RWA on Scheduled Lightpath Demands in WDM Optical Transport Networks with Time Disjoint Paths

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1 RWA on Scheduled Lightpath Demands in WDM Optical Transport Networks with Time Disjoint Paths Hyun Gi Ahn, Tae-Jin Lee, Min Young Chung, and Hyunseung Choo Lambda Networking Center School of Information and Communication Engineering Sungkyunkwan University , Suwon, Korea {puppybit, tjlee, mychung, Abstract. In optical networks, traffic demands often demonstrate periodic nature for which time-overlapping property can be utilized in routing and wavelength assignment (RWA). A RWA problem for scheduled lightpath demands (s) has been solved by combinatorial optimal solution (COS) and graph coloring, or heuristic sequential RWA (srwa). Such methods are very complex and incurs large computational overhead. In this paper, we propose an efficient RWA algorithm to utilize the time disjoint property as well as space disjoint property through fast grouping of s. The computer simulation shows that our proposed algorithm indeed achieves up to 54% faster computation with similar number of wavelengths than the existing heuristic srwa algorithm. 1 Introduction Optical virtual private networks (OVPNs) are the key service networks provided by an optical transport network (OTN) [1]. In OVPNs, connection requests offered by clients can be classified into three different types: static, scheduled, and dynamic. A set of static lightpath demands is provided by OVPN clients in order to satisfy their minimal connectivity and capacity requirements. When connection requests are dynamically established and released in time, such traffic demands are called dynamic lightpath demands. Scheduled lightpath demands may be required to increase the capacity of a network at specific times and/or on certain links. For example, suppose that periodical backups of database are required between the headquarter and production centers during office hours or between data centers during nights. Then, the lightpath demands for the backups of database are called scheduled lightpath demands (s). In real OTNs, we believe that most of demands will be considered as static or scheduled for the time being. The reason is that the traffic load in a transport network is fairly predictable because of its periodic nature [2][7]. Fig. 1 gives an This work was supported in parts by Brain Korea 21 and the Ministry of Information and Communication, Korea. Dr. Lee is the corresponding author. C. Kim (Ed.): ICOIN 2005, LNCS 3391, pp , c Springer-Verlag Berlin Heidelberg 2005

2 RWA on Scheduled Lightpath Demands in WDM 343 indication of this phenomenon. The figure shows the traffic on the New York- Washington link of the Abilene backbone network during a typical week. A similar periodic pattern was observed on all the other links of the network in the same period (This trend becomes greater during working hours). The figure shows clear evidence of the connection between the traffic intensity and the human usage pattern. Routing and wavelength assignment (RWA) finds an appropriate route for a traffic demand and assigns a wavelength to the route, and the problem is one of the most important issues in wavelength division multiplexing (WDM) optical networks [3]. Since RWA has a great impact on performance and cost of optical networks, various approaches have been proposed [3][4][5][6]. The typical objectives of RWA research are 1) to minimize the required number of wavelengths under static connection requests, 2) to minimize the blocking probability under given number of wavelengths and dynamic connection requests, or 3) to minimize overall the network cost, e.g., wavelength converters. In the conventional RWA research, traffic demands has been assumed to be either static or dynamic. Noting the nature of the scheduled lightpath demands, we can utilize more efficient RWA for s. An can be represented by 4 tuple (s, t, µ, ω), wheres and t are source and destination nodes of a demand, µ and ω are setup and teardown times of a demand. The s for which setup and teardown times are known in advance can take the advantage of the time scheduling property. That is, unless two lightpaths overlap in time, they can be assigned the same wavelength since the paths are disjoint in time. So, in this paper, we propose an efficient RWA algorithm in which s with non-overlapping service times are grouped in order to enhance the performance of RWA. Our algorithm is shown to achieve up to 52% performance improvement compared to the conventional RWA algorithms. This paper is organized as follows. First, we discuss related works on RWA in Section 2. We propose a RWA algorithm based on time disjoint path (TDP) in Section 3. Performance evaluation of the proposed algorithm is presented in Section 4. Finally, we conclude in Section 5. 2 Related Works BGAforEDP is a simple and heuristic RWA algorithm [4][5]. It is a simple edge disjoint paths scheme based on the shortest path algorithm [5]. Let G B =(V B, E B ) be the graph of a physical network, where V B and E B are the set of vertices and the set of edges, respectively. And let τ be a demand set, τ = {(s 1, t 1 ),...,(s k, t k )}. BGAforEDP operates with G B, τ, andd, whered is max(diam(g B ), E B ) [9]. The parameter d is used to limit the number of hops for the assigned paths. First, the BGAforEDP algorithm randomly selects ademandτ i =(s i, t i ) from the demand set τ and finds the shortest path P i for this request. If the path length of P i is less than the bound d, add(τ i, P i ) to the allocated path set P,andτ i to the set of routed demands α(g B, τ). Andthen it deletes the edges on P i from G B and removes τ i from τ. If the path length of

