Replanning of Optical Networks based on Defragmentation Techniques

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1 Replanning of Optical Networks base on Defragmentation Techniques Daniela Aguiar Moniz Instituto Superior Técnico, Lisboa, Portugal November 2015 Abstract The traffic growth an the heterogeneity of the generate traffic form a challenging environment for the future optical networks. At the same time, ynamically varying traffic eman is requiring an efficient an agile utilization of the optical spectrum. Flexible banwith networking emerge recently as a promising paraigm for assigning elastic spectral banwith to traffic emans with various moulation formats an spectral efficiencies. In a ynamic traffic scenario, the channels setup an tear own processes leas to fragmentation of spectral resources an there is an increasing eman from the network operators to be able to perioically reconfigure the network an return it to its optimal state. The challenge of this work is to stuy the various efragmentation techniques propose in the literature an compare them accoring to the same objective function. Keywors: Defragmentation Techniques, Fixe an Flexible Optical Networks, Fragmentation of Spectrum 1. Introuction Optical networks are unergoing significant changes, fuele by the exponential growth of traffic ue to multimeia services. There continues to be ever increasing eman for banwith, to the point where, service proviers are alreay installing higher bit rates, incluing 100Gb/s. The 50GHz ITU wavelength gri ivies the relevant optical spectrum range of nm into fixe spectrum slots, but it is likely that bit rates greater than 100Gb/s will not fit into this scheme, even if sufficiently broa spectrum is available, high-ate-rate signals become increasingly ifficult to transmit over long istances at high spectral efficiency. The Elastic Optical Network(EON) is a novel an very promising solution for 100Gb/s an beyon connection provisioning in optical networks. The EON allows to allocate flexibly appropriate-size optical banwith, by means of contiguous concatenation of optical spectrum, to an en-to-en optical path an accoring to traffic eman [3]. In ynamic traffic conitions, unexpecte networks evolution, network recovery an maintenance operations etermine channel setup an tear own processes that lea to fragmentation of spectral resources, but in the recently introuce flexible optical networks, the presence of lightpaths possibly operating at ifferent bit-rates, ifferent moulation formats an occupying a variable portion of the frequency spectrum will further eteriorate the fragmentation of spectrum resources. Fragmentation is an ol, well-stuie problem. In the very early computing systems prior to the use of paging, the system memory got fragmente as ifferent-size programs got loae an exite the system. There is a parallelism between the objective of isk efragmentation an the objective of efragmentation in flexible optical network. Disk Defragmentation attempts to create larger regions of free space using compaction to prevent the return of isk fragmentation an efragmentation in flexible optical network attempts to create larger region of free space in frequency spectrum using compaction of spectral slots The main objective of this work is the replanning of optical networks base on efragmentation techniques in fixe-gri an flexible optical networks. To minimize the problem of fragmentation it was implemente three efragmentation techniques, Push-Pull, Hop-Tuning an Replanning. The report is organize as follows. Section 2.1. introuce the problem formulation for Routing Wavelength Assignment(RWA). Problem formulation for Routing Spectrum Assignment(RSA) is presente in Section 2.2. Section 2.3. an 2.4. present integer linear programming (ILP) formulation 1

2 for Defragmentation Techniques in fixe-gri an flexible optical network, respectively. Section 2.5. introuce heuristic algorithms for Push-Pull an Hop-Tuning techniques. The numerical results are presente in section 3. Finally, the conclusions are state in section Implementation This section escribes all the problem formulations implemente in this work, in particularly for RWA problem, RSA problem, efragmentation techniques for fixe-gri optical networks an efragmentation techniques for flexible optical networks RWA Problem Formulation Firstly, RWA was formulate as an ILP in which the problem objective is to minimize the number of wavelengths use in the most loae link(ilp- RWA-1). Seconly, RWA problem was also implemente as an ILP in which the problem objective is to