An efficient heuristic waveband assignment algorithm for hierarchical optical path networks utilizing wavelength convertors

Optical Switching and Networking 10 (2013) 54–61

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An efficient heuristic waveband assignment algorithm for hierarchical optical path networks utilizing wavelength convertors Zhi-shu Shen n, Hiroshi Hasegawa, Ken-ichi Sato Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan

a r t i c l e in f o

abstract

Available online 7 August 2012

We propose a hierarchical optical path network design algorithm that allows for wavelength conversion. The algorithm sequentially solves a set of sub-problems that result from decomposing the original design problem. A novel efficient heuristic is developed to solve the waveband assignment sub-problem that is the bottleneck among the sub-problems. Numerical experiments prove that, by employing wavelength conversion, hierarchical optical path networks will be more cost effective than the single layer optical path network even in the small traffic demand area, where cost-effectiveness cannot be realized without using wavelength conversion, as well as in the relatively large traffic demand area. & 2012 Elsevier B.V. All rights reserved.

Keywords: Hierarchical optical path network Wavelength convertor Cost bound

1. Introduction The development of WDM (Wavelength Division Multiplexing) technologies enables us to expand the transmission capacity of optical fibers. The rapid deployment of broadband access including ADSL and FTTH in the world is driving the exponential increase seen in internet traffic. Backbone networks are mostly based on point-to-point WDM transmission systems and electrical forwarding and routing systems. [1]. As a result, O–E–O (Optical–Electrical–Optical) conversion is needed at every node. However, with the growth of the traffic volume, electrical routing and O–E–O conversion will become bottlenecks that hinder the construction of large scale cost-effective networks. In order to cope with this, single layer optical path networks that utilize wavelength routing made possible with reconfigurable optical add/drop multiplexers (ROADMs) [1,2] have recently been extensively introduced [3]. The penetration of new broadband services

n Corresponding author. Tel.: þ 81 52 789 2792; fax: þ81 52 789 3641. E-mail address: [email protected] (Z.-s. Shen).

1573-4277/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.osn.2012.07.003

(such as high-definition or ultrahigh-definition TV [4] and e-Science [5]) will create further traffic expansion in the near future. The scale of optical switches currently used in OXCs/ROADMs for single layer optical path networks [6] will then need to be substantially expanded. Hierarchical optical path networks that utilize wavebands, a bundle of multiple wavelength paths, have recently been investigated as an important technology to solve this problem [6–15]. In contrast to elastic optical path networks [16], which focus on the maximum utilization of spectral resources in fibers, the main goal of studies on hierarchical optical path networks is to reduce node cost. Which technology will be suitable depends on the situation. For example, for metro networks with bundles of fiber cables, fiber cost will be relatively low and the reduction of node cost is essential. Moreover, with the recent development of a WaveBand Cross-Connect (BXC) prototype [17] which is constructed with WaveBand Selective Switches (WBSSs) monolithically integrated on a PLC chip, a substantial reduction in node size and cost can be expected. However, from the viewpoint of hierarchical optical path networks, even the routing and wavelength assignment (RWA) problem for the single layer optical path networks is known to be an NP-complete task [18].

