Space division multiplexing enabled elastic optical networks (SDM-EONs) with multi-core fiber (MCF) have become a promising candidate for future optical transport networks, due to their high capacity and flexibility. Meanwhile, driven by the development of cloud computing and data centers, more types of requests are allowed in the networks, i.e., the usual immediate reservation (IR) requests, which need to be served immediately, and advance reservation (AR) requests, which support initial-delay tolerance services. However, with the introduction of AR requests, spectrum fragments occur frequently in both spatial and time dimension as lightpaths are set up and torn down, and the issue of spectrum fragmentation could be much more serious in SDM-EONs than in simple EONs. To measure fragments status in both spatial and time dimension in SDM-EONs, we first design a metric, i.e., time-dimensional spectrum compactness (TSC). Then, based on TSC, we propose a crosstalk-aware AR requests re-provisioning algorithm with two strategies to optimize the fragments in SDM-EONs. The performance of the proposed algorithm is evaluated via software simulation in terms of spectrum compactness, blocking probability, spectrum utilization, average moving times, average re-provisioning latency and average start time delay. The results show that the proposed re-provisioning algorithm can effectively improve spectrum compactness and spectrum efficiency of the networks. We also evaluate the proposed re-provisioning algorithm in different TSC thresholds, and it turns out that the proposed re-provisioning algorithm in higher threshold performs better in terms of spectrum compactness and spectrum utilization.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
With the exponential growth of IP traffic, different dimensional multiplexing technologies, such as optical time division multiplexing (OTDM) and wavelength-division multiplexing (WDM), play important roles in increasing the transmission capacity of a fiber link. OTDM contributes to signal transmission and switching entirely in optical domain . WDM technique utilizes the fiber bandwidth directly in frequency domain, rather than in time domain. In addition, wavelengths can be routed and be switched . With the increasing demands of network flexibility, Elastic Optical Networks (EONs) with flexible-grid technology is proposed to overcome the drawbacks of WDM networks [3–5], and it is supposed to offer a very effective utilization of spectrum resources by selecting suitable modulation format and fine-grained spectrum.
However, network traffic is expected to increase exponentially, and EONs based on a single-mode fiber (SCF) and single-core fiber (SCF) have almost reached its physical limitation in terms of total achievable capacity . To further scale network flexibility and capacity, the concept of EONs have been extended into the spatial domain. One approach for utilizing spatial resources is to deploy spatial-division multiplexing EONs (SDM-EONs) [7,8]. Furthermore, with SDM technology, a multi-core fiber (MCF) can be a promising candidate for SDM-EONs . In SDM-EONs, for a path set-up request, efficient routing and spectrum (RSA) algorithm is necessary to establish an end-to-end lightpath. However, traditional RSA algorithms are highly designed for single-core fiber without considering the spatial dimension. They are no longer directly appropriate for SDM-EONs, and new routing, spectrum and core allocation (RSCA) algorithms are required. Remaining several usual features of EONs, it is worthy to mention the unique features in SDM-EONs, such as the mitigation of spectrum contiguity constraint, which means that the signal can be exchanged from core to core freely while maintaining the same spectrum. There are many related research works on RSCA algorithms for various optimization objectives [10–13], and physical constraint, i.e., inter-core crosstalk, has been considered in RSCA algorithm .
With the emergence of diverse new applications and services in optical networks, different requests are placing high flexibility on these optical networks, i.e., the usual immediate reservation (IR) requests and advance reservation (AR) requests, while we mainly focus on these two types of requests to be deployed in SDM-WONs with MCF in this paper. For the two types of requests, IR request is expected to be served immediately, while AR requests can be served within a period in the future. Besides, AR requests is essential to support initial-delay-tolerance applications, e.g., data backup, data migration, grid computing, etc. Network operators need to reserve resources for these applications in advance until the starting time. From , AR requests can be classified into time-fixed ones and time-flexible ones, the former has specific starting and holding service time and the latter has a sliding time window, which means the starting and ending time are not specific time points. Network operators can benefit from the calendaring feature of AR requests and have the ability to plan their services effectively. The efficiency of network resources can be well improved by provisioning AR requests optimally .
