Dynamic time and spectrum fragmentation-aware service provisioning in elastic optical networks with multi-path routing

Optical Fiber Technology 32 (2016) 13–22

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Dynamic time and spectrum fragmentation-aware service provisioning in elastic optical networks with multi-path routing Ruijie Zhu a,b,⇑, Yongli Zhao a, Hui Yang a, Xiaosong Yu a, Jie Zhang a, Ashkan Yousefpour b, Nannan Wang b, Jason P. Jue b a b

State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China The University of Texas at Dallas, Richardson, TX 75080, USA

a r t i c l e

i n f o

Article history: Received 17 May 2016 Revised 25 July 2016 Accepted 28 August 2016

Keywords: Fragmentation-aware Multi-path Elastic optical networks Advance reservation

a b s t r a c t In this paper, we propose a multi-path fragmentation-aware routing, modulation and spectrum assignment algorithm (RMSA) for advance reservation (AR) and immediate reservation (IR) requests in elastic optical networks. Immediate reservation requests should be provided with service immediately, while advance reservation requests have specific starting times and holding times. As lightpaths are set up and torn down, fragmentation may occur in both spectrum and time domains. To decrease the two-dimensional fragmentation and to solve the problem of resource scarcity, we propose splitting requests into different parts and transferring these parts along one or more paths utilizing sliceable bandwidth variable transponders. We first introduce a model to solve the problem and propose a two-dimensional fragmentation occurrence measurement in spectrum and time domains. Then we propose a multi-path fragmentation-aware RMSA algorithm (MPFA). Simulation results show that MPFA can achieve better performance than existing algorithms in terms of blocking probability and spectrum utilization. Ó 2016 Elsevier Inc. All rights reserved.

1. Introduction With the emergence of diverse new applications and services over optical networks, different levels of QoS must be offered to network customers. Real time applications, such as IPTV and e-Science applications, need to be provided with service immediately, and the service will be torn down upon completion. These types of requests are called immediate reservation (IR) requests. On the other hand, time-sensitive applications have specific starting times and holding times, such as data backup or data migration. Network operators can reserve resources for these applications in advance, and the resources will not be used until the starting time. These types of requests are called advance reservation (AR) requests [1]. As these applications have a variety of requirements, it becomes difficult to satisfy all of these applications in a flexible manner with traditional wavelength-division multiplexing (WDM) optical networks. Enabled by orthogonal frequency division modulation (OFDM) technology and sliceable bandwidth-variable transponder, ⇑ Corresponding author at: State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China. E-mail address: [email protected] (R. Zhu). http://dx.doi.org/10.1016/j.yofte.2016.08.009 1068-5200/Ó 2016 Elsevier Inc. All rights reserved.

elastic optical networks (EONs) can be a promising candidate for these diverse requirements [2]. In EONs, the optical spectrum is partitioned into finer granularity, such as 6.25 GHz or 12.5 GHz spectrum slots. In this way, requests with different rates can be adaptively converted into a variable number of frequency slots (FSs) considering the path distance and modulation formats [3]. Further flexibility is achieved in EONs by the assignment of multi-flow transponders (MF-OTP) [4] or sliceable bandwidth variable transponders (S-BVTs) [5–6]. S-BVTs support sliceability, i.e., the capability of generating multiple optical carriers that can be used to support different lightpaths to different destinations. Fig. 1 shows the architecture of a S-BVT connected with bandwidth-variable optical cross-connects (BV-OXC). The architecture of the S-BVT adopted here is formed by a flow classifier, OTN mappers, a set of sub-transponders, and an optical MUX. In the sender part, five sub-carriers are used. These sub-carriers can support three line rates, i.e., 40 Gbps, 100 Gbps, and 400 Gbps separately. It is worth noting that request A is served with three spectrum bands, A1, A2, and A3, which can transport 40 Gbps, 100 Gbps, and 100 Gbps, respectively. A1 is allocated on Path 1, but there are insufficient spectrum resources for A2 and A3. Thus A2 and A3 are allocated on Path 2. With S-BVTs, the request can be provided with service in a multi-path way.