3 344 Hyun Gi Ahn et al. Fig. 1. Traffic on the New York-Washington link of the Abilene backbone network from April 2, 2003 to April 10, 2003 [7]. P i is greater than d, the demand τ i is not assigned the path. This is repeated until the paths are not assigned to the remaining demands in τ. Thesetα(G B, τ) then contains the demands that are assigned the same wavelength. Next, it removes α(g B, τ) from τ, and obtain the set of unassigned lightpaths τ.then BGAforEDP performs RWA on the original G B and τ to obtain the set of assigned lightpaths with another wavelength. This is repeated until τ becomes empty. The total number of assigned wavelengths is the result of this algorithm. The BGAforEDP algorithm is suitable for static demands, but not appropriate for s, since s have setup and teardown times in addition to source and destination nodes [3]. In [7], the combinatorial optimal solution (COS) for s has been proposed. COS and graph coloring [6] approach has great complexity and requires much time cost. Especially, as the number of demands increases, the cost increases exponentially. For example, if there are 30 demands and each demand has 3 possible shortest paths, the necessary number of operations is The branch and bound (B&B) search algorithm is considered to reduce the amount of calculation [10][11]. And Kuri et al. [7] proposed the meta-heuristic tabu search algorithm, since B&B still incurs a lot of computational cost [12][8]. The performance of the tabu search algorithm is somewhat low and requires high complexity. They also proposed srwa [7] based on the first fit (FF) wavelength assignment algorithm [4]. They, however, did not provide a mechanism to take the property of time overlapping into consideration. Thus, in this paper, we propose a new heuristic algorithm for s, which has very little time cost and complexity while achieving commensurate RWA performance with the others. 3 Proposed Time Disjoint Path RWA Algorithm In static demands, one wavelength can not be assigned to two or more lightpaths with overlapping links on their routes. If, however, the service times of two s do not overlap, two s can use the same wavelength on the overlapping links. In Fig. 2, there is an overlapping link between the shortest lightpaths of demands

4 RWA on Scheduled Lightpath Demands in WDM and 2. In the case of static demands, they can not be assigned the same wavelength, but in the case of s, they can be assigned the same wavelength due to the time disjoint s. We take the property into consideration. 1 (09:00 ~ ) 2 (18:00 ~ 23:00) Fig. 2. Time disjoint paths for 1 and 2. /* G(V,E):network,λ : wavelength number, :setofs, T : sets of time-disjoint s P (G, ) : set of the assigned shortest paths of demands, α(g, ) : set of assigned s */ Input : G, Ouput : λ 01: Algorithm TDP-RWA(G, ) 02: TDP-Selector(G, ) 03: d = max(diam(g), E ) 04: λ =0 05: While ( φ) 06: λ = λ +1 07: RWAforTDP(G, T,d) 08: Assign λ to all paths in P (G, ) 09: = - α(g, ) Fig. 3. Proposed TDP-RWA algorithm. Our algorithm, TDP-RWA, consists of two phases, grouping of time disjoint s (TDP-Selector) and RWA (RWAforTDP). Fig. 3 represents the pseudo code of our proposed TDP-RWA algorithm. Let G(V,E) denote a network with set of nodes V and set of links E. In the algorithm, λ,, T, P(G, ) and α(g, ) denote wavelength number, the set of demands, set of grouped demands, set of assigned shortest paths of demands, and set of assigned s, respectively. First, TDP-Selector groups s according to setup and teardown times of demands, and it returns grouped demands T (line 2). We utilize d=

