Waveband Grooming based on Layered Auxiliary Graph in multi-domain optical networks

Optical Fiber Technology 16 (2010) 162–171

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

Waveband Grooming based on Layered Auxiliary Graph in multi-domain optical networks Lei Guo a,b,c, Jiannong Cao c, Xingwei Wang a,*, Dingde Jiang a,b, Ting Yang a a

College of Information Science and Engineering, Northeastern University, Shenyang 110004, China State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China c Department of Computing, Hong Kong Polytechnic University, Kowloon, Hong Kong, China b

a r t i c l e

i n f o

Article history: Received 15 October 2009 Revised 14 February 2010 Available online 19 March 2010 Keywords: Optical networks Waveband switching Multi-domain Grooming Layered Auxiliary Graph

a b s t r a c t With the number of wavelengths on fibers keeps increasing, the size and the cost of Optical Cross-Connect (OXC) are greatly enhanced and then the control and management of optical switches become more and more complicated. Therefore, the technique called waveband switching is proposed to reduce the size and the cost of OXC; that is, to save the All-Optical (OOO) switching ports in OXC. However, the existing waveband switching algorithms are all limited in single-domain optical networks. Actually, with the scale of optical backbone keeps enlarging, the network is divided to multiple independent domains to perform the hierarchy routing for achieving the scalability. In order to reduce the size and the cost of OXC meanwhile to achieve the scalability in multi-domains, in this paper we propose a new heuristic algorithm called Waveband Grooming with Layered Auxiliary Graph (WGLAG) since the waveband grooming problem is the NP-hard to perform the inter-domain routing based on the virtual topology of multi-domain network and the intra-domain routing based on the physical topology of single-domain network. In intra-domain routing with waveband grooming of each single-domain, we propose the Layered Auxiliary Graph (LAG) that includes one virtual topology layer and multiple waveband-plane layers to compute a single-hop, or multi-hop or hybrid waveband route for each connection request based on the sub-path waveband grooming scheme. Simulation results show that, WGLAG not only can effectively save more switching ports to reduce the cost of OXC but also can obtain lower blocking probability than other algorithm. Ó 2010 Elsevier Inc. All rights reserved.

1. Introduction With the development of Wavelength-Division-Multiplexing (WDM) technology, the number of wavelengths on fibers keeps increasing and the consequent is that the size (i.e., the number of switching ports) and the cost of conventional Optical Cross-Connect (OXC) are greatly enhanced, and then the control and management of optical switches become more and more complicated. Therefore, the recent literature [1] proposed the waveband switching technique to reduce the size and the cost of OXC. The main idea of waveband switching is to use the waveband grooming scheme to bind several wavelength-level routes to one waveband-level route that can be switched by only one switching port, so that the number of All-Optical (OOO) switching ports can be saved and the cost of OXC can be reduced. In order to support the waveband-level switching meanwhile to provide efficiency for the conventional wavelength-level switching, previous work presented the Multi-Granular OXC (MG-OXC) [2,3] and proposed several * Corresponding author. Fax: +86 024 83687575. E-mail address: [email protected] (X. Wang). 1068-5200/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.yofte.2010.02.006

waveband routing and grooming schemes, such as the same source–destination scheme where the wavelength-level routes with the same source node and destination node can be grouped in a waveband route, the same source scheme where only the wavelength-level routes with the same source node can be grouped in a waveband route, the same destination scheme where the wavelength-level routes with the same destination node can be grouped in a waveband route, and the sub-path scheme where the wavelength-level routes with the same intermediate ingress node and the egress node can be grouped in a waveband route [4–13]. At the same time, with the development of intelligent optical network, the scale of network keeps enlarging. In order to achieve the scalability, same to the Internet, the current optical backbone is divided to multiple areas or domains where each domain is a local Automatic System (AS) that is managed by an independent network provider and it may use different technologies with other domains [14]. In multi-domain networks, the nodes are classified to interior nodes and gateway nodes. Each domain only distributes the partial information to other domains due to the constraint of domain management policies, so that the interior nodes in each domain cannot know the global information of the physical

