bandwidth. A given parameter which denotes the number of established end-to-content paths for each user request, k 2 ½1; K. Integer variable denoting the starting allocated FS on link (i,j), which belongs to the kth end-to-content path of request r with modulation level m. Integer variable denoting the number of the allocated FSs on link (i,j), which belongs the kth end-to-content path of request r with modulation level m. Integer variable number denoting the allocated FSs on the kth end-to-content path of request r, which terminates at datacenter d and adopts modulation level m. Binary variable that equals to 1 if link (i,j) is occupied by the kth end-to-content path of request r with modulation level m and equals to 0 otherwise. Binary variable that equals to 1 if the index of start FS on link (i,j) along the kth end-tocontent path of request r with modulation level m is smaller than that of the k’th end-tocontent path of request r’ with modulation level m’ and equals to 0 otherwise. Binary variable that equals to 1 if the kth endto-content path of request r with modulation level m and the k’th end-to-content path of request r’ with modulation level m’ use the same link (i,j) and equals to 0 otherwise. Binary variable that equals to 1 if d is the destination datacenter of the kth end-tocontent path of request r with modulation level m and equals to 0 otherwise. Binary variable that equals to 1 if modulation level m is adopted by the kth end-to-content path of request r and equals to 0 otherwise. Binary variable that equals to 1 if content c is placed in datacenter d and equals to 0 otherwise.

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Fig. 3. Dynamic content placement strategy (a) Stage I (b) Stage II.

Objective function:

Minimize

XX XX

Eqs. (6) and (7) ensure that the FSs can be allocated to link (i,j) if and only if this link is occupied by the kth end-to-content path of request r with modulation level m.

nr;k;m ði;jÞ

X X

r2R k2½1;Km2M ði;jÞ2E

The objective of the ILP model is to minimize the total spectrum consumption of all established node-disjoint end-to-content paths for all user requests.

X XX

ður;k;m  m  XÞ P br d

8r 2 R

ð1Þ

r;k;m

lði;jÞ

6 1 8r 2 R; ði; jÞ 2 E

ð8Þ

k2½1;Km2M

Eq. (8) ensures that all end-to-content paths of request r are node-disjoint. r;k;m

P lði;jÞ

r;k;m

6 ðlði;jÞ  uÞ 8r 2 R; k 2 ½1; K; m 2 M; ði; jÞ 2 E

f ði;jÞ

r;k;m

8r 2 R; k 2 ½1; K; m 2 M; ði; jÞ 2 E

ð9Þ

k2½1;K d2D m2M k–k X X X

f ði;jÞ

0

ður;k;m d

0

 m  XÞ P ðbr  pr Þ 8r 2 R; k 2 ½1; K

ð2Þ

k2½1;K d2D m2M

Eq. (1) ensures the bandwidth demand of request r. Eq. (2) ensures that when a failure occurs on end-to-content path k’, at least br  pr bandwidth capacity is reserved on other available end-to-content paths.

X

X

r;k;m

lði;jÞ 

j:ði;jÞ2E

r;k;m

lðj;iÞ ¼

j:ðj;iÞ2E

8X > xr;k;m i¼s > d > < d2D

> xr;k;m > i > : 0

i2D

; 8r 2 R;k 2 ½1; K; m 2 M

others

xr;k;m ¼ 1 8r 2 R; k 2 ½1; K d

X

r;k;m

f ði;jÞ 

j:ði;jÞ2E

X

nr;k;m ði;jÞ 

j:ði;jÞ2E

j:ðj;iÞ2E

nr;k;m ðj;iÞ ¼

8 X r;k;m > ud i¼s > > < d2D

> ur;k;m > i > : 0

i2D

0

;k ;m arr;k;m;ði;jÞ P 0

0

r;k;m

lði;jÞ

P

6 nr;k;m ði;jÞ

  r;k;m r 0 ;k0 ;m0 lði;jÞ þ lði;jÞ  1

8r; r 0 2 R; r – r 0 ; k; k0 2 ½1; K; m; m0 2 M; ði; jÞ 2 E 0

;k ;m 6 arr;k;m;ði;jÞ 0

0

ð12Þ

  r;k;m r 0 ;k0 ;m0 lði;jÞ þ lði;jÞ =2

8r; r 0 2 R; r–r0 ; k; k0 2 ½1; K; m; m0 2 M; ði; jÞ 2 E

ð13Þ

Eqs. (12) and (13) ensure that if and only if link (i,j) is used by 0

; 8r 2 R;k 2 ½1; K; m 2 M

0

8r 2 R; k 2 ½1; K; m 2 M; ði; jÞ 2 E

8r 2 R; k 2 ½1; K; m 2 M; ði; jÞ 2 E

0

0

0

;k ;m ;k ;m orr;k;m;ði;jÞ þ or;k;m ¼ arr;k;m;ði;jÞ r 0 ;k0 ;m0 ;ði;jÞ 0

0

0

0

8r; r 0 2 R; r–r0 ; k; k0 2 ½1; K; m; m0 2 M; ði; jÞ 2 E

others

Eq. (5) enforces the flow conservation on any end-to-content path of request r. This constraint ensures that the number of incoming occupied FSs equals to the number of outgoing occupied FSs for any intermediate node along the path. Moreover, each endto-content path can terminate at any datacenter which hosts the required content.