5 346 Hyun Gi Ahn et al. max(diam(g), E ) to limit unnecessarily long paths [9]. The steps from line 5 to line 9 are iterated until becomes empty. The RWAforTDP function finds appropriate paths for s and returns α(g, ) and P(G, ) (line 7). Then all the paths of P(G, ) are assigned a wavelength (line 8) and the assigned s are removed from (line 9). Input : G(V,E) ={δ 1, δ 2, δ 3,..., δ n} : set of s, which is sorted in an increasing order of ω i of δ i δ i=[s i, t i, µ i, ω i](s i :source,t i : destination, µ i :setuptime,ω i :teardown time) Output : T ={ T 1={δ 1,1,..., δ 1, T 1 }, T 2={δ 2,1,..., δ 2, T 2 },..., Tk ={δ k,1,..., δ k, Tk }}: set of grouped sets of time-disjoint s 01: TDP-Selector(G, ) 02: j = 1 03: Tj = φ 04: While ( φ) 05: i = 1 06: δ x = i th element in, δ z = i th element in 07: Tj = Tj {δ x} 08: While (δ x last element in ) 09: i=i+1 10: δ x = i th element in 11: If (µ x ω z) 12: Tj = Tj {δ x} 13: δ z = δ x 14: = - Tj 15: j=j+1 Fig. 4. Grouping algorithm (TDP-Selector). In the grouping phase (TDP-Selector), we make sets of non-time-overlapping s as illustrated in Fig. 4. First, we find a maximal set of time disjoint s. If there are some s left after this first grouping, we group the time disjoint s among the remaining s into another set. This procedure continues until all s are grouped into sets of time disjoint s. The detailed operation of the algorithm is as follows. The demands of the set aresortedinanincreasing order of teardown time ω i. At first, group index j is set to 1 (line 2) and j th set of time disjoint s, Tj,issettoφ (line 3). Line 4 line 15 are iteratively performed until becomes empty. In line 5, current index i is initialized to 1. Then, δ z and δ x are set as the i th element in the sorted (line 6). And δ x becomes the first element of Tj.After(i +1) th element of is set to δ x, teardown time ω z of δ z is compared with setup time µ x of δ x (line 9 11). If µ x ω z,thenδ x becomes an element of group Tj, since this indicates that δ x and δ z are not time-overlapping (line 12). And the reference δ z becomes δ x (line 13). Then it continues comparison with the next target δ x while δ x is not

6 RWA on Scheduled Lightpath Demands in WDM Group 3 6 Group Group Time μ ω 1 δ 1 =(3, 6, 09:00, 10:00) 09:00 10:00 2 δ 2 =(4, 2, 08:00, 11:00) 08:00 11:00 3 δ 3 =(2, 5, 11:00, 13:00) 11:00 13:00 4 δ 4 =(1, 7, 12:00, ) 12:00 5 δ 5 =(3, 5, 13:00, ) 13:00 6 δ 6 =(1, 5, 14:00, ) 14:00 7 δ 7 =(4, 7, 16:00, 18:00) 16:00 18:00 Fig. 5. An example of TDP-Selector for seven s. the last demand in. After that, the s in the set Tj are removed from (line 14). If there are still s in, j is increased and the algorithm continues from line 4. This algorithm can group as many as possible time-disjoint s. Fig. 5 shows an example of the TDP-Selector algorithm. s are sorted in an increasing order of teardown time. At first, δ 1 becomes the first element of group T 1. And teardown time of δ 1 is compared to the setup time of δ 2.As the setup time of δ 2 is earlier than the teardown time of δ 1, s 1 and 2 are time-overlapping. So the teardown time of δ 1 is now compared to the setup time of δ 3.Asthesetuptimeofδ 3 is later than or equal to the teardown time of δ 1, δ 3 is assigned to group T 1, and the new basis for comparison is now set to δ 3. Repeating comparisons, s δ 1, δ 3, δ 5 and δ 7 are allocated to group T 1, s δ 2 and δ 4 are allocated to group T 2, and δ 6 is allocated to group T 3. In the RWA phase (RWAforTDP), paths and wavelengths for s are allocated. Fig. 6 is the pseudo codes of RWAforTDP. At first, α(g, ) andp (G, ) are initialized. Line 5 line 10 are iterated as many as the number of groups times the number of elements (s) in each group. After finding a shortest path of an j in group i (line 5), this shortest path is compared to d. Ifthe length of the shortest path is not longer than d, α(g, ) includes the and