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topology in multi-domains but can have the local information of the physical topology in single-domain and the partial information of gateway nodes in other domains. The gateway node can keep both the local information of the physical topology in single-domain and the global information of aggregative virtual topology in multi-domains [15]. Therefore, in order to achieve the scalability in current optical backbone, the inter-domain routing based on aggregative information is an interesting and challenging problem due to lack of the accurate global information and it has got more attention in recent years [16–19]. The current existing waveband routing and grooming schemes mentioned above are all limited in single-domain optical networks. Since the inter-domain routing in multi-domain optical networks based on aggregative virtual topology is an interesting and challenging work to achieve the scalability and also the waveband switching can reduce the size and the cost of OXC, in this paper we consider the problem of waveband routing and grooming in multi-domain optical networks and proposed a new algorithm called Waveband Grooming with Layered Auxiliary Graph (WGLAG) since the waveband grooming problem is the NP-hard [2] to achieve the scalability of routing computation in multi-domains meanwhile to reduce the size and the cost of OXC. In this paper, we adopt the full-mesh abstract scheme in [16] to address the aggregative virtual topology in multi-domain optical networks, in which each domain is denoted as a meshed area that contains the gateway nodes and virtual links each of which is an abstraction or a map of the intra-domain physical route between

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two gateway nodes. After abstracting, the whole network is divided to two-layer topologies, i.e., high-layer topology and lowlayer topology, to form the hierarchy routing model of multi-domains. For example, Fig. 1a is a given multi-domain optical network and Fig. 1b is the corresponding high-layer and low-layer topologies. The high-layer topology includes the gateway nodes, inter-domain fiber links and virtual links each of which connects two gateway nodes in the same domain and it denotes the reachable information for the two gateway nodes. The low-layer topology includes the local information of the physical topology in each single-domain. Based on this model, the routing computation of inter-domain and intra-domain for each connection request will be performed on high-layer aggregative topology and the lowlayer physical topology, respectively. For each connection request, if the source node and destination node are in the same domain, the source node will directly compute an intra-domain route from the source node to destination node based on the low-layer topology. If the source node and destination node are in different domains, first a loose inter-domain route will be computed from a gateway node in source domain to a gateway node in destination domain based on high-layer topology. Second, an intra-domain route from source node to gateway node, an intra-domain route from gateway node to destination node, and several exact intra-domain routes for virtual links traversed by the loose inter-domain route will be computed based on the low-layer topology. Finally, the full inter-domain route can be obtained.

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In order to achieve the waveband routing and grooming for saving switching ports, in each domain the intra-domain route is computed based on Layered Auxiliary Graph (LAG) including one Virtual Topology Layer (VTL) and multiple Waveband-Plane Layers (WPL). For each connection request, WGLAG uses the sub-path waveband grooming scheme; that is, WGLAG first computes a single-hop or multi-hop route on VTL, and then if the route cannot be found, it computes a hybrid route on LAG by jointing VTL and WPL. Compared with other algorithm based on the same-destination waveband grooming scheme, WGLAG can obtain better performances. To the best of our knowledge, the work in this paper is the first study to achieve the scalability based on aggregative virtual topology of multi-domains meanwhile to reduce the size and the cost of OXC by performing waveband switching in multi-domain optical networks. This paper is organized as follows: Section 2 describes the network model and routing selection in multi-domains. Section 3 proposes the inter-domain and intra-domain waveband routing and grooming schemes. Section 4 presents the steps of WGLAG algorithm. Section 5 is for simulation and analysis. Section 6 concludes this paper. 2. Network model and routing selection 2.1. Network model The physical network topology is denoted as GðInterL; DÞ corresponding to routing computation in low-layer topology, where InterL is the set of inter-domain fiber links each of which connects two gateway nodes in different domains, and D ¼ fDr ðGN r ; INr ; IntraLr Þjr ¼ 1; 2; . . .g is the set of physical topologies of all domains in which Dr is the physical topology of domain r, GNr is the set of gateway nodes in domain r, IN r is the set of interior nodes in domain r and IntraLr is the set of intra-domain links in domain r. The aggregative virtual topology is denoted as Gv fInterL; Dvr g corresponding to routing computation in high-layer topology, where Dvr ¼ fGN r ; VLr g in which VLr is the set of virtual links in domain r. We assume each node has the MG-OXC with two-layer structure shown in Fig. 2 to achieve the wavelength-level switching by Wavelength Cross-Connect (WXC) and waveband-level switching by Waveband Cross-Connect (BXC). Another MG-OXC with single-layer structure, where the BXC and WXC are integrated in a single unit, is not considered in this paper. We assume each connection requires the bandwidth of one wavelength channel. The shortest path algorithm, i.e., Dijkstra’s algorithm, is applied to compute the route. The waveband and wavelength assignment scheme is First-Fit. The protocols, e.g., OSPF-TE, RSVP-TE, etc., for routing computation and resource assignment are supported by GMPLS [20], and the algorithm is the domain-by-domain approach