minimize the number of wavelengths use in full network(ilp-rwa-2). For the sake of simplicity, we use path-link approach for the network flow representation of RWA in both ILP. Also in both formulation a set of paths is preefine between network noes. The mathematical formulation for ILP-RWA-1 an ILP-RWA-2 are presente in sections of the issertation report. To overcome the limitation of computational time in ILP for large networks, such as UBN24, it was implemente a heuristic algorithm for the RWA problem. The heuristic algorithm was base in the LFAP algorithm propose in [4] RSA Problem Formulation As in Section 2.1. for the RWA problem, it was also implemente for RSA problem two ILP with ifferent objective functions. The first ILP being implemente was the ILP propose in [3]. The problem objective is to minimize the number of FSs in frequency spectrum that are assigne to at least one eman in the network.the problem formulation is presente in [3] as (ILP1). The problem objective for the secon ILP, esignate ILP-RSA-1, is to minimize the number of FSs(spectral slots) use in most loae link. The mathematical notation is the same as the mathematical notation presente in the article [3] for the ILP1 an the mathematical formulation for ILP-RSA-1 is presente in section of the issertation report. The computational time increases ramatically for RSA problem, so it will be essential to apply a heuristic for the RSA problem. The implemente heuristic was the AFA-CA algorithm propose in [3], because accoring to [3] the AFA-CA algorithm presents better results than other heuristics propose by other authors Defragmentation Techniques for fixe-gri Optical Networks To avoi the fragmentation problem in fixe-gri optical networks it was implemente an ILP for Push-Pull, Hop-Tuning an Replanning Techniques, in orer to evaluate the performance of efragmentation in this Techniques. The mathematical formulation an comparisons between this three techniques are presente in section 4 of the issertation report Defragmentation Techniques for Flexible Optical Networks Spectral fragmentation inevitably occurs more significantly in flexible banwith networks mainly ue to two facts: 1) the various banwith assignments increase the misalignment of available spectral slots along a path an 2) spectral resources are allocate ynamically ue to the come-an-go nature of connections. Since the fragments are neither contiguous in the frequency omain nor aligne along a path, they become strane banwiths, which increases the network s blocking probability an limits the maximum traffic accommoation volume. Many authors have ientifie fragmentation as a major owngrae of the ynamic operation of Elastic Optical Networks. To avoi this limitation it was implemente an ILP for Push-Pull, Hop-Tuning an Replanning Techniques for Elastic Optical Networks. Each technique has ifferent characteristics. The Push-Pull technique performs efragmentation by moving lightpaths only to contiguous an free spectrum frequencies along the same route of the original path, in other wors, the push-pull technique allows to shift a lightpath over free an contiguous spectral bans if the lightpath oes not change its route an if the lightpath oes not transgress other establishe lightpath. The Push-Pull technique uses the automatic frequency control (AFC) capabilities of coherent receivers. However, it is limite by the fact that it cannot support cases where there is another connection lying between original an target frequencies, so this technique may result in partial efragmentation. The ILP presente before for the Push-Pull Technique are base in [1]. A-Notation A set D of uniirectional lightpaths from source s to estination is consiere. F represents the link capacity expresse in spectral slots. In each simulation, it is reprouce a fragmente optical network (e.g. ue to a ynamic or unexpecte 2

3 networks evolution) efine by the set P 0 of active lightpaths at time t=0. The set P(e) represents the emans that use link e in its initial route. B-ILP Push-Pull Formulation Set of problem variables are: x f,t ɛ{0, 1} - equal to 1 if FS fɛf at time tɛt is selecte to be the lowest inexe slot that is assigne to a eman, an equal to 0 otherwise, y f,t ɛ{0, 1} -equal to 1 if FS fɛf at time tɛt is assigne to a eman, an equal to 0 otherwise, z t ɛ{0, 1} - equal to 1 if a eman is re-tune at time tɛt, an equal to 0 otherwise, x t ef ɛ{0, 1} - equal to 1 if FS fɛf is occupie in link eɛe at time tɛt, an equal to 0 otherwise, x t f ɛ{0, 1} - equal to 1 if FS fɛf is assigne to at least one eman in the network at time