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R. Zhu et al. / Optical Fiber Technology 32 (2016) 13–22

Fig. 1. Sliceable bandwidth variable transponder (S-BVT).

Due to the huge increase in applications, AR services are expected to be an important growing part of future networks. As these services are dynamic and lightpaths are set up and torn down, it is common for spectrum and time fragmentations to occur. As this two-dimensional fragmentation can waste many resources and decrease the network performance, it becomes extremely important for the network operator to decrease this two-dimensional fragmentation during service provisioning. Previous algorithms [7,8] can decrease fragmentation, but they focused on a single path, and if the requests cannot be provisioned on a single path, they will be blocked. One reason for blocked requests is that there are insufficient resources on a single path, therefore, a multi-path method may help to solve this problem and decrease the two-dimensional fragmentation. In this paper, to decrease the two-dimensional fragmentation and solve the problem of resources scarcity, we propose splitting AR and IR requests into smaller parts, assigning the parts to different segments, and then transferring these parts along a single path or multiple paths. We also propose a fragmentation occurrence measurement to accurately evaluate if fragmentation will occur when we assign the requests to the available resources. In this way, the spectrum and time fragmentation can be decreased, and the resource utilization will increase. It is worth noting that the differential delay between the routing paths can be addressed with additional electronic buffering in the higher layer of the destination node [9]. The rest of the paper is organized as follows. In Section 2, we review the related works. In Section 3, we describe the problem formulation and fragmentation occurrence measurement in detail. We design a multi-path fragmentation-aware RMSA algorithm (MPFA) in Section 4. The performance evaluation is presented in Section 5. Finally, Section 6 summarizes the paper.

imental results showed that their proposed system performs well and can increase total revenue-gain effectively. In [14], Li et al. studied the provisioning schemes for dynamic advance reservation multicast requests in EONs and demonstrated these schemes on a Software-defined EON testbed that utilized OpenFlow in the control plane. During the provisioning process for AR requests, as lightpaths are set up and torn down, fragmentations may occur in both the spectrum and time domains. To decrease this two-dimensional fragmentation, Wang et al. proposed a max volume selectivity algorithm to decrease the blocking probability for advance reservation requests in [7]. Lu et al. studied an adjustable routing and spectrum assignment (RSA) algorithm for bulk-data transfer to recycle spectrum fragments in EONs [8]. To further decrease the two-dimensional fragmentation, we propose a multi-path scheme. Previously, multi-path solutions have been proposed to solve problems related to the scarcity of resources and survivability in EONs [15–21]. The split spectrum approach [15], a fundamental technology for multi-path was first proposed by Dahlfort et al. and simulation results showed that split spectrum can decrease the blocking probability by over 50% and can achieve 50% higher spectral efficiency compared to non-split elastic optical networking [16]. Chen et al. designed a multipath defragmentation method which aggregated spectrum fragmentation without interrupting existing services [17]. In [18], Zhu et al. proposed several online service provisioning algorithms that incorporate dynamic RMSA with a hybrid single-/multi-path routing (HSMR) scheme. Results showed that they could decrease the network bandwidth fragmentation ratio. Yang et al. proposed multi-flow virtual concatenation (MFVC) in elastic optical networks to improve spectrum utilization using noncontiguous spectrum fragments [19]. To solve the problem of multipath routing under heavy traffic load, Fan et al. designed a dynamic multipath routing algorithm with traffic grooming [20]. In [21], Dharmaweera et al. investigated the potential gains by jointly employing traffic grooming and multipath routing techniques with a realistic physical impairment model. In [22], a multi-path provisioning protection (MPP) scheme was proposed to guarantee survivability in flexible optical networks, and it was shown to provide protection with better efficiency than single-path provisioning protection (SPP). Yin et al. presented a survivable multi-path routing and resource assignment scheme to guarantee the survivability of virtual optical networks in [23]. In this paper, we study advance reservation requests provisioning in EONs with multi-path routing, in order to solve the problem of resources scarcity and to decrease the two-dimensional fragmentation. 3. Problem formulation In this section, we first introduce a model to solve the problem, then we propose a fragmentation occurrence measurement considering both time and spectrum domains.