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in multi-domain optical networks [21]. The following concepts and notations are introduced. Gateway node: Each gateway node has a routing table that contains the local information of the physical topology in domain r and also has the global information of virtual topology in multi-domains, so that it can perform intra-domain routing in domain r by Interior Gateway Protocols (IGP) and inter-domain routing in multi-domains by Boundary Gateway Protocols (BGP). Since gateway nodes are the key components to connect different domains, we assume each gateway node has the full wavelength/waveband convertors and also has enough optical transceivers and switching ports. Interior node: Each interior node has a routing table that only contains the local information of physical topology in domain r so that it only can support intra-domain routing in domain r by IGP. Since interior nodes are much more than gateway nodes and they are also ordinary components in each domain, we assume each interior node has no wavelength/waveband convertors and also has the limited optical transceivers and switching ports. Inter-domain link: Since inter-domain links are the key components to connect different domains as well as gateway nodes, we assume each inter-link has enough wavelengths and wavebands. Intra-domain link: Since the interior fiber links are much more than inter-domain fiber links and they are also ordinary components in each single-domain, we assume each intra-domain link has the limited wavelengths and wavebands. In this paper, we assume the set of wavebands and the set of wavelengths in each intra-domain fiber link are denoted as B and W, respectively. Virtual link: Each virtual link can be computed and determined beforehand, and it contains several physical fiber links and denotes the route between two gateway nodes in single-domain. CRns;d : Connection request numbered n from source node s to destination node d. P ns;d : Primary path for CRns;d from source s and destination node d. It may be inter-domain or intra-domain routes. jXj: Number of elements in set X. xr : Physical node in physical network topology of domain r. V rx : Virtual node in virtual topology layer corresponding to node xr in domain r. VTLr : Virtual topology layer in domain r. WRLrx;z : If there is a waveband-route with free wavelengths from node xr to node zr in domain r, then there will be a wavebandroute link WRLrx;z between node V rx and node V rz . FW rx;z : Number of free wavelengths on WRLrx;z . FT rx : Number of free transceivers in node xr in domain r. WPLry : Waveband-plane layer corresponding to waveband Bry ð1 6 y 6 jBjÞ in domain r. Bry;x : Waveband-node in WPLry corresponding to node xr in domain r. WLry;x;z : If there is a fiber connection between node xr to node zr in domain r and waveband Bry on this fiber is free, then there will be a waveband link WLry;x;z between Bry;x and Bry;z on WPLry in domain r. TVLðV rx ; Bry;x Þ: If the number of free transceivers on node xr is greater than zero, then there will be a transceiver virtual link TVLðV rx ; Bry;x Þ between node V rx and node Bry;x ð8 y 2 ½1; jBjÞ in domain r. CVLðBry1;x ; Bry2;x Þ: If node xr has wavelength/waveband convertors, then there will be a conversion virtual link CVLðBry1;x ; Bry2;x Þ between node Bry1;x and node Bry2;x ð8 y1; y2 2 ½1; jBj; y1 – y2Þ in domain r. 2.2. Routing selection

R/T Fig. 2. MG-OXC in network node.

If a connection request arrives, the source node will check its own routing table to know that whether the destination node is