In SDM-EONs, as services are set up and released dynamically along the lightpath, the optical spectrum resources could be split into isolated segments due to the specific features, i.e., spectrum contiguity and consistency constraints . These fragments can waste many resources and result in low spectrum utilization. Therefore, it is very necessary to avoid less fragments during RSCA process or rearrange them afterwards. We called the process as spectrum defragmentation, which optimizes the spectrum segments and improves the spectrum condition in the network [17–21]. Attributed to the added spatial dimension, the fragments problem becomes more serious and complicated in SDM-EONs. Besides the emergence of AR requests in the network, time and spectrum fragments are supposed to occur as the consideration of time dimension. It becomes extremely important to consider these three-dimensional fragments in RSCA process and optimize them effectively. Many researches have been done to lucubrate the fragments problem in EONs and SDM-EONs. Most of spectrum defragmentation algorithms can be categorized as either proactive or reactive , the former approach is performed periodically to “clean up” the spectrum fragments in the network, while the latter is performed only when the cost of defragmentation can be minimized. The spectrum defragmentation algorithm in EONs was first proposed in . The disruption-minimized spectrum defragmentation method was designed in dynamic EONs that adopt distance adaptive modulation . Yu, et al. proposed a spectrum compactness based defragmentation scheme to maximize the profitability of defragmentation in EONs . To solve the issue of wastage of spectrum fragments in EONs , discussed the fairness in reservation for both IR and AR requests and proposed a dynamic RSA scheme. In addition, a crosstalk-aware spectrum defragmentation method triggered by appropriate spectrum compactness are discussed in SDM-EONs with spectral and spatial strategies respectively . Three-dimensional (spectral, spatial, time) RSCA scheme for AR applications is evaluated based on multi-dimensional resource compactness in SDM-EONs, which is the measurement of spectrum fragments in time and spectrum dimension . This paper mainly focuses on the re-provisioning optimization algorithm for AR requests and performance evaluation among the proposed strategies on defragmentation problem in SDM-EONs.
In this paper, we study the issue of time-spectrum defragmentation in SDM-EONs. Inter-core crosstalk is considered as a physical constraint for RSCA. To measure spectrum status in the network, a metric named time-dimensional spectrum compactness (TSC) is designed. Based on TSC, we propose a crosstalk-aware re-provisioning (CRP) algorithm with two strategies to re-provision AR requests and improve the spectrum status for defragmentation problem in SDM-EONs. The paper is organized as follows. In Section 2, the background of SDM-EONs with MCF is described, including the switch fabric, inter-core crosstalk, and crosstalk-aware RSCA. In Section 3, the definition of TSC and time-aware resources model are presented in SDM-EONs. A crosstalk-aware re-provisioning (CRP) algorithm with two strategies for AR requests is proposed in Section 4. Section 5 gives the simulation results and analysis, and Section 6 concludes the paper.
2. Physical constraints in SDM-EONs
2.1 Optical switch fabric in SDM-EONs with MCF
In SDM-EONs, there are spectrum resources in each core respectively. Spectrum slot is the basic resource unit. When performing allocation process of resources, spectrum contiguity constraint must be followed, which means an end-to-end service must use the same spectrum slots along the lightpath. Within one fiber, spectrum continuity constraint must be kept and it means that the spectrum slots occupied by the service must be continuous in the spectral dimension. The technique named orthogonal frequency division multiplexing (OFDM) should adopted for each core to improve the spectrum efficiency. As for the connections between fibers, a spatially and spectrally resolved optical switching fabric is designed as shown in Fig. 1 .
In the optical switching fabric, the functions of fiber switching, core switching and spectrum switching can be achieved, which allows adding, dropping and switching of different flexible channels with granularity down to the wavelength level. The transceiver resources consist of a transceiver pool, supplying the appropriate sub-transceivers according to the traffic requirement. In the switch fabric, the spectrum slots can be switched between different cores, but the mitigation of spectrum contiguity constraint must be followed in the process. To conclude, the signal can be exchanged from core to core freely while maintaining the same spectrum. An example is presented to illustrate this issue in Fig. 2.
2.2 Inter-core crosstalk in SDM-EONs with MCF
Apart from the contiguity and contiguity constraint above, there is a new important constraint in SDM-EONs, i.e., inter-core crosstalk. The crosstalk may occur between the adjacent cores when the same spectrum slices overlap in a fiber, and it will severely affect the quality of signals during transmission. Figure 3(a) shows a schematic diagram of the seven-core model  used in this paper. Figure 3(b) shows the schematic of a core with index trench. Furthermore, Eq. (1) and Eq. (2) are proposed to evaluate the statistical mean crosstalk of a MCF . In Eq. (1), denotes the mean increase of crosstalk per unit length. , , , and are the relevant fiber parameters, representing the coupling coefficient, bend radius, propagation constant, and core-pitch, respectively. In Eq. (2), is the number of the adjacent cores and is the fiber length. From the definition of crosstalk, we can know that the value of crosstalk mainly lies on the number of adjacent cores and the length of the fiber.