Zhi-shu Shen et al. / Optical Switching and Networking 10 (2013) 54–61

The problem of hierarchical optical path network design is much more difficult due to the complexity of establishing optical paths with different granularities while considering the path hierarchy and avoiding wavelength/waveband collisions, and, as a result, the evaluated cost effectiveness of a waveband network strongly depends on the network design algorithm adopted. Some efficient algorithms have been proposed for hierarchical opticalpath networks that do not use wavelength convertors. Research has shown that the introduction of path hierarchy reduces total network cost significantly [11,12,14–23]. For example, the cost can be reduced by upto 45% in a 9  9 regular mesh network, if the number of wavelength paths is large, i.e. in the large traffic demand area [21]. However, due to the restriction imposed by wavelength/waveband continuity constraints given the omission of wavelength conversion, no cost reduction by path hierarchy has been on the small traffic demand area. Introduction of wavelength conversion is a feasible way to ease these constraints [23]. 3R regenerators have also the capability of wavelength conversion. In a conventional work [15], a network design algorithm was proposed that considers 3R regenerator optimization subject to a given signal impairment condition. However, the work assumes non-hierarchical multi-granular optical paths and the evaluation assumes a fixed regenerator cost. In Ref. [23] we presented a preliminary report on the impact of wavelength convertors. However, the excessive computation time of the network design algorithm prevented us from achieving a sufficient improvement over [21], which did not consider wavelength convertors. This paper tackles this problem by introducing a novel network design algorithm. We use it to show, for the first time, that hierarchical optical path networks that utilize wavelength conversion can be cost effective over a wide traffic demand area. As it is impractical to solve the routing and waveband/ wavelength assignment problem for hierarchical optical path networks directly, we divide the problem into several sub-problems following [23]. Unfortunately, the computational load is still extremely large. Especially, for the waveband assignment sub-step based on an ILP algorithm, its computation load rises exponentially with the number of waveband paths to be assigned. It is not possible to obtain the results in a relatively large traffic demand area by using this method. Hence an efficient algorithm for waveband assignment is strongly demanded. Our solution is to replace the ILP approach with a novel heuristic algorithm for waveband assignment that offers greatly reduced computational complexity. Because fiber and wavelength convertors tend to dominate total facility cost, our algorithm adopts a novel measure defined by a number of wavelength paths traversing a pair of concatenated waveband paths that represents the potential need for fibers and wavelength convertors in terms of the waveband path pair; we sequentially assign waveband paths, in the descending order of this measure, so that the number of both additional fibers and wavelength convertors for each assignment should be minimized. The algorithm allows us to evaluate the cost bound of adding wavelength convertors compared to that of the

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conventional single layer optical path network in a wide traffic demand area. The proposed algorithm can be applied to a wide traffic demand area since its computation load is very practical, and the obtained results for the small traffic demand area are very close to that obtained by using the ILP approach. As a result, it is demonstrated that even if wavelength convertors are relatively expensive, hierarchical optical path networks can be cost effective over a wide range of traffic demand. 2. Hierarchical optical path networks with wavelength conversion 2.1. Hierarchical MG-OXC architecture We adopt the hierarchical MG-OXC (Multi-Granular OXC) architecture ([6–8,10,13,14,20]) shown in Fig. 1. For the hierarchical MG-OXC assumed in this paper, each node consists of two path cross-connects with different optical granularity; a BXC for routing higher order waveband paths and a Wavelength Cross-Connect (WXC) for routing lower order wavelength paths. In hierarchical optical path networks, wavelength paths are transported within waveband paths set on links. An alternative architecture is the non-hierarchical MG-OXC ([9,10–15,19]) that accommodates a fixed number of wavelength paths and waveband paths simultaneously in a fiber. Although it can minimize the number of switch ports, WXCs and BXCs cannot collaborate with each other since the grooming of wavelength paths at intermediate OXCs is not possible in the non-hierarchical MG-OXC. As a result, its effectiveness greatly deteriorates when the traffic pattern or traffic demand changes since the optimum wavelength path and waveband path configuration changes. In contrast, the hierarchical MG-OXC can provide the flexibility needed to respond to various network requirements and circumstances. The hierarchical optical path architecture is a natural approach to cost effectively deploy large scale networks as it has been adopted by not only present SDH/SONET networks [6] but also emerging OTN networks [24]. The effectiveness of waveband switching was evaluated in [21] in terms of optical switch port count ratio, the ratio of the total optical switch port count of a hierarchical optical path network to that of the equivalent single layer optical path network. The evaluation considered several key parameters including waveband capacity,

add

drop

UNI port

NNI port

Fig. 1. Generic configuration of hierarchical optical path cross-connect.