2. Related works 3.1. Problem description Researchers have previously studied various aspects of advanced reservation request provisioning over optical networks. Provisioning deadline-specific AR requests with flexible transmission rates in WDM mesh networks was proposed in [10]. Lu et al. investigated hybrid IR and AR service provisioning in elastic optical networks, with the objective to minimize IR/AR service conflicts [11]. A traffic grooming algorithm for the connection establishment of deadline-specific AR requests in elastic optical networks was studied in [12]. An OpenFlow-controlled revenue-driven advance reservation (AR) provisioning in software-defined elastic optical networks (SD-EONs) has been proposed in [13]. The exper-

The substrate elastic optical networks can be modeled as a graph Gs ¼ ðLs ; N s ; Rst ; Ds Þ, where Ls represents the set of physical optical links, Ns is the set of physical optical nodes, and Rst is the state of the resources of the physical optical links and nodes at time t. In this paper, we assume that Rst includes the resources of physical fiber links, which is the status of the spectrum of the fiber links at time t, and the resources of physical nodes, which specifies the available number of sub-transponders at a node at time t. Ds is a set of physical distances between each pair of adjacent node in Ns. For example, Ds(a, b) is the distance between node a and node

R. Zhu et al. / Optical Fiber Technology 32 (2016) 13–22

b in the EON. Different modulation formats have different reachability, and we will choose the optimal modulation format (BPSK, QPSK) for a request based on the physical length of the path. We consider two types of requests, IR requests and AR requests. IR requests should be provided with service immediately. They are denoted by RI ¼ ðs; d; w; hÞ, where s is the source node and d is the destination node for the request, w is the line rate requested by RI, and h is the holding time. RA ¼ ðs; d; w; b; hÞ represents an advance reservation request, where s and d have the same meaning as an immediate reservation request, b is the starting time, and h is the holding time of the AR request. w is the line rate requested by the AR request during the time period h from starting time b. If sufficient spectrum resources are not available for an incoming request, we attempt to split the request into different parts and allocate separate spectrum resources for each part. A simple example of the process is shown in Fig. 2. To reflect the spectrum condition in the time domain, we utilize a two-dimensional resource model and assume each time slot has the same time period. An example network is shown in Fig. 2(a) and there is an AR request from node A to node D, and the request requires two spectrum slots from time T2 to T3. Fig. 2(b) and (c) show the spectrum status of path A-C-D and path A-B-D respectively. Black slots denote the occupied slots, and white slots denote the available slots. Shaded slots are the slots assigned to the AR request. We can see that before splitting the request, sufficient resources are not available on either path A-C-D or path A-B-D. However, if the request is split into two parts, resources can be allocated on both parts simultaneously, allowing the request to be fulfilled. 3.2. Fragmentation occurrence measurement Previous work has studied how to decrease the spectrum fragmentation during the routing and spectrum allocation process [24–25], but did not consider the time dimension. In this paper, based on the two-dimensional model, we propose a time and spectrum fragmentation occurrence measurement as shown in Fig. 3. The objective of our method is to minimize the occurrence of time and spectrum fragmentation after the assignment of the spectrum slots. For simplicity, we consider a two-dimensional block from spectrum slot Ss to Se and from time slot T s to T e . Slotij is used to represent the slot at spectrum slot Si and time slot T j . Oij represents whether Slotij is occupied. If the slot is occupied by a previous request, then Oij is 1, otherwise it is 0. We then introduce Sij to describe whether spectrum fragmentation will occur if we assign a request to the slot at spectrum slot Si and time slot T j .

8 > < 1; ðOi1;j ¼ 0 and Oiþ1;j ¼ 0Þ and i–Ss # Sij ¼ 0; otherwise i 2 ðSs ; Se Þ; j 2 ðT s ; T e Þ > : ð3Þ

If spectrum fragmentation occurs when we assign a request to Slotij that requires one spectrum slot and lasts one time slot, then Sij will be 1, otherwise it will be 0. An example is shown in Fig. 3

Fig. 3. (a, b) The spectrum fragmentation occurrence if we pre-assign a spectrum slot; (c, d) the time fragmentation occurrence.