ðnr;k;m ði;jÞ =ZÞ

ð11Þ

;k ;m equals to 1. two requests at the same time, arr;k;m;ði;jÞ

ð5Þ

r;k;m lði;jÞ

r;k;m

f ðj;iÞ ¼ 0

j:ðj;iÞ2E

d2D m2M

X

X

Eq. (11) ensures that the start index of incoming occupied FSs is as same as that of outgoing occupied FSs for any intermediate node along any end-to-content path.

ð4Þ

Eqs. (3) and (4) ensure that for request r, only one end-tocontent path can be followed and only one datacenter is regarded as the destination datacenter of the kth end-to-content path of request r.

ð10Þ

Eqs. (9) and (10) ensure that FSs can be allocated to link (i,j) if and only if this link is occupied and meantime the start index of FS occupied by an end-to-content path is not larger than the total number of FSs on each fiber link.

8i 2 V=ðs [ DÞ; r 2 R; k 2 ½1; K; m 2 M

ð3Þ XX

r;k;m

ð6Þ ð7Þ

ð14Þ

 0 0 0   0 0 0  0 ;k0 ;m0 r ;k ;m r;k;m ;k ;m þ 1  arr;k;m;ði;jÞ f ði;jÞ  f ði;jÞ þ 1 6 ðu þ 1Þ  orr;k;m;ði;jÞ

8r; r 0 2 R; r–r0 ; k; k0 2 ½1; K; m; m0 2 M; ði; jÞ 2 E

ð15Þ

    r;k;m r 0 ;k0 ;m0 þ 1  ar;k;m f ði;jÞ  f ði;jÞ þ 1 6 ðu þ 1Þ  or;k;m r 0 ;k0 ;m0 ;ði;jÞ r 0 ;k0 ;m0 ;ði;jÞ

8r; r 0 2 R; r–r0 ; k; k0 2 ½1; K; m; m0 2 M; ði; jÞ 2 E 0 0

ð16Þ

k ;m Eq. (14) ensures that orr;k;m;ði;jÞ can be used to denote the relation0

ship of the index of the start occupied FSs between the two requests if and only if these two requests use the same link (i,j),

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;k ;m i.e. arr;k;m;ði;jÞ equals to 1. Eqs. (15) and (16) ensure that when two 0

0

requests use a common link, either

0 ;k0 ;m0 orr;k;m;ði;jÞ

equals to 1, meaning

the index of the start occupied FSs on link (i,j) of the k’th end-tocontent path of request r’ with modulation level m’ is larger than that of the kth end-to-content path of request r with modulation r 0 ;k0 ;m0

level m, that is, f ði;jÞ r 0 ;k0 ;m0

r;k;m

> f ði;jÞ

case f ði;jÞ

r0 ;k0 ;m0

f ði;jÞ þ nr;k;m ði;jÞ þ GB  f ði;jÞ   0 ;k0 ;m0 6 ðu þ GBÞ  1  orr;k;m;ði;jÞ þ 1  ar;k;m r0 ;k0 ;m0 ;ði;jÞ

8r; r 0 2 R; r – r 0 ; k; k0 2 ½1; K; m; m0 2 M; ði; jÞ 2 E r0 ;k0 ;m0

0

ð17Þ

;k ;m þ nrði;jÞ þ GB  f ði;jÞ   0 ;k0 ;m0 6 ðu þ GBÞ  1  or;k;m þ 1  arr;k;m;ði;jÞ r0 ;k0 ;m0 ;ði;jÞ 0

f ði;jÞ

0

r;k;m

8r; r 0 2 R; r – r 0 ; k; k0 2 ½1; K; m; m0 2 M; ði; jÞ 2 E

ð18Þ

Eqs. (17) and (18) ensure the spectrum contiguity constraint, and when two requests use a common link (i,j), there are at least GB FSs between these two requests. r;k;m

yr;k m P lði;jÞ yr;k m 6

X

8r 2 R; k 2 ½1; K; m 2 M; ði; jÞ 2 E

r;k;m

lði;jÞ

8r 2 R; k 2 ½1; K; m 2 M

ð19Þ ð20Þ

ði;jÞ2E

X

yr;k 8r 2 R; k 2 ½1; K m ¼ 1

ð21Þ

m2M

Eqs. (19) and (20) determine the modulation level adopted by the kth end-to-content path of request r. Eq. (21) ensures that only one modulation level is adopted for one end-to-content path of any request and each end-to-content path must adopt a modulation level.

 X  r;k;m lði;jÞ  Lði;jÞ 6 T m

8r 2 R; k 2 ½1; K; m 2 M

ð22Þ

ði;jÞ2E

Eq. (22) ensures that the length of any end-to-content path does not exceed the transmission reach of the adopted modulation level.