In SDM-EONs, the RSCA issue becomes more complex due to all these constraints, especially inter-core crosstalk. As the crosstalk between adjacent cores can have great impact on signals quality during transmission, it is extremely important to consider the potential crosstalk when performing a RSCA process. However, the crosstalk occurs among none-adjacent cores is quite small that we can ignore it. Note that the crosstalk checking is a complex process. When provisioning a new requested lightpath, the inter-core crosstalk between the new lightpath and other already provisioned lightpaths should satisfy a predefined threshold, to avoid worse signal quality caused by the additional crosstalk [10–13]. In SDM-EONs, spectrum status is more complex with spatial dimension than in EONs. Consequently, the spectrum defragmentation is much more serious due to dynamic arrival and departure of requests. Taking new type requests (i.e., AR requests) into consideration in the network, the additional time dimension result in time and spectrum fragments and the defragmentation problem appears to be particularly important. However, to the best of our knowledge, there are few related works on time-spectrum defragmentation in SDM-EONs.
3. Time-aware resources model of SDM-EONs
Before delving into the re-provisioning algorithm for AR requests that solves the time-spectrum fragments issue in SDM-EONs, we first define a metric named Time-dimensional Spectrum compactness (TSC) based on spectrum compactness (SC). SC describes the occupation of spectrum fragments in each core based on our previous work . TSC can be regarded as a time-dimensional SC measurement. It describes spectrum fragments in both time and core factor. Then a time-aware resources model in time, space, and spectrum dimensions is presented. Some notations used in the paper are listed in Table 1.The network model is described first as follows.
3.1 Optical switch fabric in SDM-EONs with MCF
The physical network topology of SDM-EONs is modeled as a directed graph , where is the set of physical nodes, represents the set of physical optical links, and represents the set of cores on each link. The threshold of the inter-core crosstalk is defined as. Besides, inter-core crosstalk must be taken into account during the RSCA process. When a new request is provisioned on the physical network, the inter-core crosstalk of the request should be calculated and be guaranteed to be below . Note that we primarily consider the inter-core crosstalk in this paper. Intra-core impairment is addressed through the introduction of a guard band between adjacent connections.
3.2 Spectrum compactness definition
Spectrum compactness in SDM-EONs is first defined in . Introducing time factor into the concept of SC, we design a new metric, named Time-dimensional Spectrum compactness (TSC), to measure the time-spectrum status in the network .Eq. (3), is the current time for calculating the spectrum compactness in the core of link , and represent the maximum and minimum occupied spectrum in the core of link , respectively, represents the spectrum occupied at time by the connection in the core of link , is the number of the established connections, is the number of available spectrum segments in the core of link , and denotes the spectrum resources of the available spectrum segment at time in the core of link . From the definition of time-dimensional spectrum compactness, we can see that the value of spectrum compactness represents the possibility that the vacant spectrum fragments could be used at a certain time. The larger spectrum compactness is, the greater possibility that these spectrum fragments will be used.
Figure 4 is an example of time-dimensional spectrum compactness calculation. As shown in Fig. 4, we assume that each time slot has the same time length. Taking core 0 on link 1 for example, is 7, is 2, and the total number of occupied spectrum slots is 4. Then the first half of Eq. (3) is . While, the total number of available spectrum slots is 4, and the number of available spectrum blocks is 2. So, the second half of Eq. (3) is . Then we can get the spectrum compactness of core 0 on link 1, which equals 3.
3.3 Time-aware resource problem model
As mentioned above, the physical graph is modeled as . We consider two types of requests, i.e. IR requests and AR requests. IR requests should be served immediately. AR requests allows initial delay and it could be denoted as, where and represent the accurate start time and end time respectively, is the initial deadline, is the reserved path for source to destination and is the reserved spectrum slots during on path.
In AR scenario, spectrum resource is labeled not only in link and spectrum dimension, but also in time dimension. To evaluate the resource accurately, we build a three-dimension resource model. As a simple example shown in Fig. 5, one dimension is the time, another one is the spectrum slots and the other one is the core on link. We assume that each time slot has the same length. Figure 5 shows the spectrum status of all cores on link . The plane we marked in red circle denotes the spectrum status in core 0. In this plane, the red requests, the purple requeststhe yellow requestsand the orange requestsare all AR requests, while others are IR requests.
There are some previous works studying how to minimize/decrease the spectrum fragments during RSA process [9–14], even though considering time and spectrum dimension for AR requests, but these woks mainly focus on RSA problems instead of spectrum defragmentation. In this paper, based on the three-dimensional model and making full use of the calendaring features of AR requests, we discuss the time-spectrum defragmentation problem for AR requests re-provisioning in both time and space dimension. Based on TSC metric, the spectrum status of each fiber can be measured jointly in time-spectrum dimensions. As shown in Fig. 5, heavy-SC occurs at time 3 when service 2 and service 6 is provisioned with slot [3,4] and slot [7,8] respectively. To handle this kind of un-optimal fragments condition, a new re-provisioning algorithm (CRP) for AR requests, which aims to balance the time-spectrum fragments of network, is designed as follows.