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in the same domain. If the source node and destination node are in the same domain (assume domain r), the source node will directly perform the intra-domain routing to compute a route from the source node to destination node based on the low-layer topology of domain r. If the source node and destination node are in different domains (assume they are in domain r1 and domain r2, respectively), in the first step, a loose inter-domain route will be computed from a gateway node (assume G1) that is nearest to source node in domain r1 to a gateway node (assume G2) that is nearest to destination node in domain r2 based on high-layer topology. In the second step, an intra-domain route from source node to G1, an intra-domain route from G2 to destination node, and several exact intra-domain routes each of which is for a virtual link from the ingress gateway node to egress gateway node in the intermediate domain traversed by the loose inter-domain route will be computed based on low-layer topology. Finally, the route across different domains can be obtained. In these steps, each intra-domain route will be computed based on Layered Auxiliary Graph (LAG) to achieve the waveband routing and grooming in each single-domain, which will be presented in Section 3. For example, Fig. 3a and b are low-layer physical topology and high-layer virtual topology, respectively. The gray nodes are gateway nodes and other nodes are interior nodes. When a connection request with source node 6 and destination node 14 arrives, since the source and destination nodes are in different domains, we first compute a loose route 1–9–11–13 based on the high-layer virtual topology in Fig. 3b. Then, we compute an intra-domain route 6–0– 1 from source node 6 to gateway node 1 in domain 0, an intra-domain route 13–16–14 from gateway node 13 to destination node 14 in domain 2, and an exact intra-domain route 9–10–11 for virtual link 9–11 in domain 1 based on the low-layer physical topology in Fig. 3a. Finally, the full inter-domain route is 6–0–1–9–10– 11–13–16–14. 3. Waveband routing and grooming 3.1. Intra-domain waveband routing and grooming In multi-domain optical networks, we perform the intra-domain waveband routing and grooming for each domain independently, which is same with the conventional waveband routing and grooming in single-domain [4–13]. In each single-domain, we define the Layered Auxiliary Graph (LAG) that contains the full interior information of this domain to achieve the intra-domain waveband routing and grooming. In LAG, we design two kinds of

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routing selection graph called Virtual Topology Layer (VTL) and Waveband-Plane Layer (WPL). The VTL is a single-layered graph including waveband-route links and virtual nodes. Although there may be multiple available waveband-routes between node xr and node zr in domain r, there is only one waveband-route link WRLrx;z between node V rx and node V rz while there will be multiple values of free wavelengths on WRLrx;z . In the end node of traffic, the waveband-route can be de-multiplexed to wavelengths and be switched by WXC in MG-OXC shown in Fig. 2. Since a connection request can be allowed to reach the destination node by multi-hop waveband-routes, if there is an out-of-local connection request, it can be grouped into another waveband-route link and transmitted forward together with the connection requests generated by this node. Therefore, each virtual node in VTL can be regarded as having the wavelength/waveband convertors. Also, the new coming requests can use the free wavelengths on existing waveband-route links to establish the connection. The WPL is a multi-layered graph including the free waveband links and waveband nodes. The WPL contains |B| independent subgraphs called waveband-plane layer each of which is a copy of the physical network topology, and each WPLry corresponds to a waveband Bry ð1 6 y 6 jBjÞ in domain r. In WPL, each node in physical network topology will be copied |B| times, and the free waveband Bry ð1 6 y 6 jBjÞ between node xr and node zr will be mapped to the waveband link WLry;x;z on WPLry in domain r. If we can find an intradomain route on some waveband-plane layer between two nodes, we can assign the corresponding waveband to this route. It is obvious that the problem of routing and waveband assignment can be well solved based on WPL. The LAG is an integrated graph by adding the transceiver virtual links TVLðV rx ; Bry;x Þ between node V rx on VTLr and node Bry;x on WPLry ð8 y 2 ½1; jBjÞ in domain r, and by adding the conversion virtual links CVLðBry1;x ; Bry2;x Þ between node Bry1;x on WPLry1 and node Bry2;x on WPLry2 ð8 y1; y2 2 ½1; jBj; y1 – y2Þ in domain r. If the number of free transceivers is zero at node xr in domain r (i.e., FT rx ¼ 0), all transceiver virtual links connecting with node V rx will be removed. Based on LAG, we can compute the hybrid multi-hop waveband-route in domain r; that is, for each route from source node to destination node, some sub-paths on this route may use the existing waveband-route links with free wavelengths on VTL, while other sub-paths on this route may consume new waveband links on WPL. Therefore, the waveband grooming based on LAG is the sub-path waveband grooming scheme that can save more switching ports than other schemes [13]. For each connection request, we perform the intra-domain waveband routing and grooming from node xr to node zr in domain

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r. We first compute the route from node xr to node zr with singlehop or multi-hop on VTLr. If the route cannot be found on VTLr, we perform the hybrid routing computation on LAG. We select node xr and node zr based on the following policies: (1) If the source node and destination node are both in domain r, then xr is selected as the source node and zr is selected as the destination node. (2) If the source node is in domain r and the destination node is not in domain r, then xr is selected as the source node and zr is selected as a gateway node that is the nearest to xr in domain r. (3) If the source node is not in domain r and the destination node is in domain r, then zr is selected as the destination node and xr is selected as a gateway node that is the nearest to zr in domain r. (4) If the source node and destination node are either not in domain r, then xr is selected as an ingress gateway node and zr is selected as an egress gateway node in domain r. In the following, we present an example to explain the intra-domain waveband routing and grooming. We only consider this case where the source node and destination node are both in domain r since other cases are similar with this case. We assume six connec-