P

qdc 6

P r2Rc

qdc P

P k2½1;K

m2M

xr;k;m d

Z XX X

xr;k;m d

8c 2 C; d 2 D

8c 2 C; d 2 D

ð23Þ

pc 8c 2 C

ð25Þ

d2D

X

ðqdc  cc Þ 6 cd

The heuristic MPCC algorithm (i.e. Algorithm 1, which is detailed as follows) consists of two concurrent procedures, i.e., the multipath provisioning algorithm and the DCP strategy. The multipath provisioning algorithm, from line 1 to line 5 in Algorithm 1, is responsible for conducting RMLSA for each coming request. The DCP strategy, from line 6 to line 13, is responsible for readjusting the content placement according to the distribution of user requests, which is detected periodically. In a regular interval of time Tp, the trigger condition of the DCP strategy is checked to determine whether content placement algorithm should be executed. Each time after the execution of the DCP strategy, the procedure of multipath provisioning will be informed of the new location of replicas of the content, which can be selected as the destination of the requests requiring this content. Specially, each content replica has a visit flag to indicate whether it is being visited. The replica of the content, which the DCP strategy determines to remove, will remain in the datacenter until all its users end visiting it and the visit flag turns into false (detailed in Algorithm 3). Algorithm 2, referring to the multipath provisioning algorithm is elaborated in Section 4.2. The DCP strategy including the trigger condition and Algorithm 3 are stated in Section 4.3. Algorithm 1 Heuristic MPCC Algorithm Input: requests set T 1. procedure Multipath Provisioning (T) 2. for each r 2 T do 3. Call Algorithm 2 to realize multipath provisioning; 4. end for 5. end procedure 6. procedure DCP 7. Set timer TR = Tp; 8. if TR expired do 9. if the DCP trigger condition is satisfied do 10. Call Algorithm 3 to readjust the content placement; 11. end if 12. end if 13. end procedure

4.2. The multipath provisioning algorithm

Eqs. (23) and (24) ensure that if and only if content c is placed in datacenter d, d can be regarded as the destination datacenter of the end-to-content path of request r which requires content c (Rc denotes the set of user requests whose required content is c).

qdc 6

4.1. The Heuristic MPCC Algorithm

ð24Þ

r2Rc k2½1;Km2M

X

Since the ILP model is designed for static user requests and can only obtain the optimal solution with acceptable time consumption in small-scale EODNs, we propose a heuristic MPCC algorithm for dynamic user requests in large-scale EODNs.

r;k;m

> f ði;jÞ , or orr;k;m 0 ;k0 ;m0 ;ði;jÞ equals to 1, in which

.

r;k;m

4. Heuristic algorithm for the MPCC scheme

8d 2 D

ð26Þ

c2C

Eq. (25) ensures that the number of replicas of any content is limited. Eq. (26) ensures that the total storage size of all content placed in one datacenter does not exceed the storage capacity of that datacenter.

To accommodate a newly arrived request r(s,c,b,p), we first calculate the bandwidth capacity allocated on each path according to the number of end-to-content paths K using the method stated in Section 2. Note that a larger K may not mean the best choice. Consequently, to confirm the optimal K, which consumes least spectrum resource, we search all scenarios with K ranging from 2 to the upper limit K_Paths. Secondly, K node-disjoint paths are calculated by the improved Suurballe’s algorithm [33]. Conventional Suurballe’s algorithm is not able to calculate node-disjoint paths from one source node to multiple destination nodes, while in EODNs with content connectivity, the content is placed in multiple datacenters. To address the problem, we construct a new node to which the datacenters hosting the required content are connected. Then K node-disjoint paths are calculated from the user node to the

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new-constructed node. By this means, K node-disjoint paths from the user to multiple datacenters can be obtained. Thirdly, for each node-disjoint end-to-content path, modulation level is adopted according to the path’s length, and correspondingly, the number of FSs needed to be allocated on each path is calculated. Finally, we compare all scenarios with different values of K to choose the one with the minimum number of occupied FSs and allocate spectrum resource by the first fit (FF) algorithm [34] for this request. The multipath provisioning algorithm (i.e. Algorithm 2) is detailed as follows. In line 1, relevant parameters are initialized, where PS indicates the set of calculated paths and TF indicates the total number of FSs occupied by the paths in PS. The set of datacenters DSr in which the required content is placed is obtained in line 2. From line 3 to line 20, for each request, we first calculate Cr which indicates the bandwidth capacity allocated on each end-to-content path for request r and then confirm the optimal K paths occupying the least FSs. In line 6, K node-disjoint paths from the user node to the datacenters in DSr are calculated. From line 7 to line 14, total number of FSs needed to allocate on all the K node-disjoint paths are calculated. Specially, for each path, the highest modulation level is adopted, i.e. the path length is not longer than the transmission reach Tm of the highest modulation it supports. The optimal K is confirmed in lines 15–19. Finally, for each end-to-content paths, the FF algorithm is used to allocate spectrum resource in lines 21–23. Algorithm 2 Multipath Provisioning for a Request Input: K_Paths, request r Output: PS 1. Initialize the set of calculated node-disjoint paths PS = Null, the total number of FSs occupied by the paths in PS TF = INF; 2. Obtain the datacenter set DSr hosting required content 3. for the number of paths K from 2 to K_Paths do 4. Initialize the set of K node-disjoint paths PSK = Null, the total number of FSs occupied by paths in PSK TFK = 0; 5. Calculate the bandwidth capacity allocated on each path Cr according to K, bandwidth demand br, and protection level pr; 6. Calculate K node-disjoint paths using the improved Suurballe’s algorithm based on DSr and add these paths to PSK; 7. for each path p 2 PSK 8. for each modulation level m 2 M (from high level to low level) do 9. if the distance of the path Dp  Tm do 10. Calculate the number of FSs allocated on p n ¼ dC r =ðm  XÞe þ GB, TFK = TFK + n; 11. go to Step 7; 12. end if 13. end for 14. end for 15. if |PSK| == K do 16. if TF > TFK do 17. TF = TFK, PS = PSK; 18. end if 19. end if 20. end for 21. for each path p 2 PS 22. Allocate FSs using the FF algorithm according to the number of required FSs; 23. end for