4. Crosstalk-aware re-provisioning algorithm for AR requests based on TSC for defragmentation problem in SDM-EONs
The time-spectrum fragments problem is addressed for AR requests in SDM-EONs. To utilize the time-spectrum resources efficiently, in this section, we ask for the calendaring feature of AR requests and propose a re-provisioning optimization (CRP) algorithm for AR requests based on TSC. The optimization algorithm performs two re-provisioning strategies respectively, i.e., Re-time the allocated FSs only (RE-T) and Re-time and re-allocate FSs (RE-FT). Based on these re-provisioning strategies, a crosstalk-aware re-provisioning (CRP) algorithm for AR requests based on TSC for defragmentation problem is designed.
4.1 Crosstalk-aware re-provisioning algorithm
As connection requests, i.e., IR requests and AR requests, arrive and leave dynamically in the networks, and spectrum resources are fragmented into multiple pieces in such process and it might not be optimal for future resource utilization. Especially, in AR scenario, there are additional time fragments in the network. Figure 6 corresponds to the red-circled plane on core 0 in Fig. 5. Taking it as an example, where service 1, 2, 3, 4 and 5 have already been scheduled, the coming service 6, which requires FSs between time 6 to 7, will cause 2 FSs being reserved at time slot [2,3] and the TSC value is beyond the threshold at time 3. Consequently, it is necessary to re-provision certain scheduled requests to achieve higher TSC. The CRP algorithm is designed to improve the worse condition via the following procedures: 1) find out the time-spectrum pairs whose TSC value is lower than a pre-determined threshold; 2) find out the AR requests who result in the heavy-SC block above; 3) release the reserved FSs of some AR requests and re-provision them to balance the overall SC value.
The procedures of re-provisioning optimization algorithm are shown in Algorithm 1. Firstly, as AR requests arrive, based on the latest resource status, the TSC value of each core on each link at each time slot can be calculated as formulation (3). Then, the links over SC threshold are going to be put into the heavy-SC block set with detailed information, which is sorted in an ascending order according to the SC value. Secondly, we can find out the AR requests that have been scheduled to occupy the spectrum at current heavy-SC block as a candidate request set. Since at one time point, AR requests may cross multiple time-core blocks and cause the spectrum fragments to multiple blocks, it is necessary to remove the overlapping requests one by one until the original TSC value is getting better. As Fig. 6 shows, at certain time 3, the TSC value is heavily lower than the threshold. Service 2 and service 6 are overlapped simultaneously at time 3. For service 6, the sliding time window is 2 to 5. Then different re-provisioning strategies perform to improve the spectrum continuity. In CRP algorithm table, the function of two strategies occurs in line 17. Line 6 to 8 tries to find heavy-SC set in the network, the time complexity of which is. Line 14 searches the heavy requests set, the worst time complexity of which is. Moreover, the worst time complexity of line 17 is. As a result, the worst time complexity of algorithm CRP is.
4.2 Re-provisioning strategies (RPS)
The calendaring feature of AR requests allows the elastic time sliding. Since scheduled requests have already been provisioned once, some parameters, e.g., start time, end time and allocated FSs, can be reused in the re-provisioning procedures. Reusing different kinks of parameters may result in different re-provisioning results and spectrum efficiency. To explore a better one, we propose two re-provisioning strategies to adjust scheduled AR requests by reusing these different parameters. The details of different re-provisioning strategies are described as follows.Fig. 7, the reserved time for service 2 and service 6 are [3,5] and [2,3], respectively. As for service 6, RE-T migrates it from [2,3] to [4,5] to improve the heavy-SC block at time slot 3.
The procedures of RE-T are depicted in Algorithm 2. Keeping the FSs and core resources the same, firstly, calculating all value in the same core on same link during the sliding time and puting them into a candidate set. Sorting the candidate set in a descending order according to the TSC value, and selecting an oriented time that satisfies the following conditions: 1) satisfied FSs correspondingly; 2) the crosstalk of selected time on same core beyond; 3) higher TSC value of both original and oriented time. If there is no satisfying time, the next one in setwill be checked. With this strategy, we can find the appropriate candidate time for adjustment. The corresponding time complexityis. More details are described as follows.
As for a candidate AR request, which could be denoted as, this strategy just remains the existing path, and tries to adjust the service time duration and FSs simultaneously. To achieve a joint optimization in both time and spectrum dimensions, RE-FT firstly performs to find the optimal time duration as the first step of RE-T strategy. From the optimal time duration, RE-FT should also allocate FSs along the lightpath for the request. Note that the FSs adjustment should also follow the contiguous constraint and the new time should be in the range of the tolerated deadline time. Taking Fig. 8 as an example, the reserved time for service 2 and service 6 are [3,5] and [2,3], respectively. Suppose that there is a heavy-SC block at time slot 3, RE-FT re-schedules the appropriate time and re-allocates FSs for both service 2 and service 4 during the sliding time window.