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tion requests (CR14;3 ; CR26;4 , CR36;2 ; CR46;4 , CR56;3 ; CR66;1 ) arrive at the network orderly and each of them requires the bandwidth of one wavelength channel. The physical network topology of domain r is shown in Fig. 4a, where the gray nodes are gateway nodes that have enough resources such as wavelength/waveband convertors and transceivers, and each fiber link has two available wavebands Br1 and Br2 each of which contains four available wavelengths. The initial LAG is shown in Fig. 4b, where there are one virtual topology layer VTLr and two waveband-plane layers WPLr1 and WPLr2 . The number beside each virtual node is the number of free transceivers, where MAX denotes there are enough transceivers. Initially, there are no waveband-route links between nodes on VTLr since there are no connections. For the first request CR14;3 , we obtain the route V r4  Br1;4  Br1;1  Br1;2  Br1;3  V r3 that consumes the waveband links WLr1;4;1 , WLr1;1;2 and WLr1;1;3 on WPLr1 in Fig. 4b. For the second request CR26;4 , we obtain the route V r6  Br1;6  Br1;5  Br1;4  V r4 that consumes the waveband links WLr1;6;5 and WLr1;5;4 on WPLr1 in Fig. 4b. For the third connection CR36;2 , we obtain the route V r6  Br1;6  Br1;3  Br2;3  Br2;2  V r2 that consumes the waveband links WLr1;6;3 on WPLr1 and WLr2;3;2 on WPLr2 in Fig. 4b. Obviously, there exists a wavelength conversion at node 3 since this route traverses the conversion virtual link CVLðBr1;3 ; Br2;3 Þ. Therefore, LAG will be up-

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dated in Fig. 4c by removing the consumed waveband links on WPLr1 and WPLr2 and by adding the waveband-route links WRLr4;3 , WRLr6;4 and WRLr6;2 on VTLr. The numbers beside WRLr4;3 , WRLr6;4 and WRLr6;2 denote the free wavelengths FW r4;3 , FW r6;4 and FW r6;2 on these waveband-route links, respectively. Since each waveband contains four wavelengths and each connection consumes one wavelength, FW r4;3 , FW r6;4 and FW r6;2 need to be all updated to 3. In addition, FT r2 , FT r4 and FT r6 will be updated to 1, 0 and 0 respectively, since each waveband-route consumes two transceivers at the two end nodes. Due to FT r4 ¼ 0 and FT r6 ¼ 0, transceiver virtual links TVLðV r4 ; Br1;4 Þ, TVLðV r4 ; Br2;4 Þ, TVLðV r6 ; Br1;6 Þ and TVLðV r6 ; Br2;6 Þ will be removed on LAG. Here, the number of free transceivers at node 3 does not need to be updated because it has enough transceivers. In the following, for the fourth request CR46;4 , we can find an available single-hop route V r6  V r4 on VTLr , and then FW r6;4 will be updated to 2. For the fifth request CR56;3 , we can find an available two-hop route V r6  V r4  V r3 on VTLr , and then FW r6;4 and FW r4;3 will be updated to 1 and 2 respectively, shown in Fig. 4d. Since the two routes are established on existing waveband-route links on VTLr , they will not consume new transceivers. For the sixth request CR66;1 , we can find a hybrid route V r6  V r2  Br2;2  Br2;1  V r1 that includes a new waveband-route V r2  Br2;2  Br2;1  V r1 on WPLr2 and an exiting waveband-route link V r6  V r2 on VTLr shown in Fig. 4e. Finally, the updated LAG is shown in Fig. 4f.

