GA-Based Hybrid Algorithm for MBR Problem of FIPP p-cycles for Node Failure on Survivable WDM Networks

Transcription

1 GA-Based Hybrid Algorithm for MBR Problem of FIPP p-cycles for Node Failure on Survivable WDM Networks Der-Rong Din Department of Computer Science and Information Engineering, National Changhua University of Education No. 1, Jin De Road, Changhua 500, Taiwan R.O.C Abstract. In this paper, the minimal backup reprovisioning (MBR) problem is studied, in which, the failure-independent path protecting p- cycles (FIPP p-cycles) scheme is considered for single node-failure on WDM networks. After recovering the affected lightpaths from a node failure, the goal of the MBR is to re-arrange the protecting and available resources such that working paths can be protected against next node failure if possible. This is a hard problem, a hybrid algorithm which combines heuristic algorithm and genetic algorithm is proposed to solve this problem. The simulation results of the proposed method are also given. Keywords: WDM, node failure, MBR, FIPP p-cycles, GA. 1 Introduction In an optical network employing WDM, the failure of a single link (or node) may lead to tremendous data loss since a single link can carry a huge amount of data (on the order of terabits per second). Therefore, several schemes have been proposed to achieve survivability by protection or restoration on the optical layer [1]. In a protection scheme, extra bandwidth is reserved when the connection is provisioned. The primary and backup paths are usually link (or node) disjoint, which guarantees that at least one path is available when any single link (or node) failure occurs in the network [1]. When a node failure occurs, all the traffic flows that go through the node and all the local traffic that is collected and distributed by the node are interrupted. The path-based protection techniques can be employed [2]. Setting protection paths for the possible failed nodes may be cheaper and flexible approach because there are huge wavelengths provided by the system and it can be extended more easily than setting up double switches. Note that it is not possible in any scheme to recover lightpaths from a failure at their own source/destination nodes. Node failure protection through network reconfiguration is therefore only concerned with restoring traffic flows that were transiting failed nodes [3]. This work was partly supported by the National Science Council (NSC) of Taiwan, R.O.C. under Grant Number NSC E D.-S. Huang et al. (Eds.): ICIC 2011, LNBI 6840, pp , c Springer-Verlag Berlin Heidelberg 2012

2 184 D.-R. Din 1.1 FIPP p-cycles The FIPP p-cycles protection method proposed by Kodian and Grover [4] is a pre-connected protection scheme with an end-to-end failure-independent path protection property. In the FIPP p-cycles scheme, several mutually node-disjoint paths can form a disjoint route set (DRS) [4]. For a DRS, a single FIPP p-cycle which passes through all end-nodes of the paths in DRS is pre-established. Since any two paths in the same DRS are node-disjoint, only one path in a DRS may be affected by a single node failure. Moreover, the FIPP p-cycles scheme is pathoriented, it can be used to recover traffic transiting through a failed node. More details about the FIPP p-cycles scheme can be found in [4]. 1.2 Backup Reprovisioning Recently, reprovisioning new backups for working paths to combat the effect of multiple concurrent failures (where concurrent means that a new failure occurs before a previous failure is repaired) is the goal of backup reprovisioning (BR) [5]. When a failure occurs, the traffic through the affected node is switched to backups. To protect lightpaths against next potential failure, new backups are provided for the paths that become unprotected or vulnerable because of losing their primary or their backup due to the previous failure or due to backup resource sharing. This approach is called Minimal Backup Reprovisioning (MBR). The numerical results show that [5], using MBR, the connection vulnerability can be significantly reduced even when the network is heavily loaded. According to the survey by authors, there is no article studied the backup reprovisioning problem for the FIPP p-cycles on WDM networks against node failure. In this paper, the MBR problem on WDM networks with FIPP p-cycles protection for node failure is studied A hybrid algorithm which combined heuristic algorithm and genetic algorithm [6] is proposed to solve this problem. 2 Problem Definition In this paper, the physical and virtual topologies of a WDM network, the set of working paths, the disjoint route sets and the set of FIPP p-cycles are fixed and known. For each working path in network, there is a single FIPP p-cycle can be used to protect it in an on-cycle or straddling manner. For each edge (or link) of physical topology, there is a single fiber connects the end-nodes of link such that data can be transmitted bidirectional. All nodes in physical network are with full wavelength converting capabilities. Only the node failure scenario is considered. 2.1 Notations G(V,E): the physical topology, where V = {v 1,v 2,..., v V } is the set of nodes and E = {e 1,e 2,..., e E } is the set of physical links. Each node of the network can also be represented by the number assigned to it.