The procedures of RE-FT are depicted in Algorithm 3. Based on Algorithm 2, firstly, a candidate time set should be found in the same core on same link. As for each candidate time in the set, if there is one satisfying all conditions, then try to adjust the FSs to another FSs resource in the same core on same link at the selected time until satisfying the three conditions. The corresponding time complexity is .With this strategy, we can find appropriate time and spectrum resources for adjustment. The details are described as follows.
There may be some request interruptions during the process of FSs adjustment due to laser switching and reconfiguration of the switching device. This impact can be measured in terms of spectrum moving times in the simulation results section.
5. Numeric results and analysis
The proposed CRP algorithm is evaluated through the simulation on the topology with 14 nodes and a topology with 11 nodes, as shown in Fig. 9. It is assumed that each fiber has 7 cores, and each core has 320 spectrum slots. Each frequency slot is 12.5 GHz and the guard band is assumed to be 25 GHz (2 slots). BPSK is applied to the connections as the normalized modulation format, and multiple modulation formats will be illustrated in our future work. The fiber parameters , , , in formulation 1 are set as , and the threshold of the crosstalk is −32dB . The service requests consist of an equal amount of IR requests and AR requests, and they are generated randomly among any node pairs. The arrival of service requests follow Poisson process with a rate of requests per minute, and the holding time has a negative exponential distribution with parameter . In addition, the deadline time of each request is generated as , and the sliding window of AR is generated as the same negative exponential distribution with . The traffic demands of requests have been converted to the required number of spectrum slots, and it is even randomly generated between 1 and 10 spectrum slots. 100,000 service requests are generated each time, and we run the simulation for 10 times. The simulation results are obtained from the average of these 10 times. We adopted a revised crosstalk-aware RSCA algorithm with the SC metric as the benchmark algorithm . As the crosstalk-aware RSCA algorithm in previous work only consider IR requests. To make it comparable, we revised it with expended time domain considering the AR requests in this paper. First-fit strategy is adopted in the benchmark algorithm, which considers the inter-core crosstalk when assigning the spectrum resources. The performances of the proposed CRP algorithm with two re-provisioning strategies are compared with the benchmark in terms of average spectrum compactness (ASC), blocking probability (BP), spectrum utilization (SU), average moving times (AMT), average re-provisioning latency (ARL) and average start time delay (ASD). The CRP algorithm with two re-provisioning strategies is triggered when the link SC value of any arrived AR request is below SC threshold when being provisioned by the benchmark.
5.1 Average spectrum compactness
In this section, we evaluate the proposed CRP optimization algorithm based on the simulation results. First, we compare the CRP algorithm with the benchmark algorithm in terms of Average Spectrum Compactness (ASC). The benchmark algorithm performs crosstalk-aware first-fit RSA based on SC metric, yet without re-provisioning process. Besides, we discuss the CRP algorithm in different SC thresholds, i.e., the threshold of 10 and 50. The performance of ASC is shown in Fig. 10 and it is analyzed as follows.
Firstly, it can be observed that the average SC value is dropping gradually with traffic load increasing. The reason is that the more services are being served in the network, the more irregular spectrum distribution is. Thus, it causes spectrum contiguity in a fragmental condition and brings lower SC value.
Secondly, when comparing the results of the CRP algorithm with that of the benchmark algorithm, it can be observed that the CRP algorithm achieves higher ASC for all traffic loads in both 10 and 50 thresholds, especially the algorithm with RE-FT strategy. RE-FT can maximally achieve about 10 times higher average spectrum compactness than the benchmark. This is because the CRP algorithm can make full use of re-provision opportunity in AR scenario, and optimize pieces of spectrum resources via re-provisioning multiple scheduled AR requests from the overall perspective either in time and spectrum dimension. Then the continuity of the spectrum resources can be improved effectively. However, the benchmark algorithm do not perform any re-provisioning operation.
In terms of CRP algorithm with the two strategies, the SC value of RE-FT is much higher than RE-T, while RE-T has less effect than the benchmark. As taking the spectrum dimension into consideration, RE-FT almost take full advantage of spectrum resource to re-provision fragments effectively. However, considering the constraints in SDM-EONs, i.e., crosstalk and continuity, there are few spectrum resources to utilize for only adjusting in time dimension (RE-T). Besides, keeping the FSs unchanged is a very strict constraint for RE-T. The corresponding worse performance of RE-T can be also observed from the SMT and STD curves in Fig. 13 and Fig. 15. The successful time-dimensional adjusting times of RE-T is much less and the difference between original and oriented start time is quite small.