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waveband utilization ratio, and average hop count of established waveband paths. The blue region in Fig. 2 represents the area where the port count ratio is less than 1. It can be concluded that the hierarchical optical path network is very effective over a wide parameter range, and the cost effectiveness of hierarchical optical path networks is enhanced as the average hop count of waveband paths increases or the waveband utilization ratio improves. 2.2. Hierarchical optical path networks considering the introduction of wavelength convertors In this paper, we assume that wavelength convertors are applied to the NNI (Network-Network Interface) ports of WXC when necessary as shown in Fig. 3. This arrangement yields the node structure called the dedicated Wavelength Convertible Switch (WCS) Architecture [25]. Compared with alternatives such as the one that considers the Wavelength Convertor Bank (WCB), the dedicated WCS offers lower implementation complexity. Employing wavelength convertors at each WXC (NNI) port [22] offers the best utilization of fibers, however, the total facility cost can be very large. We propose an algorithm

that minimizes network equipment cost by introducing wavelength convertors only at carefully selected ports as shown in Fig. 3. By this way, only those wavelengths that require wavelength conversion are directed to wavelength convertors, and therefore we can achieve a significant reduction in the total network facility cost by reducing the number of unnecessary wavelength convertors. Compared to our previous work [23], the computational load is significantly reduced and the proposed algorithm can provide results very close to those obtained by the ILP approach. The developed algorithm is shown to be applicable to larger traffic areas where the ILP approach fails to offer any advantage. 3. Proposed routing and waveband/wavelength assignment algorithm 3.1. Problem statement To evaluate the cost of hierarchical optical path networks that use wavelength convertors, we adopt the cost parameters shown in the Appendix. Our general objective here is to minimize the total cost of the network including

Fig. 2. Ratio of the number of switch ports: hierarchical to single layer optical path networks.

Fig. 3. Reduction in the number of wavelength convertors.

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facility cost which includes optical cross-connect ports, fibers, and wavelength convertors. The minimization problem is known to be NP-complete [18] even if we do not consider path hierarchy, so the routing and waveband/wavelength assignment for hierarchical optical path networks design problem cannot be solved directly. Our previous study [23] divides the original problem into 3 sub-steps: optimization of routing, waveband assignment, and wavelength assignment. Optimization of routing means accommodating the wavelength paths within wavebands and routing the waveband paths. Optimization of waveband assignment requires the assignment of waveband indexes to all waveband paths while that of wavelength assignment is assigning wavelength indexes to all wavelength paths so that network cost can be minimized. Among the 3 sub-steps, the computational load is highest for the waveband assignment step that is based on an ILP-based formulation described in [23]. For the routing sub-steps, the number of variables depends on the number of links in the network topology [26] while for the waveband assignment substep, the necessary number of variables depends on the number of waveband paths, which increases greatly with the traffic demand. As a result, we could not complete the waveband assignment sub-step except for small traffic demand area and the impact of wavelength convertors for large traffic demand area has not been verified so far. The waveband assignment sub-step is, therefore, a critical part in the hierarchical optical path network design process. In this paper, we try to minimize cost increment in waveband assignment step. The routes of wavelength/waveband paths and the inclusive relationship between wavelength and waveband paths are already determined in the route optimization sub-step and the objective is to minimize the cost increment stemming from additional fibers that are needed to resolve waveband collision and added wavelength convertors necessary for wavelength paths that traverse pair of concatenated waveband paths having different waveband indexes (See Fig. 4(b)). Wavelength convertors will also be introduced in the wavelength assignment sub-step to resolve the wavelength collision in each waveband path, however, through the numerical experiments in the previous study [23], wavelength convertors added in waveband assignment sub-step are the majority. In this study, we find all necessary physical resources, including the number of fibers and convertors, to satisfy a given traffic demand. Therefore, it is a static network