3 GA-Based Hybrid Algorithm for MBR Problem of FIPP p-cycles 185 P = {P k k =1, 2,..., P }: the set of working paths, where P k P is the working path. Nodes v sk and v dk are the source and destination nodes of P k, respectively. BP k : the backup path for the working path P k, k =1, 2,..., P and path BP k should be node-disjoint to P k. v f : the failed node. N(v f ): the set of adjacent nodes of node v f. E(v f ): the set of links adjoined to node v f, E(v f ) E. FC: the set of FIPP p-cycles used to protect all paths in P. PoC j : the set of paths which is protected by the FIPP p-cycle C j,where C j FC, PoC j P.AnytwopathsinPoC j are mutually node-disjoint. P f : the set of working paths affected by the failed node v f, P f P. The goal of the problem is to recover the protecting capabilities of the set of FIPP p-cycles to protect working paths such that the total capacities can be minimized. The proposed hybrid method consists of two algorithms, the first one is the Preprocessing Algorithm and the second one is the Genetic Algorithm. 3 Preprocessing Algorithm When node v f fails, the recovering procedure is performed to recover the affected paths. In the recovering procedure, if path P k is affected by the node failure, first, the primary path is switched to the backup path BP k which is provided by the protecting FIPP p-cycle. After recovering, the FIPP p-cycle may lose its protecting capability and those paths originally protected by the FIPP p-cycle and the backup path BP k are vulnerable now. If a node failure occurs again, these paths cannot be protected. In backup reprovisioning, not only the affected working paths are recovered by current FIPP p-cycles, the protecting capabilities of affected FIPP p-cycles are also recovered and working paths can be survived at the sequent node failure such that total capacities can be minimized. 3.1 Cases of Failure In this subsection, working paths together with the FIPP p-cycles affected by the node failure can be classified into four cases: (1) End-node failure: the failed node is the source (or destination) node of the working paths, these working paths cannot be recovered. (2) Straddling-path failure: the failed node is an interior node of the working path P k, but not on the protecting FIPP p-cycle C i. (3) On-cycle-path failure: the failed node is an interior node of the working path P k and also a node on the protecting cycle. In this case, the working path P k can still be recovered by using the remaining part of the FIPP p-cycle. (4) Cycle failure: the failed node is on the cycle but all paths protected by the cycle are unaffected, then the cycle affected by the failure will lose its protecting capabilities.