Thirdly, we compare the performance of two re-provisioning strategies in SC threshold of 10 with that of 50, and Fig. 10 shows that the ASC in 50 performs better than 10. That is because the re-provisioning strategy in SC threshold of 50 has triggered more re-provisioning times than the threshold of 10, which means that it adjusts more fragments per one period.
5.2 Blocking probability
Figure 11 compares the performance of two re-provisioning strategies with the benchmark in different SC thresholds in terms of Blocking Probability (BP).
We can see that the CRP algorithm achieves lower BP than the benchmark for all traffic loads in both 10 and 50 thresholds. It is notable that the CRP algorithm in SC threshold of 50 has about 12% lower average blocking probability than the benchmark maximally. That is because both two re-provisioning strategies optimize pieces of spectrum resources in time and spectrum dimension, and effectively improves the spectrum continuity status. Then, more requests are allowed in the network. As requests arrive and depart, spectrum fragments are generated in a large number, the benchmark without re-provisioning cannot allow more incoming requests, as the spectrum assignment must keep spectrum continuity and consistency constraints . However, the CRP algorithm can perform re-provisioning in time and spectrum dimension to remedy this issue from the overall perspective. Consequently, the BP performance with CRP algorithm can be reduced lower.
Moreover, the proposed two re-provisioning strategies have almost the same performance, even though it tries to make FSs adjustment. That is because RE-FT may find an optimal FSs slot for this fragment, but it gets a little efficiency due to the same number of FSs occupation. When comparing BP curves of the CRP algorithm in 10 and 50 thresholds, it is shown in Fig. 11 that BP in 50 is lower than 10, because the re-provisioning strategy in SC threshold of 50 makes more adjustments to defragment spectrum pieces and accommodates more requests in the network, and it slightly improves the BP performance in a period.
5.3 Spectrum utilization
The simulation results on Spectrum Utilization (SU) are given in Fig. 12. We can observe that the CRP algorithm with two strategies performs better than the benchmark algorithm under all traffic loads in both 10 and 50 thresholds. It has the opposite trend as BP curves, but has the same sense that re-provisioning operations can be beneficial to network performance. It is notable that the CRP algorithm in SC threshold of 50 has about 5% higher average spectrum utilization than the benchmark maximally. That is because re-provisioning operated in time and spectrum dimension can effectively integrate the spectrum resources from other time or FSs slot, and it tries to gather spectrum fragments to provision more requests. Thereby spectrum utilization can be improved. In terms of this metric, the proposed two re-provisioning strategies have also almost the same performance.
The results also indicate that the CRP algorithm with two re-provisioning strategies in SC threshold of 50 achieves higher SU than in SC threshold of 10, because the CRP algorithm in 50 can trigger more re-provisioning operations. As a result, the spectrum status can be more continuous and usable, and thus can accommodate more requests in the network.
5.4 Average moving times
The value of Average Moving Times (AMT) is the ratio of the successful shifting number (satisfying all constraints, i.e. time, continuous FSs, crosstalk and better SC) to average running time, which represents the average moving number per unit time. In other words, it is the number of service interruption times. As shown in Fig. 13, comparing the two strategies, RE-FT perform more AMT than RE-T in both 10 and 50 threshold. The reason is that RE-T only considers time dimension for re-provisioning, while RE-T tries to find available spectrum resources based on RE-T in other time. It is a very strict constraint to keep the FSs unchanged, which results in more failures for re-provisioning of RE-T.
When the SC threshold is 50, the CRP algorithm has slightly higher AMT than that of 10. Corresponding to the results of BP and SU, a SC threshold of 50 performs more adjustments than that of 10, and results in a lower AMT, which can be shown in Fig. 13.
5.5 Average re-provisioning latency
The performance of Average Re-provisioning Latency (ARL) is described in Fig. 14. ARL refers to the consumed time for re-provisioning one AR request operations, measured in second (s). It ranges from the time when CRP algorithm starts to the time it succeeds. An analogous concept named average number of operations for EONs can be referred from . From the simulation results plotted in Fig. 14, RE-FT runs two times as long as RE-T, and the CRP algorithm in the SC threshold of 50 performs higher ARL than that of 10. It is because RE-FT tries to find optimal FSs along the lightpath and performs more re-provisioning operations, especially in the SC threshold of 50, which leads to taking more average running time than RE-T.