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design algorithm that deals with the traffic demand given in advance. The approach is also particularly useful in evaluating the generic performance of networks. On the other hand, if all network facilities such as fibers and node hardware are fixed and wavelength paths are dynamically established or torn down, the objective could be, for example, the minimization of path establishment blocking probability. Such a problem is discussed in other works, for example in [14]. Our solution for waveband assignment is presented in Section 3.3. The structure of the proposed algorithm is summarized in the next section. 3.2. Hierarchical routing and waveband/wavelength assignment algorithm In the proposed algorithm, we divide the original problem into 3 steps following [23]: accommodate wavelength paths within waveband paths and route the waveband paths, assign wavebands, and assign wavelengths. The last two sub-stages consider the minimization of the number of wavelength convertors. Wavelength convertors are classified into two types; for conversion between wavebands with different indexes as shown in Fig. 4(b) and for resolving wavelength collisions in a waveband. The first and second classes are respectively minimized in the waveband assignment and wavelength assignment sub-stages. The full algorithm is summarized as follows: oProposed Design Algorithm for Hierarchical Optical Path Networks Utilizing Wavelength Conversion4 Step 1: Accommodation of Wavelength Paths and Routing of Waveband Paths. We establish a set of waveband paths accommodating the given wavelength path demand and assign routes to waveband paths by using a two-stage ILP based algorithm [22]. In this step, we set waveband paths, i.e. decide the routes and locations of source/destination nodes of waveband paths, and the inclusive relationship between wavelength paths and waveband paths. The objective is to minimize the total cost of the BXC ports, WXC ports, and fibers. The waveband/wavelength continuity constraints are not considered in this step. Step 2: Waveband Assignment We utilize the waveband assignment algorithm which will be explained in Section 3.3. In this sub-step,

Node

Wavelength convertor

WBP1

WBP1 WBP2

WBP2 WLP

WLP

Fig. 4. Wavelength convertor set in waveband assignment sub-step. (a) Without wavelength convertor (wavelength convertor to resolve wavelength collision may be needed in the wavelength assignment step, band index of WBP1 equals that of WBP2) and (b) With wavelength convertor (band index of WBP1 is not equal to that of WBP2). NOTE: WLP¼Wavelength path, WBP=Waveband path. Only waveband index is assigned in this step.

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we obtain the number of additional fibers needed to resolve waveband collisions and the number of wavelength convertors necessary for a wavelength path that traverses a pair of concatenated waveband paths having different waveband indexes. In the next stage, wavelength assignment, we may need to add fibers and/or wavelength convertors to resolve wavelength collision. Step 3: Wavelength Assignment If a wavelength path traverses a pair of concatenated waveband paths with different waveband indexes, we virtually split the path at the boundary into two wavelength paths. For all new wavelength paths that result, we assign wavelength indexes in descending order of the number of waveband paths that each wavelength path traverses. For each assignment, we try to minimize the number of wavelength convertors while resolving wavelength collision. 3.3. Waveband assignment algorithm considering potential need for wavelength convertors and additional fibers In this section, we describe our heuristic algorithm for waveband assignment (Step 2 in the Section 3.2). In assigning wavebands, we may need to add fibers to eliminate waveband collision at links. The probability of adding a fiber to one link is independent from that of another link. Here, we assume that the probability of adding fiber at each link is p, so for a k-hop count waveband path, the expected number of additional fibers is kUp during the process of assigning a waveband index to the path. Although the independence of fiber addition probability does not hold exactly, the number of waveband/wavelength paths is relatively large and we can adopt the approximation to simplify the situation. Suppose that we have a pair of concatenated waveband paths, each of which carries a group of wavelength paths (See Fig. 4). If the same waveband index is assigned to both waveband paths, no wavelength convertor is needed in this process (please note that the later wavelength path index assignment process may introduce a wavelength convertor). However, if different waveband indexes are assigned, we must assign a wavelength convertor to each wavelength path at the boundary node. Therefore, in order to suppress the introduction of wavelength convertors, we must try to assign the same waveband index to concatenated waveband paths if they carry many wavelength paths. In summary, we can estimate the potential cost increment to accommodate a pair of concatenated waveband paths from the sum of the hop count of waveband paths and the number of wavelength paths traversing the waveband paths. oProposed Waveband Assignment Algorithm Considering Potential Need for Wavelength Convertors and Additional Fibers 4