Complexity analysis: In line 2, the complexity of obtaining the set of datacenters hosting the required content is OðjDjÞ, where jDj is the

number of datacenters. In lines 3–20, we compare all scenarios with different K to select the scenario with minimum spectrum resource consumption. The value of K_Paths is normally set to two or three, which depends on network connectivity. Hence, the procedure from line 4 to line 19 dominates the complexity of total algorithm. For a certain K, the complexity of Suurballe’s algorithm is OðjEj þ jVj log jVjÞ, where jEj is the number of fiber links and jVj is the number of optical nodes. The complexity of the for loop in lines 7–14 is OðKjMjÞ, where jMj is the number of optional modulation levels. From line 21 to line 23, the complexity of the resource allocation procedure is OðK uÞ, where u is the total number of FSs on a fiber link. Thus, the complexity of the algorithm is OðK Paths  ðjEj þ jVj log jVj þ KjMjÞ þ K uÞ. In general, the time complexity of Algorithm 2 is polynomial. 4.3. The DCP strategy In the DCP strategy, the variation of the distribution of user requests in EODNs is detected periodically. As long as trigger condition is satisfied, the DCP algorithm is executed to readjust the location of each content. The trigger condition is stated as follows:

reqc CRc P NP reqtotal c2C CRc

8c 2 C

ð27Þ

In Eq. (27), reqc and reqtotal are the number of users requesting content c and the total number of users respectively, N (N > 1) is the sensitivity factor, and CRc is the number of current replicas of content c. The value of N determines the execution frequency of the DCP algorithm.

gc ¼

reqc X  reqtotal c2C

pc

ð28Þ

ARc ¼ maxfdc ; minfgc ; pc gg

ð29Þ

Once the DCP algorithm is triggered, we should calculate the new number of replicas of the content first. Eq. (28) denotes the ideal number of replicas of content c, which is proportional to the number of users requesting it. Nevertheless, the maximum number of replicas of content is usually limited due to various cost such as storage cost and synchronization cost. For content c, pc indicates the maximum replica number and dc indicates the minimum replica number (pc P dc P 2). Eq. (29) calculates the actual replica number of content c. If a datacenter hosts too much popular content, many requests will be blocked due to the lack of spectrum resource on the fiber links around this datacenter. Hence, content placement should avoid causing a datacenter to overload. In the DCP strategy, we trade off the spectrum resource consumption and the load of datacenter. To this end, we measure the average cost of content c as follows:

P AV c ¼

r2Rc

P

k2½1;K nr;k

ARc

8c 2 C

ð30Þ

In Eq. (30), nr;k is the number of occupied FSs on the kth end-tocontent path of request r with modulation level PDM-BPSK (so the actual occupied FSs may be fewer). ARc is the new replica number of content c. The accumulated cost of content in datacenter d should be limited within a threshold, which is denoted as TLthreshold. The pseudo code of the DCP algorithm is detailed as follows. Line 1 initializes relevant parameters, where CDc indicates the list of candidate datacenters for content c placement, TLd indicates the accumulated cost of content in datacenter d, and APSc indicates the set of actual datacenters for content c placement. In line 2, the content is sorted such that the content with the largest number of users will be placed first. From line 3 to line 24, we calculate the APSc for each content c, where Nd indicates the counter of datacen-