5.6 Average start time delay
The Simulation results on Average Start Time Delay (ASD) are described in Fig. 15. ASD represents the start time delay for AR requests doe to time adjustment. RE-T in the SC threshold of 50 have almost the same performance as that in 10, so is the RE-FT. Besides, compared with RE-FT, RE-T also performs almost the same. However, both RE-T and RE-FT have a bit lower ASD than the benchmark. The phenomena is corresponding to the performance of BP and SU, for time dimension in all the re-provisioning strategies is considered. The CRP algorithm tries to re-accommodate the AR requests in an earlier time-spectrum area, and the average start time can be reduced accordingly.
5.7 Curves of ASC and SU in different SC threshold
Simulation results with traffic load 1000 are depicted for different thresholds in Fig. 16 and Fig. 17. As shown in Fig. 16, we focus on the threshold range from 10 to 50 as an example, the ASC increases as the threshold increases in the threshold range from 10 to 50. The reason is that it takes more times for re-provisioning in time and spectrum with higher SC threshold, and the spectrum continuity can be improved effectively. Consequently, the ASC of the CRP algorithm can get better performance with higher SC threshold. It can be also observed that the CRP algorithm performs better than the benchmark, especially the RE-FT, the reason is described detailed in ASC performance of Part A accordingly. RE-FT has revealed more advantages compared with others.
Figure 17 shows the SU curves in different thresholds. It is expected that SU performs better in higher SC threshold as it tries to execute re-provisioning operations as long as below the SC threshold, and it also triggers more times to achieve better performance. Comparing these two algorithms, the CRP algorithm get higher SU than the benchmark, while RE-T and RE-FT have almost the same performance, for the CRP algorithm with two strategies makes full use of time and spectrum resources. From Figs. 16 and 17, we observe that the SC threshold of 50 is the best among these all thresholds, as it has the highest ASC and SU performance.
This paper studies on the issue of time-spectrum defragmentation problem for AR requests re-provisioning in SDM-EONs. A concept of time-dimensional spectrum compactness (TSC) is defined to measure the time-spectrum resource status in SDM-EONs. A crosstalk-aware re-provisioning (CRP) algorithm with two re-provisioning strategies for AR requests based on TSC for time-spectrum defragmentation is proposed, and they have been verified via simulations. The results shows that the proposed CRP algorithm with two re-provisioning strategies can achieve better performance than the benchmark algorithm in terms of average spectrum compactness, blocking probability and spectrum utilization. Between the proposed re-provisioning strategies, re-schedule and re-allocate FSs performs better. As for the related results, the strategy of re-schedule and re-allocate FSs have more average moving times and average re-provisioning latency, but it can reduce average start time delay than re-schedule the allocated FSs. Moreover, the average spectrum compactness and spectrum utilization increases as the threshold increases in our example threshold range (from 10 to 50), spectrum compactness threshold of 50 has better performance than other thresholds. There are also some other issues, such as different spectrum resources, different service ratios and different modulations, which will be considered and verified in the future.
National Science and Technology Major Project (2017ZX03001016); National Natural Science Foundation of China (NSFC) (61601052, 61822105, 61571058); State Key Laboratory of Advanced Optical Communication Systems Networks of China.
1. H. Weber, R. Ludwig, S. Ferber, C. Schmidt-Langhorst, M. Kroh, V. Marembert, C. Boerner, and C. Schubert, “Ultrahigh-Speed OTDM-Transmission Technology,” J. Lightwave Technol. 24(12), 4616–4627 (2006). [CrossRef]
2. Y. Pointurier, M. Brandt-Pearce, S. Subramaniam, and Bo Xu, “Routing and wavelength assignment in all-optical networks,” IEEE J. Sel. Areas Comm. 26(6), 32–44 (2008). [CrossRef]
3. A. Lord, P. Wright, and A. Mitra, “Core networks in the flexgrid era,” J. Lightwave Technol. 33(5), 1126–1135 (2015). [CrossRef]
4. O. Gerstel, M. Jinno, A. Lord, and S. J. B. Yoo, “Elastic optical networking: A new dawn for the optical layer?” IEEE Commun. Mag. 50(2), s12–s20 (2012). [CrossRef]
5. Y. Ji, J. Zhang, X. Wang, and H. Yu, “Towards converged, collaborative and co-automatic (3C) optical networks,” Sci. China Inf. Sci. 61(12), 121301 (2018). [CrossRef]
7. D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013). [CrossRef]
8. R. Proietti, L. Liu, R. P. Scott, B. Guan, C. Qin, T. Su, F. Giannone, and S. J. B. Yoo, “3D elastic optical networking in the temporal, spectral, and spatial domains,” IEEE Commun. Mag. 53(2), 79–87 (2015). [CrossRef]
9. G. M. Saridis, D. Alexandropoulos, G. Zervas, and D. Simeonidou, “Survey and evaluation of space division multiplexing: from technologies to optical networks,” IEEE Comm. Surv. and Tutor. 17(4), 2136–2156 (2015). [CrossRef]
10. S. Fujii, Y. Hirota, H. Tode, and K. Murakami, “On-demand spectrum and core allocation for reducing crosstalk in multicore fibers in elastic optical networks,” J. Opt. Commun. Netw. 6(12), 1059–1071 (2014). [CrossRef]
11. A. Muhammad, G. Zervas, and R. Forchheimer, “Resource Allocation for Space-Division Multiplexing: Optical White Box Versus Optical Black Box Networking,” J. Lightwave Technol. 33(23), 4928–4941 (2015). [CrossRef]
12. H. Tode and Y. Hirota, “Routing, Spectrum and Core Assignment on SDM Optical Networks,” Optical Fiber Communication Conference and Exhibition (2016).