tɛt, an equal to 0 otherwise, F T ɛz + - Number of spectral slots use in the frequency spectrum at time T. minimize subject to F T fɛf xf,t =1, ɛd, tɛt (1) x f,0 =1, ɛd (2) x f i,t y f j,t 0, ɛd, pɛ P, tɛt, (3) f i,f jɛf one i=1,.., F n +1, e j=i,..,i+n 1 x f i,t =0, ɛd, pɛ P, tɛt (4) f iɛf,one i= F n +2,.., F ɛp (e) xf,t =xt ef, fɛf, tɛt, eɛe (5) ɛd zt 1, tɛt (6) x f,t xf,t+1 z t+1, ɛd, tɛ(t 1), fɛf (7) x f,t xf,t+1 + (8) +x f+1,t+1 eɛe xt ef E xt f +x f 1,t+1, ɛd, tɛ(t 1), fɛf, fɛf, tɛt (9) fɛf xt f =F T (10) The ILP Push-Pull for flexible optical networks was base on ILP Push-Pull presente in section 4.1. for fixe-gri Optical Networks of the issertation report. The main change involves aing the variables x f,t an y f,t, in which xf,t represents the lowest inexe slot that is assigne to a eman at time t an y f,t represents the set of contiguous FS that is assigne to a eman at time t. Base on this new variables it is necessary to a constraint (3) an (4). The constraint (3) is the contiguous FS assignment constraints. If FS f i is selecte as the lowest inexe slot for eman, the consecutive slots f j, where j = i,..., i + n 1, shoul be assigne to this eman. The constraint (4) aim to exclue FS as the lowest inexe slot selection for which there is no enough space for the FS assignment in the frequency spectrum. Constraint (1) is FS selection constraint,(2) imposes the initial routing at time t=0, (5) avois lightpath superposition on link i-j, (6) an (7) impose up to one lightpath rerouting per time perio,(8) imposes the specific Push-Pull constraint,in other wors, constraint (8) imposes that lightpaths can only be move to contiguous an free spectrum frequencies. Finally (9) an (10) are use to etermine F T. The Hop-Tuning technique can move the spectral slots of a connection to any esire location in the spectrum omain without interfering with existing connections an the en-to-en bi-irectional coorination between the transmitter an receiver is conucte automatically. This technique assumes that both transmitter an receiver are equippe with fast tunable lasers. C-ILP Hop-Tuning Formulation The mathematical formulation for the Hop-Tuning technique is equal to the mathematical formulation for the push-pull technique without constraint (8), seeing that the constraint (8) imposes the specific Push-Pull constraint,i.e. the re-tuning to only contiguous spectral slots along the same route. Without constraint (8), the constraint (1) ensures the possibility to move the spectral slots of a lightpath to any esire location in spectrum omain. The Replanning Technique allows move the spectral slots of a connection to any esire location in the spectrum omain an also it allows the change its route for any other pre-compute routes in k-shortestpaths algorithm. D-ILP Replanning Formulation Set of problem variables are: x f,t,p ɛ{0, 1} - equal to 1 if FS fɛf on path pɛp at time tɛt is selecte to be the lowest inexe slot that is assigne to a eman, an equal to 0 otherwise, y f,t,p ɛ{0, 1} - equal to 1 if FS fɛf on path pɛp at time tɛt is assigne to a eman, an equal to 0 otherwise, z t ɛ{0, 1} - equal to 1 if a eman is re-tune at time tɛt, an equal to 0 otherwise, x t ef ɛ{0, 1} - equal to 1 if FS fɛf is occupie in link eɛe at time tɛt, an equal to 0 otherwise, x t f ɛ{0, 1} - equal to 1 if FS fɛf is assigne to at least one eman in the network in time tɛt, an 3

4 equal to 0 otherwise, F T ɛz + - Number of spectral slots use in the frequency spectrum at time T. minimize subject to F T fɛf pɛp x f,t,p =1, ɛd, tɛt (11) x f,0 =1, ɛd (12) x f i,t,p y f j,t,p 0, ɛd, pɛ P, tɛt (13) f i,f jɛf one i=1,.., F n +1, e j=i,..,i+n 1 x f i,t,p =0, ɛd, pɛ P, tɛt (14) f iɛf,one i= F n +2,.., F PeɛE xf,t,p =x t ef, fɛf, tɛt, eɛe (15) ɛd zt 1, tɛt (16) x f,t xf,t+1 z t+1, ɛd, tɛ(t 1), (17) fɛf, pɛp x f,t,p (18) fɛf pɛp x f,t+1,p, ɛd, tɛ(t 1), fɛf, pɛp eɛe xt ef E xt f, fɛf, tɛt (19) fɛf xt f =F T (20) The main ifference in ILP for the Replanning technique is in constraint 18 allowing lightpaths to move spectral slots to any esire location in the spectrum omain along the same initial route or change its route for another caniate path on P. The rest of the constraints have the same meaning as constraints in ILP Push-Pull or ILP Hop-Tuning. In section results is presente comparisons between the three techniques for Flexible Optical Networks Heuristic algorithms for Push-Pull an Hop- Tuning technique The main limitations of ILP presente in section 2.4. are the computational time an simulation time,(t -input parameter in ILP), that increases when we consier more complex