  where max hop p1 ,p2 represents the maximum of hop counts of waveband paths p1 and p2 . Step 2 For all concatenated waveband path pairs where each  waveband path pair p1 ,p2 is traversed by at least one wavelength path and at least p1 or p2 is not accommodated yet, calculate C ðp1 ,p2 Þ in Eq. (1). Find the path pair ðpi ,pj Þ with largest C ðpi ,pj Þ . If both pi and pj are not accommodated yet, find a waveband index for the longest one so that the cost for additional fibers is minimized. For the rest, if the same waveband index can be assigned without adding any fibers, assign that index. Otherwise, assign a waveband index such that the cost of additional fibers is minimized. If pi or pj is already accommodated, then follow the latter half of the above procedure. Repeat until all waveband pairs are accommodated. NOTE: After finishing this step, all waveband paths that are not accommodated yet are end-to-end waveband paths; i.e. each waveband path carries only wavelength paths whose source and destination nodes coincide with those of the waveband path. Step 3 Accommodate the remaining waveband paths in descending order of hop counts of their shortest routes.

4. Numerical experiment To confirm the proposal we employed a 5  5 polygrid network (Fig. 5(a)) COST266 pan-European network (Fig. 5(b), [27]) with randomly distributed traffic demands, represented by the average number of wavelength paths requested between each node pair. Here, we assume that all link lengths are fixed at 500 km. Each fiber accommodates 8 wavebands and each waveband supports 8 wavelengths. The network cost is approximated by the weighted sum of the numbers of switch ports, wavelength convertors and fibers, in addition to a constant cost that represents control systems and other overheads [see Appendix]. Fig. 6 shows the normalized network costs for hierarchical optical path networks with different network topology sizes that do not introduce wavelength conversion; the data was derived by using the most efficient existing heuristic algorithm [21]. The result demonstrates that the hierarchical optical path network can be more cost effective than the conventional single layer optical path network (we apply the algorithm in [28] to calculate

Step 1 Let Nðp1 ,p2 Þ be the number of wavelength paths that traverse the concatenated waveband path pairðp1 ,p2 Þ. Eq. (1) is the cost function for ðp1 ,p2 Þ. C ðp1 ,p2Þ ¼ max hopðp1 ,p2 Þ þ Nðp1 ,p2 Þ

ð1Þ

Fig. 5. Network topology for numerical experiment. (a) 5  5 polygrid network and (b) COST266 Pan-European network

Zhi-shu Shen et al. / Optical Switching and Networking 10 (2013) 54–61

5x5 1.6

7x7

1.4

9x9

1.2 1 0.8 0.6 0.4 0

1

2

3

4

5

6

7

8

Average number of wavelength paths requested between node pairs

Fig. 6. Cost comparison between hierarchical and single layer optical path networks against different network topology.

Proposed (With Conversion) ILP method (With Conversion) [23]

1.2

Without Conversion [21]

1

0.8

0.6

0

1 2 3 4 5 6 7 8 Average number of wavelength paths requested between node pairs

Normalized Netwrok Cost (Hierarchical/Single-layer)

1.5 Proposed (With Conversion) 1.3

Without Conversion [21]

1.1

0.9

60

0.7 0 1 2 3 4 5 6 7 8 Average number of wavelength paths requested between node pairs

Fig. 7. Cost comparison between hierarchical and single layer optical path networks over a wide traffic demand area. (a) 5x5 network and (b) COST266 network.