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ter, ADDc indicates the set of datacenters to which a replica of content c will be added, and DELc indicates the set of datacenters from which the replica of content c will be removed. In lines 6–8, according to distribution of current users requesting content c, the nearest datacenters are selected and added to CDc. From line 10 to line 21, datacenters to place content c are finally selected from CDc. In this phase, the datacenter nearer to most users requiring content c is preferred to be chosen and meantime, the datacenter should be guaranteed not to be overloaded (lines 12–17). Based on the calculated APSc and OPSc which indicates the set of original datacenters hosting content c, we obtain ADDc and DELc in line 22. For datacenters in ADDc, we add a replica of content c to them as shown in line 23. For datacenters in DELc, the replica of content c will not be removed until all its users end visiting it to guarantee current connections will not be interrupted as shown in lines 25–31. To do so, VFd,c is defined to indicate whether any user is visiting the content c in datacenter d, which equals to true if datacenter d hosting content c is being visited. Algorithm 3 DCP Algorithm Input: TLthreshold, content set C, Output: NPS 1. Set the list of candidate datacenters CDc = Null, accumulated cost of content in datacenter d TLd = 0, the set of actual datacenters for content c placement APSc = Null; 2. Sort the content in C in descending order according to the number of users requesting content c reqc; 3. for c 2 C do 4. Compute new number of replicas of c ARc, average cost of c AVc; 5. Set datacenter counter Nd = 0, the set of datacenters to add a replica of c ADDc = Null, the set of datacenters from which the replica of c will be removed DELc = Null; 6. for every user requesting for c do fCDc [ fdgg, 7. Find out the nearest datacenter d, CDc Nd ++; 8. end for 9. Sort the datacenters in CDc in descending order according to Nd; 10. for i = 1 to |CDc| do 11. d = CDc[1]; 12. if TLd + AVc  TLthreshold do fAPSc [ fdgg; CDc fCDc =fdgg; 13. APSc 14. TLd = TLd +AVc; 15. else 16. go to Step 10; 17. end if 18. if jAPSc j ¼¼ ARc do 19. break; 20. end if 21. end for 22. ADDc fAPSc  APSc \ OPSc g; DELc fOPSc  APSc \ OPSc g; 23. Add a replica of c into the datacenters in ADDc; 24. end for 25. for each c 2 C do 26. for each d 2 DELc do 27. if VFd,c == false do 28. Remove the replica of c from d; 29. end if 30. end for 31. end for

Complexity analysis: In lines 1–24, for each content, we compute the set of new datacenters for its placement. Sorting of content in line 2 requires OðjCj lg jCjÞ, where C is the set of content. In lines 6–8, we find the nearest datacenter for each user. Since the distance information for each source-destination pair is stored in the database in the initiation phase of the program, this step can be achieved by searching the database and the complexity is OðjRjÞ, where R is the set of user requests. Sorting datacenters in line 9 requires OðjDj lg jDjÞ, where D is the set of datacenters. In the for loop from line 10 to line 21, we compute the set of new datacenters for content c, whose complexity is OðjDjÞ. Thus, the complexity of the for loop from line 3 to line 24 is OðjCjðjRj þ jDj lg jDjÞÞ. In lines 25–31, we remove the replica of content c from datacenters in DELc when the online traffic terminates and the complexity for this step is OðjCjjDjÞ. Taking all steps into consideration, the time complexity of Algorithm 3 is OðjCjðlg jCj þ jRj þ jDj lg jDjÞÞ. Obviously, the algorithm runs in polynomial time. 5. Performance evaluation In this section, we first evaluate the performance of the MPCC scheme through the ILP model and heuristic algorithms under static traffic scenario in small-scale EODNs. Then the performance of the proposed heuristic algorithms is evaluated under dynamic traffic scenario in large-scale EODNs. Specifically, the performance of the heuristic MPCC algorithm considering the time-varying characteristic of user requests is also stated. 5.1. Static traffic scenario The ILP model and heuristic algorithms under static traffic scenario are conducted on the topology shown in Fig. 2, which has 6 nodes and 9 links. We assume that each datacenter has the same capacity 150 G and there are four kinds of content, which occupy 40 G, 50 G, 60 G, and 80 G storage resource respectively. The requests are generated randomly offline in advance and their bandwidth demand and protection level are uniformly distributed in a range of [100 Gbps, 500 Gbps] and [0.5, 1] respectively. The granularity of a FS is 12.5 GHz with a total of 50 slots on each fiber link and the transmission rate of a FS which adopts modulation level PDM-BPSK is 50 Gbps. The guard bandwidth between two adjacent traffics is 1 FS. For the scheme adopting distance-adaptive spectrum allocation, four modulation levels {PDM-BPSK, PDM-QPSK, PDM-8QAM, PDM-16QAM} are optional for each end-to-content path, while for the scheme adopting the lowest modulation level based spectrum allocation, only the modulation level PDM-BPSK can be adopted. The data rate per subcarrier and transmission reach of these modulation levels are shown in Table 1. We compare the spectrum consumption of the MPCC scheme with that of the FPCC scheme and the MPEE scheme (the number of node-disjoint paths is set to 3) through the ILP model, which is implemented using ILOG CPLEX v12.5. Moreover, we compare the spectrum consumption of heuristic algorithms with the optimal results obtained from the ILP model under static traffic scenario. Parameter K_Paths in Algorithm 2 is set to 3. Due to the high computational complexity, the simulation of the ILP model for the MPCC scheme consumes more than 4 h when there are over 10 requests. Consequently, the ILP model becomes inefficient and optimal results are difficult to be obtained when the request number exceeds 10. For heuristic algorithms, the results are obtained in time below 1 ms. Fig. 4(a) and (b) show the spectrum consumption of different schemes with distance-adaptive spectrum allocation and the