(a) and (b). These two figures show the process to judge whether the spectrum fragmentation will occur, where black slots are the occupied slots, and white slots are the available slots. In Fig. 3(a), the shaded box is the pre-assigned slot, and we can see that it will not result in fragmentation in the spectrum dimension. If Slot22 is selected, as shown in Fig. 3(b), the available spectrum resource at time T 2 will be separated into two parts, resulting in spectrum fragmentation. Thus we define S22 to be 1. In a similar way, the occurrence of time fragmentation is described below:

8 > < 1; Oi;j1 ¼ 0 and Oi;jþ1 ¼ 0 T ij ¼ 1; Oi;j1 ¼ 0 and j ¼ T e i 2 ðSs ; Se Þ; j 2 ðT s ; T e Þ > : 0; otherwise

ð4Þ

If time fragmentation occurs when we assign a request to Slotij, then Tij will be 1, otherwise it will be 0. The measurement is illustrated in Fig. 3(c) and (d). To measure the real availability of the spectrum slots in this two-dimensional model, we sum the Sij and Tij of all available spectrum slots. We first sum the Sij and Tij separately. We will call the total occurrence of spectrum fragmentation Scut and the total occurrence of time fragmentation Tcut.

Scut ¼ and

T cut ¼

X

Sij;

iðSs ;Se Þ;jðT s ;T e Þ

X

T ij:

iðSs ;Se Þ;jðT s ;T e Þ

ð5Þ

ð6Þ

We then sum Scut and Tcut to obtain the total fragmentation occurrence number to reflect the status of this block. We define this number to be Acut as described below:

Acut ¼ aScut þ bT cut;

Fig. 2. (a) The example network; (b) the spectrum situation of Path ACD; (c) the spectrum situation of Path ABD.

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ð7Þ

where a and b are simply weight factors that decide the importance of Scut and Tcut in the calculation of Acut. We assume a and b are both 1 (Scut and Tcut have equal weight). When the number of occupied slots of a resource block are kept to be the same, a larger Acut means that there is less fragmentation and that more requests can be assigned to the block. We show a detailed example in Fig. 4(a) and (b). The number on the left side

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computation complexity can be decreased, and the twodimensional fragmentation can still be measured accurately. When the requests cannot find suitable resources in a single block, we will split the request into different parts to assign them into different resource blocks along a single path or multiple paths. In this way, we can decrease the fragmentation and increase resource utilization. 4. Dynamic RMSA algorithm In this section, we design a RMSA algorithm, named the multipath fragmentation-aware (MPFA) algorithm, which is based on the fragmentation occurrence measurement. This algorithm consists of three stages: fragmentation-aware stage, parallel fragmentation stage, and multi-path fragmentation-aware stage. First we try to find suitable resources to be assigned to the incoming request while minimizing the occurrence of fragmentation. If there are not enough resources for the request in a single spectrum block, we will split the request into different parts and transmit these parts over a single path or over multiple paths. 4.1. Fragmentation-aware stage Fig. 4. Two-dimensional fragmentation occurrence calculation.