the cost of the single layer optical path network) over a wide range of traffic demands and that its effectiveness is enhanced as the network topology size increases. Conversely, when network size becomes smaller, the ineffective traffic demand area increases. Fig. 7 shows the cost ratio of proposed hierarchical optical path networks to single layer equivalents when the cost of a wavelength convertor is set equal to that of an NNI port of WXC. (Please note that for a 5  5 network the result of conventional method in [23] is available only in the small traffic demand area due to its intensive computation load). This experiment indicates that hierarchical optical path networks employing wavelength conversion can be cost effective, not only in the small traffic demand area, where the algorithm [21] that does not utilize wavelength convertors cannot offer any cost reduction, but also in the large traffic demand area. Next we evaluated the upper bound of wavelength convertor cost that permits the hierarchical optical path network to be more cost effective than the single layer

Wavelength Converter Cost/ WXC (NNI) Port Cost

Normalized Netwrok Cost (Hierarchical/Single-layer)

1.4

optical path network. Suppose that the number of utilized wavelength convertors is #WC, and the designed hierarchical optical path network cost (cH ) should be less than the cost of an equivalent single layer optical path network (cSL ). The upper bound cost is determined by cWC ¼ ðcSL  cH Þ=ð#WCÞ. Fig. 8 shows the estimated upper bounds of wavelength convertor cost against the single layer optical path networks (please note that for the COST266 network, while the traffic demand is less than 0.8, cost reduction cannot be achieved even if the cost of the wavelength convertor is 0). As traffic demand increases, the bound becomes larger. It is also demonstrated that hierarchical optical path networks that introduce wavelength convertors can still be cost effective even when the wavelength convertor cost is relatively high, particularly if the traffic demand is relatively large. From Fig. 7, for hierarchical optical path networks that use/do not use wavelength conversion, the normalized network cost decreases as the traffic demand increases. However, in this area, the cost reduction achieved by introducing wavelength conversion is relatively small, therefore, for this area, Fig. 9 describes the upper bound of wavelength convertor cost against the corresponding hierarchical optical path networks without considering wavelength conversion. It demonstrates that if the wavelength convertor cost can be smaller than a certain value, the introduction of wavelength conversion to hierarchical optical path networks can achieve enhanced cost reduction in both the large and small traffic demand areas. For the waveband assignment step, the computation time of the proposed algorithm is much shorter than that of the ILP method [23]. Although the computation time

Proposed (5x5) 50

ILP method (5x5) [23]

40

Proposed (COST266)

30 20 10 0 0

1

2

3

4

5

6

7

8

Average number of wavelegnth paths requested between node pairs

Fig. 8. Estimated bound of wavelength convertor cost for different traffic demands against corresponding single layer optical path networks.

Wavelength Converter Cost/ WXC (NNI) Port Cost

Normalized Network Cost (Hierarchical/Single-layer)

1.8

59

12 Proposed (5x5) Proposed (COST266)

8

4

0 2

3

4

5

6

7

8

Average number of wavelegnth paths requested between node pairs

Fig. 9. Estimated bound of wavelength convertor cost for different traffic demands against corresponding hierarchical optical path networks without wavelength conversion in large traffic demand area.

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Table 1 Parameters for cost evaluation. Given parameters CB_NNI CB_UNI CBXC CW_NNI CW_UNI CWXC CF CAMP CWC DAMP W B K Dij Variables Fij B_NNIi B_UNIi W_NNIi W_UNIi WC n

BXC NNI (Network-Network Interface) port cost per waveband BXC UNI (User-Network Interface) port cost per waveband BXC base cost WXC NNI port cost per wavelength WXC UNI port cost per wavelength WXC base cost Optical fiber cost per km Amplifier cost Wavelength convertor cost Amplifier span Maximum number of wavelength per waveband Maximum number of waveband per fiber Number of nodes in network Distance between node i and node j; Dij ¼ 0 for node pair that is not physically adjacent to each other. Number Number Number Number Number Number

of of of of of of

1 1.2 4 1 1.2 4 0.012 2.04 (n) 60

fibers between node i and node j BXC NNI ports at node i BXC UNI ports at node i WXC NNI ports at node i WXC UNI ports at node i wavelength convertors