7 348 Hyun Gi Ahn et al. Input : G,, d Output : α(g, ), P (G, ) 01: Algorithm RWAforTDP(G, T,d) 02: α(g, ) =φ, P (G, ) =φ 03: for i = 1 to T 04: for j = 1 to Ti 05: find shortest path P i,j for δ i,j 06: if ((path length of P i,j) d) 07: select path P i,j for δ i,j 08: α(g, ) =α(g, ) δ i,j 09: P (G, ) =P (G, ) P i,j 10: Delete the edges of the shortest paths in P (G, ) fromg Fig. 6. Proposed RWA algorithm (RWAforTDP). P(G, ) includes the edges passed by the shortest path. Then all the edges of the shortest paths in P(G, ) are removed from G in line 10. Fig. 7 shows an example of the procedure of the overall TDP-RWA algorithm. It first generates three groups of time disjoint s. Then, it performs RWA for group 1, i.e., δ 1, δ 3, δ 5 and δ 7, with the 1st wavelength. Note that since they are not overlapping in time, all of them can be assigned the same wavelength. The edges of the assigned paths are removed from the graph. Thus, in the 2nd group, only δ 8 is assigned the wavelength since δ 2 and δ 4 cannot find paths (Fig. 7(b), (c)). Similarly, in the 3rd group, δ 6 is not able to be assigned a path (Fig. 7(c)). Since there are still s waiting for RWA, another new wavelength is considered. At this point, original graph is recovered. Then δ 2 and δ 4 (group 2) and δ 6 (group 3) are assigned the paths and the 2nd wavelength (Fig. 7(d), (e)). 4 Performance Evaluation We evaluate and compare the performance of TDP-RWA with that of BGAforEDP [5], srwa [7], and COS [7] in terms of the number of wavelengths and running time. Network topologies used for performance evaluation are randomly generated networks. We generate a random network by specifying the number of nodes ( V ) in a graph G and the probability of an edge between any two nodes p e. The demands are generated according to the probability of a demand between any two nodes p l. On any source-destination pair, we assume that there can be multiple demands N c.wedenotet service as the average service time of demands and service time is assumed to be uniformly distributed among 0 and 24 hours. The smaller this value, the smaller the probability of time-overlapping among s becomes. We conduct simulations 1000 times for each simulation condition and obtain the average number of wavelengths assigned. Fig. 8(a) shows the number of wavelengths as p l increases in random networks with 20 nodes when N c is 3 or 5, p e is 0.4 and T service is 4 hours. Since the number of demands increases as N c and p l increase, the number of wavelengths increases in general. In case of BGAforEDP the amount of increase in the number

8 RWA on Scheduled Lightpath Demands in WDM 349 Y Y Y X Z ^ X Z ^ X Z ^ [ [ [ \ \ \ ] ] ] 1 =(3, 6, 09:00, 10:00) 3 =(2, 5, 11:00, 13:00) 5 =(3, 5, 13:00, ) 7 =(4, 7, 16:00, 18:00) 09:00 10:00 11:00 13:00 13:00 16:00 18:00 2 =(4, 2, 08:00, 11:00) 4 =(1, 7, 12:00, ) 8 =(6, 7, 17:00, 18:00) 08:00 11:00 12:00 17:00 18:00 6 =(1, 5, 14:00, ) 14:00 (a) RWA of 1 st group (=1) (b) RWA of 2 nd group (=1) (c) RWA of 3 rd group (=1) Y Y X Z ^ X Z ^ [ [ \ \ ] ] 2 =(4, 2, 08:00, 11:00) 08:00 11:00 6 =(1, 5, 14:00, ) 14:00 4 =(1, 7, 12:00, ) 12:00 (d) RWA of 2 nd group (=2) (e) RWA of 3 rd group (=2) Fig. 7. An example of the proposed TDP-RWA algorithm. of wavelengths increases more as p l increases than TDP-RWA does. Especially, for N c = 5, this phenomenon becomes much greater. There is little difference between TDP-RWA and srwa. TDP-RWA is shown to reduce the number of wavelengths up to about 25% than BGAforEDP. Our TDP-RWA uses slightly more wavelengths than optimal COS. Fig. 8(b) shows the number of wavelengths as p e increases in random networks with 18 nodes when N c is 3 or 5, p l is 0.3 and T service is 4 hours. Since increasing the number of edges makes the network more connected and thus generates more candidate paths, the number of wavelengths is shown to decrease. The performance of BGAforEDP is very low comparing to other algorithms and the performance of our proposed TDP-RWA is similar srwa (up to 2.1% difference). COS is shown to reduce the number of wavelengths up to about 9.1% 9.3% than TDP-RWA or srwa. In Fig. 8(c), the number of wavelengths in random networks ( V = 20) is presented when N c is 3 or 5, p l is 0.3 and p e is 0.3. Varying T service affects the property of time overlapping for s. Since the probability of time overlapping