of each available slot is the spectrum fragmentation Sij, and the number on the right side of each slot is the time fragmentation Tij. Then we sum the Sij for each time slot, as shown in the column on the right side of the entire block. These numbers reflect the spectrum situation at a certain time slot. In the same way, we sum the value of Tij for each spectrum slot as shown in the row at the top of the entire block. This number reflects the situation of the time resource for a specific spectrum slot. We sum Sij and Tij separately. As shown in Fig. 4(a), the sum of Sij, Scut is 6 and the sum of Tij, Tcut is 8. Then we sum Scut and Tcut, to obtain Acut. The value of Acut in Fig. 4(b) is 18, which is larger than Acut of Fig. 4(a). This result means that there is greater fragmentation for the spectrum state in Fig. 4(a) compared to the spectrum state in Fig. 4(b). During the RMSA process, we try our best to maintain a high value of Acut to reduce the occurrence of spectrum and time fragmentation. To make it clearer, we state a simple example in Fig. 4(c) and (d). We assume that there a AR request that requires one spectrum slot, starts at time T 2 and lasts for one time slot. If we assign this request to Slot12 or Slot22, the corresponding will be changed to 9, or 11, respectively. Then allocating this request to Slot22 will be a better solution to maintain a higher value of Acut, and the decrease of Acut is only 3. In some cases the Acut may be the same after the request allocation based on different resource allocations. In this scenario, the first-fit resource allocation that achieves the lowest decrease of Acut of the block will be chosen as the allocation for the request. It is worth noting that when we allocate a request, only the status of the slots surrounding the allocated slots and the status of the allocated slots will be changed. Therefore, in order to decrease the computation complexity, we will just need to consider the status of the allocated slots and the status of the slots surrounding the allocated slots other than the whole resource block. As shown in Fig. 4(c) and (d), the slots that are included in the dashed red rectangle will be used to measure the decrease of Acut after the request allocation. In Fig. 4(c), for the resource block included by the red dashed rectangle, its Acut is 8 before allocating the request to Slot12, and its Acut will be changed to 3 after the allocation. Thus, the decrease of the Acut of the resource block included by the red dashed rectangle is 5. In the same way, the decrease of the Acut of the resource block included by the red dashed rectangle in Fig. 4(d) is 3. In this way, the

First we use the k-shortest path algorithm to find k candidate paths for the incoming request. Then for each candidate path, we can select an optimal modulation format for the request considering the distance between the source and destination nodes. In this way, the number of required slots can be decreased. Based on the two-dimensional resource model for each candidate path, we will search the whole resource block from the lowest spectrum index to find all suitable spectrum allocation solutions, where each solution has consecutive slots within the specific time domain that can satisfy the request’s requirement. After the allocation of each solution, the spectrum status will be changed. To evaluate the degree to which each allocation affects the fragmentation, we calculate Alcut ðSs ; Se ; t s ; te Þ for each link of this candidate path before we assign the spectrum resource to the request, where Ss is the starting spectrum, Se is the ending spectrum, ts is the starting time and t e is the ending time. We sum Alcut ðSs ; Se ; ts ; t e Þ for all the links in this candidate path, and then we obtain Abefore cut ðSs ; Se ; t s ; t e Þ: In the same way, after allocation of the spectrum, we obtain Aafter cut ðSs ; Se ; t s ; t e Þ. Then we obtain DAcut ðSs ; Se ; t s ; te Þ for all the links of this candidate path as follows, after DAcut ðSs ; Se ; ts ; t e Þ ¼ Abefore cut ðSs ; Se ; t s ; t e Þ  Acut ðSs ; Se ; t s ; t e Þ

ð8Þ

We will select the spectrum allocation whose DAcut ðSs ; Se ; ts ; t e Þ is the minimum for this candidate path. After that, we have DAcut ðSs ; Se ; t s ; te Þ for each candidate path. Then we will choose one candidate path and its corresponding spectrum allocation scheme that has the minimum DAcut among all the candidate paths. As shown in Fig. 4(c) and (d), we note that only the status of allocated slots and the status of the slots surrounding the allocated slots will change after the allocation of a request. Thus, in order to decrease the computation complexity, we just need to consider the status of the allocated slots and the status of the slots surrounding the allocated slots to calculate DAcut rather than the whole resource block. The resource block used for calculating DAcut of each available spectrum allocation scheme is set to be ðSs ; Se ; t s ; t e Þ, where Ss is the starting spectrum slot index of this spectrum allocation minus one spectrum slot, Se is the starting spectrum slot index of this spectrum allocation plus the required spectrum slots plus one spectrum slot, t s is the future starting time for AR request, and t e is the starting time plus the holding time plus one time slot. For IR requests, ts is set to the current time and t e is set to the hold-

R. Zhu et al. / Optical Fiber Technology 32 (2016) 13–22

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ing time plus one time slot. Ss and Se are set in the same way that they are set in AR requests. It is worth noting that if the starting spectrum slot index of a spectrum allocation is 0, then Ss is set to be 0. In a similar way, if the starting spectrum slot index of a spectrum allocation plus the bandwidth requirement is the last spectrum slot of this fiber, then Se is set to be the last spectrum slot of this fiber. In this way, we can choose the best spectrum allocation method for the incoming request considering the fragmentation for the links of the path. The details of this stage are shown below.