ing for connection request from source node 4 to destination node 15, we first compute a loose route 3–10–9–13 on high-layer topology in Fig. 5b, and then compute the exact route 4–1–2–3 in domain 1, exact route 10–7–8–9 in domain 2 and exact route 13– 14–15 in domain 3 on low-layer topology in Fig. 5c. Finally, we obtain the full inter-domain route 4–1–2–3–10–7–8–9–13–14–15. When computing the exact route in each domain on low-layer physical topology, we need to perform the intra-domain waveband routing and grooming. In Fig. 6a, for the case in Fig. 5 where each fiber link is assumed to have two wavebands each of which contains four wavelengths, route 4–1–2–3 is established on WPL11 in domain 1, route 10–7–8– 9 is established on WPL21 in domain 2 and route 13–14–15 is established on WPL31 in domain 3. We can see that, in Fig. 6a, there are two transceiver virtual links with opposite directions at each gateway node between WPLe1 and VTLe ðe ¼ 1; 2; 3Þ. For example, TVLðB11;3 ; V 13 Þ denotes the waveband-level traffic is switched from the output of BXC to the input of waveBand-ToWavelength (BTW) de-multiplexer at node 3, and TVLðV 13 ; B11;3 Þ denotes that wavelength-level traffic is switched from the output of BTW de-multiplexer to the input of WXC at node 3. According to the policy of intra-domain waveband routing and grooming, after accepting this connection, we need to update the graph as shown in Fig. 6b, where there are three waveband-route links WRL14;3 , WRL210;9 and WRL313;15 which can be used by new coming requests if they have free wavelengths. Thus, the inter-domain waveband routing and grooming is realized.

3.2. Inter-domain waveband routing and grooming

4. Heuristic algorithm

The inter-domain waveband routing and grooming is the combination of all intra-domain processes, where each domain independently executes the process of waveband routing and grooming. In this paper, all gateway nodes are assumed to have enough switching ports since the gateway nodes are key components and have abundant resources. Therefore, at each intermediate egress gateway node on the route, the waveband traffic can be de-multiplexed to wavelength traffic and be transmitted on inter-domain link. At each intermediate ingress gateway node on the route, the wavelength traffic can be multiplexed to waveband traffic and be transmitted on intra-domain link. For example, Fig. 5a and b are the low-layer physical topology and high-layer virtual topology, respectively. In inter-domain rout-

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Fig. 6. Illustration of inter-domain waveband routing and grooming based on LAG in multi-domains.

tion node d based on LAG of this domain. If this route can be found, go to step 6; otherwise, block this connection request and go back to step 2. Step 5: Compute a loose inter-domain route from the gateway node (assume G1) that is nearest to source node s in source domain to the gateway node (assume G2) that is nearest to destination node d in destination domain based on high-layer topology. Then, compute an intra-domain route that may be a single-hop, or multi-hop or hybrid path from source node s to node G1 based on LAG of source domain, compute an intradomain route that may be a single-hop, or multi-hop or hybrid path from node G2 to destination node d based on LAG of destination domain, and compute the exact intra-domain routes each of which may be a single-hop, or multi-hop or hybrid path for a virtual link from the ingress gateway node to egress gateway node in intermediate domain traversed by the loose interdomain route based on LAG of each intermediate domain. If these routes can all be found, go to step 6; otherwise, block this connection request and go back to step 2. Step 6: Accept this connection. Remove all consumed waveband links on waveband-plane layer, add new waveband-route links on virtual topology layer, update the number of free transceivers at each node and the number of free wavelengths on each waveband-route link, and go back to step 2. Step 7: Remove this connection from the network. Update the number of free transceivers at each node and the number of free

wavelengths on each waveband-route link. If the number of free transceivers in a node becomes greater than zero, add the transceiver virtual links at this node. If the number of free wavelengths in a waveband-route link is equal to the total number of wavelengths belonging to this waveband, remove this waveband-route link from virtual topology layer, add the corresponding waveband links on waveband-plane layer, and go back to step 2. We consider the time complexity of routing computation in WGLAG for each connection request in the worst case. In highlayer topology, the time complexity is approximately OðM þ Y log YÞ according to [22] where M is the total number of gateway nodes and Y is the total number of links in all domains since we will run one time of Dijkstra’s algorithm to compute a loose route. In low-layer topology of each single-domain, the time complexity is approximately OððN þ L  log LÞ þ ðjBj  N þ jBj  L  logðjBj  LÞÞÞ where N is the total number of physical nodes and L is the total number of physical links in each single-domain since we will run one time of Dijkstra’s algorithm to compute a route on VTL with N nodes and L links or run one time of Dijkstra’s algorithm to compute a route on LAG with jBj  N nodes and jBj  L links if the route computation on VTL is failed. Therefore, for each connection request across jDj domains in the worst case, the time complexity of our proposed WGLAG algorithm is approximately OððM þ Y log YÞ þ jDj  ððN þ L  log LÞþ ðjBj  N þ jBj  L  logðjBj  LÞÞÞÞÞ.