T. Gao et al. / Optical Fiber Technology 36 (2017) 353–365

lowest modulation level based spectrum allocation respectively. In Fig. 4(a) and (b), MPCC, FPCC, and MPEE represent the results of the MPCC scheme, the FPCC scheme, and the MPEE scheme obtained from the ILP model respectively, while H-MPCC represents the results of heuristic MPCC algorithm. Comparing Fig. 4(a) with (b), we can find that the distance-adaptive spectrum allocation can reduce the spectrum consumption dramatically. Moreover, MPCC presents good performance for both distance-adaptive spectrum allocation and the lowest modulation level based spectrum allocation. It can reduce the spectrum consumption by as high as 20% and 28% than FPCC and MPEE respectively for the distanceadaptive spectrum allocation. Meantime, although H-MPCC consumes a bit more spectrum resource than MPCC, it still outperforms FPCC and MPEE. H-MPCC saves over 15% spectrum resource than FPCC and over 20% spectrum resource than MPEE in more reasonable execution time. For the lowest modulation level based spectrum allocation, MPCC can reduce over 35% and 21% spectrum consumption than FPCC and MPEE respectively. HMPCC achieves similar results to that in distance-adaptive spectrum allocation, which reduces the spectrum consumption by over 23% and 12% than FPCC and MPEE respectively. Furthermore, with a larger K, MPCC will consume more spectrum resource. That is because more end-to-content paths cause more guard bandwidth consumption and the average length of end-to-content paths may be longer, which leads to more spectrum consumption. These results also show that without distance-adaptive spectrum allocation, FPCC consumes much more spectrum resource than MPEE. The reason is that, in FPCC, the FSs allocated to each end-tocontent path are almost twice than the FSs allocated to each end-to-end path in MPEE. Though the total hops of the paths in FPCC may be fewer than that in MPEE, the former will consume more spectrum resource than the latter. In conclusion, our proposed MPCC scheme achieves better spectrum efficiency than other two schemes in both cases. The benefits come at the cost of the replicas of content among multiple datacenters. As shown in Table 2, the average number of content replicas, which is calculated through dividing the number of all replicas of all content by the number of all content, is evaluated for different schemes with distance-adaptive spectrum allocation. From Table 2, we can find that both MPCC (K = 3) and H-MPCC replicate each content to all datacenters (there are 2 datacenters in total in the network topology). It is because in a small-scale network, by placing a replica of content in each datacenter, adequate

361

node-disjoint end-to-content paths can be obtained. While as the most spectrum-efficient scheme, MPCC (K = 2) has a smaller average number of content replicas, which is close to that of FPCC and a bit larger than that of MPEE. In conclusion, there is a tradeoff between the spectrum utilization and datacenter capacity utilization, while to improve the network survivability and the spectrum efficiency, it is reasonable to replicate the content to multiple datacenters appropriately. In Table 3, we present the average gap to optimal results yielded by the ILP model for each heuristic algorithm. Specifically, at each request number, we calculate the optimality gap between heuristic algorithms and optimal results, and finally take the average. For all heuristic algorithms under static traffic scenario, we run the simulation program 10 times to obtain the average value. The MPCC scheme (H-MPCC) provides the best results compared with the MPEE scheme (H-MPEE) and the FPCC scheme (H-FPCC). For H-FPCC, we can find that adopting the distance-adaptive spectrum allocation has a significant effect on improving the spectrum efficiency. In conclusion, under both scenarios with distanceadaptive spectrum allocation and the lowest modulation level based spectrum allocation, the optimality gap of our proposed heuristic algorithm is about 7%–9%, which is much smaller than other schemes. 5.2. Dynamic traffic scenario Under dynamic traffic scenario, heuristic algorithms are conducted on two representative network topologies NSFNET (14 nodes and 21 links) and COST239 (11 nodes and 26 links) shown in Fig. 5(a) and (b). We assume that NSFNET and COST239 both have three datacenters, each link has 200 FSs, each datacenter has the same capacity 150 G, and there are four kinds of content, which occupy 40 G, 50 G, 60 G, and 80 G storage resource respectively. Every user request is generated randomly online with the bandwidth demand and protection level uniformly distributed in a range of [100 Gbps, 500 Gbps] and [0.5, 1] respectively. The arrival of traffic follows a Poisson distribution with k requests per second and the request holding time follows the exponential distribution with a mean 1/l. Consequently, the traffic load is measured as k/l in erlang. Moreover, in the MPCC scheme, the maximum number of node-disjoint paths K_Paths in Algorithm 2 (denoted as K for short in this section) is set to 2 and 3. We run the simulation program 10 times in every traffic load scenario

Fig. 4. Total spectrum consumption of MPCC (K = 3), MPCC (K = 2), H-MPCC, FPCC, and MPEE (a) employing distance-adaptive spectrum allocation and (b) employing the lowest modulation level based spectrum allocation.