Please see the 3rd–5th paragraph of Section 3.1.

for the ILP method strongly depends on the acceptable gap, when the average number of wavelength paths requested between node pairs is 1, the ILP method takes 7 days while the proposed one takes only about 1 min. Given the introduction of the proposed algorithm, the computation complexity in Step 1 will be dominant and its relaxation should be discussed elsewhere.

link cost (including optical fibers and amplifiers). The costs of node/link are expressed as follows by using the given parameters and variables in Table 1. We include a constant that represents the costs of control systems and other overheads. Specific cost values used for the calculations are up-dated equivalents of the values given in [28]. Node cost: BXCs, WXCs and wavelength convertors

5. Conclusion

C Node ¼

N X

ðC B_NNI  B_NNIi þ C B_UNI  B_UNIi þ C BXC

i¼1

We proposed a routing and waveband/wavelength assignment algorithm for hierarchical optical path networks that use wavelength convertors. We used the algorithm to evaluate the cost reduction achieved by introducing wavelength conversion. Since the proposal adopts a heuristic algorithm instead of an ILP-based one for waveband assignment, it can significantly reduce the computation load, and as a result, succeeds in making the use of wavelength convertors, which yield hierarchical optical path networks, cost effective over a wide traffic demand area. It should be noted that the obtained results are very close to those obtained by using ILP-based algorithms which can only solve the problem in the relatively small traffic demand area. The results obtained herein proved that hierarchical optical path networks that use wavelength conversion can be cost effective over a wide traffic demand area.

Acknowledgment This work was partly supported by NICT. Appendix The network cost is evaluated by the sum of node cost (including BXCs, WXCs and wavelength convertors) and

þ C W_NNI  W_NNIi þ C W_UNI  W_UNIi þC WXC Þ þ C WC  WC

ð2Þ

Link cost: optical fibers and amplifiers C Link ¼

N X N X

ðC f iber ði,jÞ  F ij Þ

ð3Þ

i¼1j¼1

where C f iber ði,jÞ ¼ C F  Dij þ C AMP 



Dij DAMP

 ð4Þ

References [1] K. Sato, Advances in Trasport Network Technology: Photonic Networks, ATM, and SDH, Artech House, 1996. [2] T.S. El-Bawab, Optical Switching, Springer, 2006. [3] K. Sato, Recent developments in and challenges of photonic networking technologies, IEICE Transactions on Communications E90-B (3) (2007) 454–467. [4] ITU-R Recommendation, Parameter Values for an Expanded Hierarchy of LSDI Image Formats for Production and International Program Exchange, BT.1796, 2006. [5] G.K. Edwards, Today’s Optical Network Research Infrastructures for E-Science Applications, in: Proceedings of the OFC,OWU3, 2006. [6] K. Sato, H. Hasegawa, Prospects and challenges of multi-layer optical networks, IEICE Transactions on Communications 90 (8) (2007) 1890–1902.