4 186 D.-R. Din 3.2 Preprocessing In this subsection, the details of the proposed algorithm Preprocessing Algorithm are described. When node v f fails, node v f and the links in E(v f ) are removed from G to form a new network G (V \{v f },E \ E(v f )). If path P k is affected by the node failure, the default path BP k on FIPP p-cycle is used to recover the affected working path. To provide backup reprovisioning, first, an empty set P f is constructed. Then, for each path (say P k ) together with the protecting cycle (say C i ), the respective case described in previous subsection is checked and applied. To reduce the total capacities used for protecting all paths in P f,cyclesin the current FC are examined first for whether they can be used to protect paths in P f. For each working path P k in P f, for each existing cycle C j in FC,ifpath P k is node-disjoint to all paths in PoC j,thencyclec j can be used to protect path P k and PoC j is updated by uniting path P k. And then path P k is removed from P f. This process is repeated performed until no cycle in FC can be found to protected path in P f. Then, for all unprotected paths in P f, the Genetic Algorithm is performed to find new FIPP p-cycles to protect them. The details of the Preprocessing Algorithm are shown in Algorithm 1. Algorithm 1. Preprocessing Algorithm 1: Input: G, P, FC, v f ; Output: G, FC; 2: Remove failed node v f and edges in E(v f )fromg to form the graph G (V \{v f },E\ E(v f )). 3: Construct the empty set P f. 4: for all (working path P k P ) do 5: Let cycle C i FC be the FIPP p-cycle used to protect path P k. 6: According the case of failure, perform the respective case (1) (4): (1) End-node failure 7: Remove working path P k.removec i from FC. 8: Release the network resources of path P k and cycle C i.addallpathsinpoc i to P f. 9: (2) Straddling-path failure: 10: Find a new path P new from v sk to v dk on G which is node-disjoint to all paths in PoC i. 11: if (P new can be found) then 12: Use P new as the new working paths. Release the network resources of path P k. 13: Use BP k to recover the original FIPP p-cycle C i. Add path P new to P f. 14: else 15: Remove C i from FC. Release the network resources of path P k and cycle C i. 16: Add all paths in PoC i and path BP k to P f. 17: end if 18: (3) On-cycle-path failure: 19: Remove C i from FC. Release the network resources of path P k and cycle C i. 20: Add all paths in PoC i and path BP k to P f. 21: (4) Cycle failure: 22: Remove C i from FC. Release the network resources of path P k and cycle C i. 23: end for 24: for all (working path P k P f ) do 25: for all (working path C j FC) do 26: if (path P k is node-disjoint to all paths in PoC j) then 27: Update PoC j = PoC j P i.removep k from P f. 28: end if 29: end for 30: end for

5 GA-Based Hybrid Algorithm for MBR Problem of FIPP p-cycles Genetic Algorithm 4.1 Chromosome Encoding Because the problem involves representing the protecting cycles for vulnerable paths, a coding scheme that uses positive integer is employed. After performing the Preprocessing Algorithm, the network G(V,E) is updated as G (V \{v f },E\ E(v f )) and the set P f of unprotected paths is constructed. For the current physical network G (V \{v f },E\E(v f )), the Cycle Finding Algorithm proposed in [7] is performed to form the set (NC) of all possible cycles in G (V \{v f },E\E(v f )). All cycles in NC are sorted and indexed in non-descending order according to the length of the cycles. For each path P k in P f,theset(nc k NC)ofcycles which can be used to protect path P k is formed. A chromosome consisting of an integer array with size 2 P f is introduced to represent the protecting cycles of vulnerable paths. The chromosome consists of two genes: the Protecting Cycle Gene (PCG)andCopy Gene (CG). For each unprotected path P k in P f,letv sk and v dk be the source and destination nodes of the path P k, respectively. The PCG can be represented as {PCG 1,PCG 2,..., P CG P f }, wherec PCGk (k=1, 2,..., P f ) is a cycle in NC k and the index of cycle is in {1, 2,..., NC}. TheCG can be represented as {CG 1,CG 2,..., CG P }, wherecg f k (k=1, 2,..., P f ) means that the path P k is protected by the CG k -th copy of the protected cycle C PCGk. 4.2 Population Initialization Let FC new be the set of selected cycles which are used to protected the vulnerable paths in P f. Initially, FC new is an empty set. Let z j represent the maximal copy of the cycle C j NC, initially z j =0,forj =1, 2,..., NC. For each copy of the selected cycle C j,createasetpoc j,zy for storing those paths currently protected by the z y -th (integer 1 z y z j )copyofcyclec j. The population of the genetic algorithm is generated by following steps: First, random selected an integer k (1 k P f ). For the selected path P k,afipp p-cycle in NC k FC new is selected randomly to protect it. This means that those cycles currently deployed are selected first if possible. If FC new NC k is nonempty, then those cycles in FC new NC k are selected first and tested whether there is a cycle in FC new NC k can be used to protect the path P k.it is worth noting that path P k can be protected by the z y -th (1 z y z j )copy of C j only if path P k is node-disjoint to all paths in PoC j,zy of the z y -th copy of selected cycle C j FC new NC k. If a cycle C j (FC new NC k )andthez y copy is found and satisfied the constraint, then add path P k to the set PoC y,zy. IfthepathcannotbeprotectedbythecyclesinFC new NC k, then a new cycle C j is selected from NC k to protect path P k. For the selected cycle C j, increase z j by 1, create a set PoC j,zj to store path P k,addc j to the set FC new, then set the value of PCG k as j and CG k as z j. Then, increase k by 1. If k> P f,setk to 1. Repeat the above steps to determine the protected cycle of next path until all contents of PCG and CG are set, then the initialization process is terminated.