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Table 2 Average number of content replicas of MPCC(K = 3), MPCC (K = 2), H-MPCC, FPCC, and MPEE. Requests number

1

2

3

4

5

6

7

8

9

10

MPCC(K = 3) MPCC(K = 2) H-MPCC FPCC MPEE

2 1 2 1 1

2 1 2 1 1

2 1.333 2 1.333 1

2 1.250 2 1.250 1

2 1.400 2 1.200 1

2 1.167 2 1.167 1

2 1.429 2 1.571 1

2 1.375 2 1.375 1

2 1.222 2 1.333 1

2 1.200 2 1.300 1

Table 3 Performance of heuristic algorithms in static traffic scenario – the average gap to optimal results.

Distance-adaptive spectrum allocation The lowest modulation level based spectrum allocation

H-MPCC

H-FPCC

H-MPEE

7.3% 9.1%

45.4% 60.1%

29.7% 33.8%

and take the average to obtain precise results. For each simulation run, there are 10,000 requests arriving in EODNs. Fig. 6(a) and (b) show the blocking probability (BP) for the MPCC scheme, the FPCC scheme, and the MPEE scheme in NSFNET and COST239 respectively. The results show that our proposed MPCC scheme dramatically reduces the blocking probability comparing with the FPCC scheme and the MPEE scheme. Specially, at 1% of BP in NSFNET, the networks in the MPCC (K = 3) scheme can support about 250 Erlang of traffic, 61.3% more than 155 Erlang in the MPEE scheme and 47.1% more than 170 Erlang in the FPCC scheme. While in COST239, the networks in the MPCC (K = 3) scheme can support 520 Erlang of traffic, 48.6% more than 350 Erlang in both the FPCC scheme and the MPEE scheme at 1% of BP. With respect to different values of K, the MPCC scheme with a greater number of node-disjoint paths achieves lower blocking probability. That is because, with a larger K in the MPCC scheme, the FSs to be allocated on each path may be fewer than that with a smaller K, which makes the request less likely to be blocked when the spectrum resource is insufficient. In addition, the blocking probability is obviously higher in NSFNET than that in COST239. The reasons consist of two aspects. On the one hand, requests with the longer paths in NSFNET consume more FSs, which leads to the tension of resource, but the situation is alleviated in COST239. On the other hand, the mean node degree of COST239 is higher than that of NSFNET, which means more node-disjoint end-to-content paths are available. We also evaluate the spectrum resource utilization rate of the MPCC scheme, the FPCC scheme, and the MPEE scheme in NSFNET and COST239 respectively as shown in Fig. 7(a) and (b). For both

topologies, the MPCC scheme achieves higher spectrum efficiency than the FPCC scheme and the MPEE scheme. In traffic loads close to 1% of BP (250 Erlang in the MPCC (K = 3) scheme, 170 Erlang in the FPCC scheme, and 155 Erlang in the MPEE scheme) in NSFNET, the MPCC scheme consumes 23.4% spectrum resource less than that in the FPCC scheme and 24.6% spectrum resource less than that in the MPEE scheme. In COST239, the MPCC scheme consume 18.7% more spectrum resource than that in the MPEE scheme and 26.7% more spectrum resource than that in the FPCC scheme in traffic loads close to 1% of BP. Different from the results in NSFNET, the MPCC scheme consumes more spectrum resource than other schemes in COST239, which is due to the large increase of traffic loads. Moreover, with the increasing of traffic loads, the gap of spectrum consumption between the MPCC scheme and other schemes declines because many requests are blocked at high traffic loads in the FPCC scheme and the MPEE scheme. Furthermore, these results show that with a greater K, the heuristic MPCC algorithm achieves lower spectrum resource utilization rate, which is contrary to that of the ILP model for static traffic scenario. That is because, in the heuristic MPCC algorithm, we compare the spectrum consumption among different numbers of node-disjoint end-to-content paths, which range from 2 to K, and then choose the scenario that consumes the least spectrum resource. However, for the ILP model, the number of node-disjoint paths is fixed, which means the requests may occupy more spectrum resource when K is set to a greater value. Comparing Fig. 7(a) with (b), all schemes consume less spectrum resource in COST239 than that in NSFNET. That is obviously because that the average length of paths in COST239 is much shorter than that in NSFNET, which leads to lower spectrum consumption.

5.3. The DCP strategy based MPCC scheme under dynamic traffic scenario We evaluate the performance of the DCP strategy based MPCC (DCP-MPCC) scheme in the situation where the distribution of user requests is time-varying. The simulation parameters of requests are the same as those in Section 5.2. The distribution of user

Fig. 5. Test network topologies (link length in km) (a) NSFNET (b) COST239.

T. Gao et al. / Optical Fiber Technology 36 (2017) 353–365

363

Fig. 6. Blocking probability for MPCC (K = 3), MPCC (K = 2), FPCC, and MPEE (a) NSFNET (b) COST239.