13. Y. Zhao, J. Han, Y. Tan, R. Zhu, and J. Zhang, “Mode and Wavelength Allocation in Multi-Dimensional Optical Networks,” Asia Communications and Photonics Conference. Optical Society of America (2014). [CrossRef]
14. K. Rajah, S. Ranka, and Y. Xia, “Advance reservations and scheduling for bulk transfers in research networks,” IEEE Trans. Parallel Distrib. Syst. 20(11), 1682–1697 (2009). [CrossRef]
15. W. Wang, Y. Zhao, H. Chen, J. Zhang, H. Zheng, Y. Lin, and Y. Lee, “Re-Provisioning of Advance Reservation Applications in Elastic Optical Networks,” IEEE Access 5, 10959–10967 (2017). [CrossRef]
16. Y. Zhao, B. Chen, J. Zhang, and X. Wang, “Energy Efficiency with Sliceable Multi-Flow Transponders and Elastic Regenerators in Survivable Virtual Optical Networks,” IEEE Trans. Commun. 64(6), 2539–2550 (2016). [CrossRef]
17. A. N. Patel, P. N. Ji, J. P. Jue, and T. Wang, “Defragmentation of transparent flexible optical WDM (FWDM) networks,” Optical Fiber Communication Conference (OFC) (2011). [CrossRef]
18. T. Takagi, H. Hasegawa, K. Sato, Y. Sone, A. Hirano, and M. Jinno, “Disruption minimized spectrum defragmentation in elastic optical path networks that adopt distance adaptive modulation,” European Conference and Exhibition on Optical Communication (ECOC) (2011). [CrossRef]
19. X. Yu, J. Zhang, Y. Zhao, T. Peng, Y. Bai, D. Wang, and X. Lin, “Spectrum compactness based defragmentation in flexible bandwidth optical networks,” National Fiber Optic Engineers Conference. Optical Society of America (2012). [CrossRef]
20. S. Sugihara, Y. Hirota, S. Fujii, and H. Tode, “Routing and spectrum allocation method for immediate reservation and advance reservation requests in elastic optical networks,” Photonics in Switching (PS), 2015 International Conference on. IEEE (2015). [CrossRef]
21. Y. Zhao, L. Hu, R. Zhu, X. Yu, X. Wang, and J. Zhang, “Crosstalk-Aware Spectrum Defragmentation Based on Spectrum Compactness in Space Division Multiplexing Enabled Elastic Optical Networks With Multicore Fiber,” IEEE Access 6, 15346–15355 (2018). [CrossRef]
22. R. Zhu, Y. Zhao, H. Yang, H. Chan, J. Zhang, and J. P. Jue, “Multi-dimensional resource assignment in spatial division multiplexing enabled elastic optical networks with multi-core fibers,” Optical Communications and Networks (ICOCN), 2016 15th International Conference on. IEEE (2016).
23. J. Tu, K. Saitoh, M. Koshiba, K. Takenaga, and S. Matsuo, “Design and analysis of large-effective-area heterogeneous trench-assisted multi-core fiber,” Opt. Express 20(14), 15157–15170 (2012). [CrossRef] [PubMed]
24. G. M. Saridis, D. Alexandropoulos, G. Zervas, and D. Simeonidou, “Survey and Evaluation of Space Division Multiplexing: From Technologies to Optical Networks,” IEEE Comm. Surv. and Tutor. 17(4), 2136–2156 (2015). [CrossRef]
25. R. Zhu, Y. Zhao, H. Yang, H. Chan, J. Zhang, and J. P. Jue, “Crosstalk-aware RCSA for spatial division multiplexing enabled elastic optical networks with multi-core fibers,” COL 14(10), 100604 (2016).
26. M. Zhang, Y. Yin, R. Proietti, Z. Zhu, and S. J. B. Yoo, “Spectrum Defragmentation Algorithms for Elastic Optical Networks using Hitless Spectrum Retuning Techniques,” Optical Fiber Communication Conference. Optical Society of America (2013). [CrossRef]