4.3. Multi-path fragmentation-aware stage For requests that are blocked in both the first and second stage, we run the third stage in which the three split requests are routed along two or three different paths among the set of found candidate paths in Stage 1. First we find all the candidate path combinations hP ðs;dÞ ; P0ðs;dÞ i out of the set of candidate paths. Then we try to find

4.2. Parallel fragmentation-aware stage Requests that are blocked in the first stage are split into multiple parts. In this algorithm, we assume a request can be split into at most three parts R1, R2, and R3. Based on the line rates that the subcarriers can provide, some requests cannot be split. For example, in our simulation, we have three line rates that can be used to support the requests, 40 Gb/s, 100 Gb/s, and 400 Gb/s. Requests with line rate of 80 Gb/s, 140 Gb/s, or 200 Gb/s can be split into two parts by a combination of 40 Gb/s and 100 Gb/s subcarriers, and requests with line rate of 120 Gb/s, 180 Gb/s, or 300 Gb/s can be split into three parts by the combination of 40 Gb/s and 100 Gb/s subcarriers. However, a request with a line rate 40 Gb/s can not be split into smaller parts. We will use the k candidate paths that have been found in the fragmentation-aware stage. For each candidate path, we can allocate optimal modulation formats for R1, R2, and R3 separately, considering the distance of the candidate path. First, based on the two-dimensional resource model for each candidate path, we can find all the spectrum allocation schemes for R1. Then for each spectrum allocation scheme of R1, we will find the spectrum allocation schemes for R2. In the same way, for each spectrum allocation solution of R2, we will find the spectrum allocation solutions for R3. For each of the combination of spectrum allocation schemes for R1, R2, and R3, we will obtain DAcut ðSs ; Se ; ts ; t e Þ as in Stage 1. We will select the spectrum allocation combination whose DAcut ðSs ; Se ; t s ; te Þ is the minimum for this candidate path. We then have DAcut for each candidate path. Finally, we will choose one candidate path and its spectrum allocation combination that has the minimum DAcut as the routing and spectrum assignment method. The details of the parallel fragmentation-aware stage are shown below.

the groups hG0 ; G00 i ¼ hR1 ; R2 ; R3 i, where G0 is one request chosen out the set {R1, R2, R3}, and G00 contains the remaining two requests. On path P ðs;dÞ , we try to find the suitable spectrum allocation solutions for the request in G0 using Stage 1 and calculate DAcut ðSs ; Se ; t s ; te Þ as shown in Eq. (8). We define this as DA0cut . Then for the requests in G00 , we will use Stage 2 to find the suitable spectrum allocation solutions and calculate DAcut, defined as DA00cut . We can obtain the sum of DA0cut and DA00cut as DAall cut . Using this approach, for each path combination, we can obtain the corresponding DAall cut . At last we select the minimum DAall cut and its corresponding path combinations, modulation format and spectrum allocation as the RMSA method for R1, R2, and R3. To make it clearer, we state an example shown in Fig. 5(c). We can see that the requests R1, R2 and R3 are separated into two groups R1 and R2R3 (G0 and G00 ). R1 is routed along path A-C-D, and requests R2 and R3 are routed along path A-E-D. However, we might still not be able to find the available resources for split requests. In this case, we find all the combination of three paths hPðs;dÞ ; P 0ðs;dÞ ; P 00ðs;dÞ i out of the set of candidate paths, and we will try to allocate the requests on one candidate path of the permuted set hPðs;dÞ ; P 0ðs;dÞ ; P00ðs;dÞ i. For example, on path Pðs;dÞ , we find the optimal modulation format for R1 and find all the spectrum allocation strategies for R1 based on the twodimensional resource model. For R2 and R3, we will do the same thing but on candidate paths P 0ðs;dÞ and P 00ðs;dÞ respectively. In this way, we can try all the combinations of path selection, modulation format and spectrum allocation strategies for R1, R2 and R3. For each combination method, we will calculate DAcut according to Eq. (8). Finally, we select the minimum DAcut and its corresponding path selection, modulation format and spectrum allocation strategy as the RMSA method for R1, R2 and R3. The process is