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Fig. 7. Test network topology in simulation.

We simulate a dynamic network environment with the assumptions that connection requests arrive according to an independent Poisson process with arrival rate b and the connections’ holding times are negatively exponentially distributed 1/l, i.e., the network load is b/l Erlang. In simulation, we set l = 1. If the algorithm could not find a feasible route, the connection request is rejected immediately without waiting queue. The test network is shown in Fig. 7 where each node-pair is interconnected by a bi-directional link, each of which contains two unidirectional fibers with contrary direction. We assume that each fiber contains 64 wavelengths, the required bandwidth of each connection request is one wavelength channel, and the number of transceivers on each node is enough. The computer used in simulation is configured with 2.3 GHz CPU and 1G DDRRAM and the software is VC++6.0. In simulation, we test the performances of estimated Blocking Probability (BP) and Average Port-Cost (APC) for WGLAG on various situations. The BP is defined as the ratio of the number of blocked connection requests over the number of arrival connection requests. To obtain BP, we calculate the blocking probability after running 5000 requests for each time; that is, we will obtain 200 values of blocking probability in the simulated 106 connection requests. Finally, we take the average value of them as the BP. The APC is defined as the number of all consumed ports over the number of accepted connection requests. Obviously, lower BP means higher network throughput and smaller APC means less ports consumption. We compare WGLAG with PWR, where in each single-domain WGLAG performs the sub-path waveband grooming while PWR performs the same source–destination waveband grooming in [8]. We first test the performances of BP and APC for WGLAG with different parameters of Waveband Merging Ability (WMA) that is the ability of merging wavelengths to wavebands in MG-OXC; that is, bigger WMA means more wavebands are available to carry on the grouped wavelengths. For example, WMB = 0.5 means half of wavebands in a fiber are available to carry on the grouped wavelengths, and WMB = 1 means all wavebands in a fiber are available to carry on the grouped wavelengths. In Figs. 8 and 9, we assume the waveband granularity is 8; that is, there are 8 wavebands. In Fig. 8, we can see that, BP gradually reduces with WMA increases in different network load. When WMA = 1, BP is equal to zero. The reason for this is that, bigger

WMA means more wavebands are available to carry on the grouped wavelengths, so that more switching ports for wavelength-level traffic can be saved to be used by new coming requests, and then BP can be reduced. In Fig. 9, it is shown that with WMA increases, APC first increases, then gradually reduces and finally is gradually close to a constant. The reason for this is that, when WMA is smaller than some value (e.g., 0.375), the increased cost of WTB/BTW for merging more wavelength-level traffic exceeds the reduced cost of switching ports for by-passing more waveband-level traffic, so that the total cost increases. When WMA is greater than some value (e.g., 0.375), the increased cost of WTB/BTW for merging more wavelength-level traffic is less than the reduced cost of switching ports for by-passing more waveband-level traffic, so that the total cost decreases and is gradually close to a constant. In the following, we set WMA to 1 so that BP is only affected by wavelength or waveband resources. In Fig. 10, it is shown that BP increases with the network load increases in different waveband granularities. In Fig. 11, we can see that BP decreases with the waveband granularly increases in different network loads. The reasons for this is that, when the waveband granularly increases, more wavelength-level traffic can be grouped into fewer wavebands to be switched by fewer ports, so that more switching ports can be saved and BP can be reduced. In Fig. 12, we assume the network load is 200. It is shown that, when the waveband granularity is smaller than some value (e.g.,

Blocking probability (BP)

5. Simulation and analysis

100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0.125

network load = 100 network load = 130 network load = 160

0.375

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Waveband merging ability (WMA) Fig. 8. Performance of blocking probability for WGLAG in different waveband merging ability.

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Average port-cost (APC)

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Fig. 9. Performance of average port-cost for WGLAG in different waveband merging ability.

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Fig. 13. Comparison of average port-cost between WGLAG and PWR in different network load.

Network load in Erlang Fig. 10. Performance of blocking probability of WGLAG in different network load.