6 188 D.-R. Din 4.3 Fitness Definition Generally, GA uses fitness function to map objective to cost and to achieve the goal of a minimal cost. Let l(c j ) be the length of cycle C j NC and z j be thenumberofcopiesofthecyclec j. An objective function value is associated with chromosome and represented by the following equation: minimize OBJ = NC j=1 z j l(c j ) = C j FC new z j l(c j ). Since the best-fit chromosomes should have a probability of being selected as parents that is proportional to their fitness, they need to be expressed in a maximization form. 4.4 Crossover Operators and Mutation The Single Point Crossover is used to develop th GA. First, randomly select a crossover site (integer) i from interval [1, P f ]. In SPC, the operator is applied on both the PCG and CG. For the mutation, the Single Protecting Cycle Mutation (SPCM) is applied to GA. First randomly select an integer i in the interval [1, P f ], assume path P k be protected by the z j -th copy of cycle C j,spcm changes the protecting cycle of paths in the PoC j,zj by selecting a cycle C a with minimal length, if possible. The cycle is selected from the set CS of cycles, where CS = P k PoC j,zj {NC k }, with minimal length. 4.5 Chromosome Adjustment Algorithm (CAA) After performing crossover and/or mutation operations, it may generate infeasible chromosomes. Thus, these chromosomes should be adjusted to a constraintsatisfied solutions by performing the CAA. To adjust the chromosome to a constraint-satisfied one, first, the chromosome can be considered as two parts separated by the crossoversite i. It is worth noting that, before performing crossover, each part is constraint-satisfy. Random select a part (left or right) and a direction (increasing-direction or decreasing-direction) for adjustment. The increasing-direction means that the adjustment is performed from 1 to i and from i +1to P f for the left part and right part, respectively. And the decreasing-direction is the reverse direction of the increasing-direction. If the left part is selected and the increasing-direction is to be apply, the right part of the chromosome is packed and preserved. The details of CAA are described as follows. First, construct empty set FC new. For each cycle C j used in the right part, put it into FC new and construct the sets PoC j,zj. Second, two paths assigned to same cycle but not to same copies are tried to merge so as the number of copies of cycle can be reduced. Third, according to the direction of adjustment, the protecting cycle for path P k (1 k i) is adjusted. For the selected path P k, a FIPP p-cycle in NC k FC new is selected randomly to protect it. If FC new NC k is nonempty, then those cycles in FC new NC k are selected first and tested whether there is a cycle in FC new NC k can be used to protect the path P k. It is worth noting that path P k can be protected by the z y -th (1 z y z j )copyofc j only if path P k is node-disjoint to all paths in PoC j,zy of the z y -th copy of selected cycle