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4.4. Complexity analysis The first step in the algorithm is finding the k-shortest paths (k = 3) from source to destination. For this we use the KSP [26] whose time complexity is OðjLs j þ jN s j log jN s jÞ. In Stage 1, the complexity of steps 2–7 is OðS  r  hÞ, and steps 8–12 take a constant time to run, where S is the number of spectrum slots of the physical link, r is the number of spectrum slots that the request required and h is the holding time of the request. Because the maximal number of potential spectrum allocations is S, and the number of spectrum slots and time slots that are used to calculate DAcut is ðr þ 2Þ  ðh þ 2Þ. The overall complexity of Stage 1 is OðjLs j þ jN s j log jN s j þ k  S  r  hÞ. In Stage 2, the time complexity of steps 4–10 is OðS  S  S  r  hÞ. Since the rest of the steps take conFig. 5. (a) Fragmentation-aware stage; (b) parallel fragmentation-aware stage; (c, d) multi-path fragmentation-aware.

illustrated in Fig. 5(d), we can see that request R1 is routed along path A-C-D, request R2 is routed along path A-E-D and request R3 is routed along path A-B-D. When different parts of a request are transferred over multiple paths, differential delay between these routing paths may occur. This issue can be addressed with additional electronic buffering in the higher layer of the destination node [9]. The details of the multi-path fragmentation-aware algorithm are shown below

stant time, the overall complexity of Stage 2 is Oðk  S3  r  hÞ. In Stage 3, the complexity of steps 1–5 is Oðk  kðS þ S  SÞ  r  hÞ, because the number of permutations of the groups is k  ðk  1Þ. Steps 9–18 take Oðk  k  k  S  S  S  r  hÞ, because the number of permutations of the paths isk  ðk  1Þ  ðk  2Þ. The rest steps of Stage 3 take constant time, so the complexity of Stage 3 is 3

Oðk  S3  r  hÞ. Hence the algorithm’s worst time complexity is 3

OðjLs j þ jN s j log jN s j þ k  S3  r  hÞ.

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R. Zhu et al. / Optical Fiber Technology 32 (2016) 13–22 Table 1 Simulation parameters.

5. Simulation results and discussion We evaluate the proposed algorithm through simulation using the 14-node NSFNET and 24-node USFNET as shown in Fig. 6. We assume that the substrate network is an elastic optical network and it is configured in the C-band, in which the bandwidth of each fiber link is 4.475 THz. Based on O-OFDM technology, a spectrum frequency slot regularly occupies 12.5 GHz, thus, there are 358 slots on each fiber link. Each physical node is equipped with 50 sliceable bandwidth variable transponders (S-BVTs) and each SBVT can be sliced into 10 sub-transponders (Transponder resources are overprovisioned). The supported line rates and modulation formats are 40 Gb/s DP-BPSK or 40 Gb/s DP-QPSK, 100 Gb/s DP-BPSK or 100 Gb/s DP-QPSK, and 400 Gb/s DP-16QAM or 400 Gb/s DPQPSK. Different line rates and modulation formats have their corresponding reachability and bandwidth requirement, as shown in Table 1 [27]. In this simulation the line rate for each request is uniformly distributed over {40 Gb/s, 80 Gb/s, 100 Gb/s, 120 Gb/s, 140 Gb/s, 180 Gb/s, 200 Gb/s, 240 Gb/s, 300 Gb/s, 400 Gb/s}. The requests consist of an equal amount of IR requests and AR requests. We assume that the duration of each time slot is 10 min. Each AR request has a fixed starting time, and the starting time of AR requests is equally distributed between 10 time slots and 30 time slots. The incoming requests follow a Poisson process with a rate of

Rate [Gb/s]

Channel width [GHz]

Modulation format

Reach [km]