Fig. 7. Spectrum consumption utilization rate of MPCC (K = 3), MPCC (K = 2), FPCC, and MPEE (a) NSFNET (b) COST239.

requests in EODNs varies randomly during the program runtime. The way to simulate the variation of the distribution of user requests is similar to the way to simulate the variation of disaster probabilities in [25]. More specifically, we divide the network topologies into 3 user zones, and at a random interval of time (according to the generated random digit) the users of a certain zone may request a certain kind of content intensively, meaning that the users in this zone will request a certain kind of content with a high probability (0.7 in our simulation). The user zone(s) where the variation occurs and the kind of content which is requested intensively are both randomly selected. In general, the average occurrence time of such variations during the program runtime in our simulation is about 10 (times). We compare the performance of the fixed content placement (FCP) based MPCC scheme (FCP-MPCC) as well as the DCP-MPCC scheme when sensitivity factor N equals to 1.2, 1.5, and 2.0. TLthreshold in the Algorithm 3, which is used to measure whether the datacenter is overloaded or not, is set to 0.8. Fig. 8(a) and (b) show the blocking probability for the FCPMPCC scheme and the DCP-MPCC scheme with different N in NSFNET and COST239 respectively. The DCP-MPCC scheme achieves better performance for all traffic load scenarios in both topologies. In more detail, at 1% of BP in NSFNET, the networks in the DCP-MPCC (N = 1.2) scheme can support about 300 Erlang of traffic, 74.4% more than 172 Erlang in the FCP-MPCC scheme.

While in COST239, the networks in the DCP-MPCC (N = 1.2) scheme can support 64% more traffic loads than that in the FCP-MPCC scheme. The reason is that the load balance is taken into consideration when content placement is dynamically readjusted, which avoids the case that traffic is blocked due to lacking spectrum resource on the fiber links connected to the datacenter hosting the required content. Comparing Fig. 8(a) with (b), we can find that the DCP-MPCC scheme gains higher performance improvement in COST239 than in NSFNET. It is because COST239 has a higher mean nodal degree than NSFNET and the users can benefit more in COST239 than in NSFNET to get the required content from the nearest datacenter through an end-to-content path with fewer hops. The result also shows that with greater N, the DCP-MPCC scheme achieves better blocking probability but the performance gap among N = 1.2, 1.5, and 2.0 is small. Smaller N means higher frequency for content placement, which increases the cost of content synchronization and replication. Consequently, we can set N to 1.5 or 2.0 to trade off between the spectrum resource consumption and the cost of content placement. With respect to the spectrum resource utilization rate as shown in Fig. 9 (a) and (b), in every traffic load scenario, the FCP-MPCC scheme consumes more spectrum resource than the DCP-MPCC scheme. The DCP-MPCC (N = 1.2) scheme can reduce spectrum resource consumption by 17.4% and 8.2% at the traffic loads of 600 Erlang in NSFNET and at the traffic loads of 800 Erlang in

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Fig. 8. Blocking probability for FCP-MPCC, DCP-MPCC(N = 2.0), DCP-MPCC(N = 1.5), and DCP-MPCC(N = 1.2) (a) NSFNET (b) COST239.

Fig. 9. Spectrum resource utilization rate for FCP-MPCC, DCP-MPCC(N = 2.0), DCP-MPCC(N = 1.5), and DCP-MPCC (N = 1.2) (a) NSFNET (b) COST239.

COST239 respectively. Specially, in both NSFNET and COST239, the DCP-MPCC (N = 1.2) scheme consume almost as much spectrum resource as that in the FCP-MPCC scheme in the traffic loads close to 1% of BP. The advantage of the DCP-MPCC scheme is remarkable because the content placement is dynamically readjusted corresponding to the variation of the distribution of user requests, which avoids the spectrum resource waste caused by transmitting data through a long end-to-content path from the datacenter hosting the required content to the user. Similarly, the gap of spectrum resource utilization among the DCP-MPCC schemes with different values of N is small, which verifies that setting N to a value equal to or larger than 1.5 is appropriate.

DCP-MPCC scheme achieves better performance than traditional protection schemes in both spectrum resource utilization rate and blocking probability and has a great adaption to the variation of the distribution of user requests. Acknowledgments Part of this work appeared in the proceeding of OECC 2016, Niigata, Japan. This work is supported in part by the National Natural Science Foundation of China (Nos. 61331008, 61601054 and 61571058), the National Science Foundation for Outstanding Youth Scholars of China (No. 61622102). References

6. Conclusions Improving the survivability and spectrum efficiency is an important issue in EODNs with content connectivity. The proposed MPCC scheme can further reduce the spectrum resource consumption comparing with traditional protection schemes, meanwhile, the survivability of networks is improved. With the factor that the distribution of user requests varies with time passing by taken into consideration, the content placement is dynamically readjusted to minimize the spectrum resource consumption through our proposed DCP strategy. The numerical results show that the

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