7 GA-Based Hybrid Algorithm for MBR Problem of FIPP p-cycles 189 C j FC new NC k. If a cycle C j (FC new NC k )andthez y copy is found and satisfied the constraint, then add path P k to the set PoC y,zy. If the path cannot be protected by the cycles in FC new NC k, then the original protecting cycle (say C j ) is preserved to protect path P k. For the selected cycle C j,increase z j by 1, create a set PoC j,zj to store path P k,addc j to the set FC new,then set PCG k to j and CG k to z j. 5 Experimental Results The proposed algorithms were conducted by using C++ programming language and Boost Graph Library [8]. All the simulations were run on a PC with Celeron 2 Duo 1.8 GHz CPU, 2.0G RAM, and with Windows Vista operating system. Two physical topologies were used for experiments, they are COST239 and National networks. All nodes in the network may fail and the failed nodes were generated randomly. The connection requests were generated randomly. A set of FIPP p-cycles is used to protect primary lightpaths. The parameters of GA were determined through simulations, and the crossover probability is set to 1.0, mutation probability is set to 0.1, and population size is set to 500. To know the efficiency of the proposed methods, the node-disjoint paths (NDPS) protection method was implemented for comparison. First, WDM networks with different number of connections were generated. Each case was examined 20 times and the result was evaluated and compared. Let Backup resources ratio be the ratio of the total capacities to that of the Fig. 1. BRR performance for different number of connections on (a) COST239 with different number of connections, (b) National with different number of connections, (c) COST239 with different number of wavelengths, (d) National with different number of wavelengths

8 190 D.-R. Din working capacities. Figure 1(a) shows the comparison of the average(avg.), minimal(min.) and maximal(max.) BRR performances of the GA to that of the NDPS methods on the network COST239. The average BRR value of the GA decreases from 1.5 to 1.15 and it is better than that of the NDPS. Even the maximal case of GA can get better performance than NDPS. For the case of the National network, the BRR performance of GA is better than that of the NDPS Figure 1(b). For the limited number of wavelengths (W in {20, 40, 60, 80, 100, 120}), WDM networks with 120 connections were generated for these experiments. In Figure 1(c), the BRR value of the GA method decreases about 0.2 on networks and it is better than that of the NDPS. For the case of the National network, the BRR performance of GA is also better than that of the NDPS Figure 1(d). 6 Conclusions In this article, the minimal backup reprovisioning (MBR) problem for FIPP p-cycles on WDM networks for node failure was studied. After recovering the working paths affected by the failed node, the protecting capabilities of FIPP p-cycles is recovered by performing MBR against the subsequent nodes failure on WDM networks. A hybrid algorithm was proposed to solve this problem. Simulation results show that the performance of GA is better than the traditional node-disjoint paths protecting method. References 1. Ramamurthy, A., Mukherjee, B.: Survivable WDM Mesh Networks-part II: Restoration. In: Proc. of IEEE ICC, pp (1999) 2. Su, H.K., Wu, C.S., Chu, Y.S.: IP Local Node Protection. In: Proc. of Second International Conference on Systems and Networks Communications, ICSNC, vol. 58 (2007) 3. Stamatelakis, D., Grover, W.D.: IP layer Restoration and Network Planning Based on Virtual Protection Cycles. IEEE Journal on Selected Areas in Communications 18(10), (2000) 4. Kodian, A., Grover, W.D.: Failure-independent Path-protecting P-cycles: Efficient and Simple Fully Pre-connected Optical Path Protection. Journal of Lightwave Technology 23(10), (2005) 5. Tornatore, M., Lucerna, D., Pattavina, A.: Improving Efficiency of Backup Reprovisioning in WDM Networks. In: Proc. of IEEE Inforcom Phoenix, AZ, USA, pp (15 17) (2008) 6. Holland, J.: Adaptation in Natural and Artificial Systems. Univ. of Michigan Press, Ann Arbor (1975) 7. Liu, C., Ruan, L.: Finding Good Candidate Cycles for Efficient P-cycle Network Design. In: Proc. of Int. Conf. on Computer Communications and Networks, ICCCN 2004, Chicago, USA, pp (11 13) (2004) 8. Boost Graph Library,