40 40 100 100 400 400

25.0 50.0 37.5 50.0 75.0 125.0

DP-QPSK DP-BPSK DP-QPSK DP-BPSK DP-16-QAM DP-QPSK

1800 2500 1700 2000 600 1200

k requests per minute, and the holding time has a negative exponential distribution with parameter l. The results are extracted from 100,000 requests. In order to evaluate the performance of the MPFA algorithm, we select the First-Fit algorithm [3], the MVS algorithm [7], and multipath spectrum fragmentation aware (MFSA) algorithm for comparison. For MPSA algorithm, it is a specific scenario of MPFA algorithm, where a is set to be 1 and b is set to be 0 in Eq. (7). 5.1. Blocking probability analysis Fig. 7 compares the performance of the proposed MPFA algorithm with First-Fit (FF), MVS, and MPSA in terms of blocking

(a) 14-node NSFNET

(b) 24-node USFNET Fig. 6. Simulation topology.

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Fig. 7. Blocking probability (NSFNET).

probability with the NSFNET topology. For MPFA, a and b are set to be 0.7 and 0.3, respectively. From the results, we can see that MPFA can greatly reduce the blocking probability compared to FF, MVS, and MPSA. When the traffic load is 800 Erlang, the blocking probability of MPFA will decrease approximately 37% with l equal to 0.1, compared to the FF algorithm. The reason is that MPFA takes into account the time resource and the spectrum resource to decrease the two-dimensional fragmentation. Compared with MVS, when the request cannot be assigned to a single path, it will be split into different parts and will be assigned to multiple paths. In this way, the previous blocked requests will be changed into smaller granularity requests and will be assigned into the fragments of multiple paths. This approach improves the status of the spectrum and further decreases the blocking probability. As to MPSA, the time fragmentation is considered in MPFA. Thus the blocking probability can be decreased further. We observe that when l increases, the performance of MPFA will be improved. As the holding time decreases, the two-dimensional fragmentation measurement that we proposed can measure the fragmentation more accurately, thus the arriving requests will encounter less fragmentation The USNET network topology has also been used to evaluate the performance of the proposed MPFA algorithm in terms of blocking probability in a larger topology. As shown in Fig. 8, the blocking

probability follows the similar trend with the results in NSFNET. So the proposed algorithm can achieve similar performance improvement under different network topologies. To evaluate MPFA’s performance based on different weights of Eq. (7), the weights a and b are set to be different numbers. From the figures shown in Fig. 9, we can note that when a equals 0.7 and b equals 0.3, MPFA can achieve the best performance. The reason is that the spectrum fragmentation is more critical than the time fragmentation. At the same time, we can not ignore the time fragmentation, as b equals 0 gives the worst results. 5.2. Spectrum Utilization Analysis The spectrum utilization among the three different RMSA algorithms is illustrated in Fig. 10. For MPFA, a and b is also set to be 0.7 and 0.3, respectively. We can see that the proposed MPFA algorithm obtains better performance than FF, MVS and MPSA. As l increases, the performance of MPFA will be improved. The reason is that the spectrum resources are divided into smaller pieces of spectrum blocks based on the two-dimensional resource model, and the requests are split into smaller granularities and assigned to multi-paths when they are blocked in single path. In this way, the time and spectrum resources can be more efficiently used, and more requests can be allocated.

Fig. 8. Blocking probability (USFNET).

R. Zhu et al. / Optical Fiber Technology 32 (2016) 13–22

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Fig. 9. Blocking probability based on different weights (NSFNET).

Fig. 10. Spectrum utilization (NSFNET).

6. Conclusion In this paper, a multi-path fragmentation-aware (MPFA) algorithm is proposed to address the issue of resources scarcity along a single path and to decrease the two-dimensional fragmentation with the provisioning of AR requests. We first propose a two-dimensional fragmentation evaluation method to evaluate the fragmentation accurately. Based on this fragmentation evaluation method, a multi-path fragmentation-aware algorithm, i.e., MPFA, is proposed. For different traffic loads and different average holding time, we evaluate the performance of MPFA, and the simulation results show that the MPFA can decrease the blocking probability and increase the resource utilization. In our future work, we plan to set transponder resources to be limited to evaluate how the performances of the algorithms are affected in this situation. Acknowledgement This work has been supported in part by NSFC project (61271189, 61571058 and 61501049), 863 program (2015AA015503), Fund of State Key Laboratory of Information Photonics and Optical

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