50% 45% 40% 35% 30% 25% 20% 15% 10% 5% 0%

network load = 200

Blocking probability (BP)

Blocking probability (BP)

16), APC of WGLAG is smaller than that of PWR; when the waveband granularity is greater than some value (e.g., 16), APC of WGLAG is similar with that of PWR. The reason for this is that, when the waveband granularity is smaller, there will be more wavebands that can be used to establish more waveband-route links on VTL. If the single-hop routes on VTL are not available, WGLAG may still have higher probability to find the multi-hop routes on VTL without consuming new switching ports while PWR needs to establish new waveband routes on WPL with consuming new switching ports. Therefore, APC of WGLAG is smaller than that of PWR in the situation of smaller waveband granularity. When the waveband granularity is bigger, there will be fewer wavebands that can be used to establish fewer waveband-route links on VTL. Then, WGLAG may have lower probability to find the multi-hop routes on VTL without consuming new switching ports; that is, WGLAG also needs to establish new waveband routes on WPL with consuming new switching ports, which is similar

network load = 150 network load = 100

2

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with PWR. Therefore, APC of WGLAG is similar with that of PWR in the situation of bigger waveband granularity. In Fig. 13, we assume the waveband granularity is 16; that is, there are 4 wavebands. We can see that APC of WGLAG is smaller than that of PWR. The reason for this is that, for each request, if the single-hop route on VTL cannot be found, WGLAG can search a multi-hop route on VTL without consuming new switching ports based on the sub-path waveband grooming scheme while PWR needs to search a new waveband route on WPL with consuming new switching ports based on the same source–destination waveband grooming scheme. Therefore, WGLAG can save more switching ports than PWR and then the APC of WGLAG is smaller than that of WGLAG. In Fig. 14, we assume the network load is 200. In Fig. 15, we assume the waveband granularity is 16. The results in two figures show that that BP of WGLAG is smaller than that of PWR. The reason for this is that, WGLAG can save more switching ports than PWR, and then more free switching ports can be used by new coming requests and then BP of WGLAG can be reduced. In addition, if the single-hop route on VTL cannot be found for each request, WGLAG can search a feasible multi-hop route on VTL by effectively using the free wavelengths in existing waveband-route links, and

16

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Waveband granularity Fig. 14. Comparison of blocking probability between WGLAG and PWR in different waveband granularities.

Blocking probability (BP)

L. Guo et al. / Optical Fiber Technology 16 (2010) 162–171

cation (108040), the Specialized Research Fund for the Doctoral Program of Higher Education (20070145096, 20070145017), the Program for New Century Excellent Talents in University (NCET08-0095), the Special Fund for Basic Scientific Research of Central Colleges at Northeastern University (N090504001, N090504003, N090504006, N090404014), and the State Key Laboratory of Networking and Switching Technology in Beijing University of Posts and Telecommunications (SKLNST-2009-1-04).

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Network load in Erlang Fig. 15. Comparison of blocking probability between WGLAG and PWR in different network load.

then more waveband links can be saved to be used by new coming requests for reducing the blocking probability. However, if the single-hop route on VTL cannot be found, PWR needs to search a new waveband route by consuming the new waveband links on WPL, and then more waveband links may be consumed and the blocking probability may be increased. Therefore, BP of WGLAG is smaller than that of PWR. 6. Conclusion This paper proposed a new algorithm named Waveband Grooming with Layered Auxiliary Graph (WGLAG) in multi-domain optical networks to improve the scalability of routing computation and to reduce the cost of OXC. In order to achieve the scalability, WGLAG performs the inter-domain routing based on the virtual topology of multi-domain network and the intra-domain routing based on the physical topology of single-domain network. In order to save the switching ports for reducing the cost of OXC, in the intra-domain routing with waveband grooming of each single-domain, we propose the Layered Auxiliary Graph (LAG) that includes one virtual topology layer and multiple waveband-plane layers to compute a single-hop, or multi-hop or hybrid route for each connection request based on the sub-path waveband grooming scheme. Simulation results showed that, compared with other algorithm, WGLAG obtained better performances on blocking probability and average port-cost. Acknowledgments The preliminary work of this paper was presented at the International Conference on Computer and Automation Engineering (ICCAE) 2010. This work was supported in part by the Hong Kong Polytechnic University Postdoctoral Fellowships Scheme (GYX2E), the National Natural Science Foundation of China (60802023, 70931001, 60673159, 70671020), the National HighTech Research and Development Plan of China (2007AA041201), the National Science and Technology Pillar Program (2008BAH3 7B03, 2008BAH37B07), the Key Project of Chinese Ministry of Edu-

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