Zhi-shu Shen et al. / Optical Switching and Networking 10 (2013) 54–61

[7] K. Sato, H. Hasegawa, Optical networking technologies that will create future bandwidth abundant networks, Journal of Optical Communications and Networking 1 (2) (2009) A81–A93. [8] K. Harada, K. Shimizu, T. Kudou, T. Ozeki, Hierarchical optical path cross-connect systems for large scale WDM networks, Proceedings of the OFC 2 (1999) 356–358. [9] L. Noirie, C. Blaizot, E. Dotaro, Multi-granularity optical crossconnect, Proceedings of the ECOC 3 (2000) 269–270. [10] X. Cao, V. Anand, C. Qiao, Framework for waveband switching in multi-granular optical networks: part I, JOptBet 5 (12) (2006) 1043–1055. [11] M. Lee, J. Yu, Y. Kim, C. Kang, J. Park, Design of hierarchical crossconnect WDM networks employing a two-stage multiplexing scheme of waveband and wavelength, IEEE Journal on Selected Areas in Communications 20 (2002) 166–171. [12] P.-H. Ho, H.T. Mouftah, J. Wu, A scalable design of multigranularity optical cross-connects for the next-generation optical internet, IEEE Journal on Selected Areas in Communications 21 (2003) 1133–1142. [13] M. Iyer, G.N. Rouskas, R. Dutta, A hierarchical model for multigranular optical networks, Proceedings of the Broadnets (2008) 444–451. [14] Y. Wang, X. Cao, A study of dynamic waveband switching in multigranular optical networks, Journal of Optical Communication and Networking 3 (2011) 390–398. [15] S. Varma J.P. Jue, Regenerator Placement and Waveband Routing in Optical Networks with Impairment Constraints, in: Proceedings of the ICC, 2011. [16] M. Jinno, B. Kozicki, H. Takara, A. Watanabe, Y. Sone, T. Tanaka, A. Hirano, Distance-adaptive spectrum resource allocation in spectrum-sliced elastic optical path network, IEEE Communication Magazine 48 (8) (2010) 138–145. [17] K. Ishii, H. Hasegawa, K. Sato, M. Okuno, S. Kamei, H. Takahashi, An ultra-compact waveband cross-connect switch module to create cost-effective multi-degree reconfigurable optical node, Proceedings of the ECOC (2009).

61

[18] I. Chlamtac, A. Ganz, G. Karmi, Lightpath communications: an approach to high-bandwidth optical WAN’s, IEEE Transactions on Communications 40 (7) (1992) 1171–1182. [19] J. Yamawaku, A. Takada, W. Imajuku, T. Morioka, Evaluation of amount of equipment on single-layer optical path networks managing multigranularity optical paths, Journal of Lightwave Technology 23 (6) (2005) 1971–1978. [20] P. Torab, V. Hutcheon, D. Walters, A. Battou, Waveband Switching Efficiency in WDM Networks: Analysis and Case Study, in: Proceedings of the OFC, OtuG3, 2006. [21] I. Yagyu, H. Hasegawa, K. Sato, An efficient hierarchical optical path network design algorithm based on a traffic demand expression in a cartesian product space, IEEE Journal of Selected Areas in Communications 26 (6) (2008) 22–31. [22] H. Le, H. Hasegawa, K. Sato, Hybrid hierarchical optical path network design algorithm with 2-stage ILP optimization, Proceedings of SPIE 7989 (2010) 33–34. [23] Z. Shen, H. Hasegawa, K. Sato, Design of hierarchical optical path networks that utilize wavelength conversion and evaluation of the allowable cost bound, Proceedings of SPIE 8310 (2011) 831007. [24] ITU-T Recommendation, G.709/Y.1331, December 2009, Interfaces for the Optical Transport Network (OTN). [25] J. Zheng, H.T. Mouftah, Optical WDM Networks—Concepts and Design Principles, IEEE Press, 2004. [26] M. Tornatore, G. Maier, A. Pattavina, WDM Network Optimization by ILP Based on Source Formulation, Proceedings of INFOCOM 3 (2002) 1813–1821. [27] R. Inkret, A. Kuchar, B. Mikac, Advanced Infrastructure for Photonic Networks—Extended Final Report of COST 266 Action. Faculty of Electrical Engineering and Computing, University of Zagreb, 2003. [28] S. Kaneda, T. Uyematsu, N. Nagatsu, K. Sato, Network design and cost optimization for label switched multilayer photonic IP networks, IEEE Journal on Selected Areas in Communications 23 (2005) 1612–1619.