9 350 Hyun Gi Ahn et al TDP_RWA(Nc=3) BGAforEDP(Nc=3) srwa(nc=3) COS(k=3,Nc=3) TDP_RWA(Nc=5) BGAforEDP(Nc=5) srwa(nc=5) COS(k=3,Nc=5) TDP_RWA(Nc=3) BGAforEDP(Nc=3) srwa(nc=3) COS(k=3,Nc=3) TDP_RWA(Nc=5) BGAforEDP(Nc=5) srwa(nc=5) COS(k=3,Nc=5) Number of wavelengths Number of wavelengths p l P e (a) Number of wavelengths as p l increases (p e=0.4, N c=3 or 5, T service=4). (b) Number of wavelengths as p e increases (N c=3 or 5, p l =0.3, T service=4) TDP_RWA(Nc=3) srwa(nc=3) COS(k=3,Nc=3) TDP_RWA(Nc=5) srwa(nc=5) COS(k=3,Nc=5) TDP_RWA BGAforEDP srwa 14 Number of wavelengths Execution time Average service time p l (c) Number of wavelengths as T service increases (N c=3 or 5, p l =0.3, p e=0.3). (d) Average execution time as p l increases (N c=3, p e=0.4, T service=4). Fig. 8. Performance evaluation of TDP-RWA. is low in case of smaller T service, the number of wavelengths is shown to decrease as T service becomes smaller. Our TDP-RWA is shown to utilize almost the same wavelengths as srwa (up to 2.98% difference). In Fig. 8(d), we illustrate average execution time as p l increases in random networks ( V = 20) when N c is 3, p e is 0.4 and T service is 4 hours. The average execution time of COS is more than 2000 sec, which can not be shown in the figure. But the average execution time of other heuristic algorithms is 5

10 RWA on Scheduled Lightpath Demands in WDM 351 sec 37 sec. BGAforEDP is the fastest algorithm since it does not utilize any time overlapping property. Our TDP-RWA is faster than srwa up to 54%. Because of fast grouping, our proposed TDP-RWA has similar execution time with BGAforEDP. The reason why srwa is slow is that it requires edge comparison for already assigned paths when a demand is assigned a path and a wavelength. 5 Conclusion In this paper, we have proposed the TDP-RWA algorithm to solve the RWA problem efficiently for s. The optimal COS has very high complexity and requires large time cost, and srwa based on the FF algorithm requires additional execution time cost and huge memory overhead due to edge comparison. The proposed TDP-RWA is shown to be a fast algorithm to utilize time disjoint paths through fast grouping as well as conventional space disjoint paths. The simulation results for random networks show that our TDP-RWA has the faster execution time than srwa without additional memory overhead while its performance is commensurate with srwa. References 1. Architecture of Optical Transport Network, ITU-T Recommendation, G (2001) 2. Advanced Networking for Research and Education, Online, Available: 3. Ramaswami, A., Sivarajan, K.: Routing and Wavelength Assignment in All-Optical Network, IEEE/ACM Transactions on Networking, Vol. 3. No. 5. (1995) Zang, H., Jue, J.P., Mukherjee, B.: A Review of Routing and Wavelength Assignment Approaches for Wavelength-routed Optical WDM Networks, Optical Networks Magazine, Vol. 1. No. 1. (2000) Manohar, P., Manjunath, D., Shevgaonkar, R.K.: Routing and Wavelength Assignment in Optical Networks from Edge Disjoint Path Algorithms, IEEE Communications Letter, Vol. 5. (2002) Kirovski, D., Potkonjak, M.: Efficient Coloring of a Large Spectrum of Graphs, Proc. 35th Conf. Design Automation, (1998) Kuri, J., Puech, N., Gagnaire, M., Dotaro, E., Douville, R.: Routing and Wavelength Assignment of Scheduled Lightpath Demands, IEEE Journal on Selected Areas in Communications, Vol. 21. No. 8. (2003) Kuri, J., Puech, N., Gagnaire, M., Dotaro, E.: Routing Foreseeable Lightpath Demands Using a Tabu Search Meta-heuristic, Proc. GLOBECOM 2002, Taipei, Taiwan, (2002) Kleinberg, J.: Approximation Algorithms for Disjoint Paths Problems, Ph. D. dissertation, MIT, (1996) 10. Clausen, J.: Branch and Bound Algorithm-Principles and Examples, Online, Available : jha/ 11. Clausen, J., Perregaard, M.: On the Best Search Strategy in Parallel Branch-and- Bound-Best-First-Search vs. Lazy Depth-First-Search, Annals of Operations Research, No. 90. (1999) Glover, F., Laguna, M.: Tabu Search, MA:Kluwer-Academic, (1997)