network scenarios, for example if we consier a Simple network with 30 emans, we have to consier a simulation time equal to 30 for ILP Hop-Tuning, but if we consier a Simple network with 60 emans, we have to consier a simulation time equal to 60 for ILP Hop-Tuning. When we increase the simulation time the computational time increases ramatically(section 3), thus it will be essential to implement a heuristic algorithm for the Push-Pull an Hop-Tuning techniques. The main steps of Hop-Tuning heuristic are presente in Algorithm 1. The heuristic is applie only when it provies an event in spectrum as when a eman is isable, so one of the input parameters is the set of isable emans, as well as the initial state of spectrum. Algorithm 1 Hop-Tuning algorithm Input: initial state spectrum; set of isable emans; 1: Upate the spectrum with isable emans an Upate list-free-spectrum with new free spaces in spectrum; 2: for each n in list-free-spectrum o create a list-aux with all emans that may be relocate to entry n 3: for each entry j in list-aux o 4: if exists enough space along the route of eman j in free space n then Put j=1; Put n=1 an go to 6 5: else j=j+1 an go to step 8 6: if List-free-sprectrum is empty then Relocate eman j in free space n; Upate list-free-spectrum; Eliminate list-aux an Terminate 7: else Relocate eman j in free space n; Upate listfree-spectrum; ; Eliminate list-aux an go to 2 8: if List-aux is empty then n=n+1 an go to 10 9: else go to 3 10: if List-free-sprectrum is empty then terminate 11: else go to 2 In each iteration of the algorithm the list-freespectrum in Algorithm 1 represents the set of free spaces in frequency spectrum. Each entry in list-free-spectrum inicates the free spectral slots an which link it belongs. As shown in Algorithm 1, for each entry in list-free-spectrum it must create a list esignate list-aux. List-aux represents all emans that may be relocate to a free space presents in entry n in list-free-spectrum, in other wors in list-aux it only inclues emans occupying spectral slots with higher inex than spectral slots in free space, as well as emans who share the same link that free space. In each iteration, the list-aux is sorte in escening orer of the number of spectral slots occupie by each eman, thus it is giving priority to re-tune emans occupying a larger number of spectral slots. The heuristic of Push-Pull technique is base on Hop-Tuning heuristic, taking to account that 4

5 lightpaths oes not transgress other establishe lightpaths, so the main ifference in Algorithm 1 is step 2. For each free space on the spectrum can only be reallocate emans that are allocate immeiately then in the spectrum, i.e. emans that has the lowest inexe slot one greater than the last free spectral slot. Comparisons between Hop-Tuning heuristic an ILP Hop-Tuning an Push-Pull heuristic an ILP Push-Pull are presente in Section The next figures show the evolution of F T for Push-Pull, Hop-Tuning an Replanning techniques for networks scenarios exhibite in table Results In this section, we compare Push-Pull, Hop-Tuning an Replanning performance results obtaine with ILP an heuristics propose in section 2.5. for Push-Pull an Hop-Tuning techniques Results of ILP Push-Pull, Hop-Tuning an Replanning Techniques To evaluate the performance of mathematical formulations(ilp), we evaluate the number of FSs of the occupie frequency spectrum at time T (F T ) an the computation time (T[s]). I use gurobi [2] on an Intel Core(TM) i5-3317u 1.70GHz computer to solve ILP. The results are obtaine for Simple an Cost239 networks. I assume P = 3, ɛd an path are the shortest path calculate with k- ShortestPaths algorithm. The eman pairs (s, t ) are generate ranomly an the number of requeste FSs n is uniformly istribute on 1,..., S where Sɛ{5, 15}. In table 1, it was consiere as an initial state (t=0) the results from ILP-RSA-2 presente in section To reprouce a fragmente optical network, it was generate ranomly isable emans that emans were remove from initial state proucing a fragmente optical network ue to a ynamic network evolution. In table 1, F represents the number of FSs of the occupie frequency spectrum at time t=0. The results are average over 10 ranomly generate eman sets. We consiere a simulation time equal to 10, so F T represents the result from efragmentation techniques after 10 time perio. Figure 1: Comparisons between Push-Pull, Hop- Tuning an Replanning techniques for Simple network D=30 an S=5 Figure 2: Comparisons between Push-Pull, Hop- Tuning an Replanning techniques for Simple network D=60 an S=5 Figure 3: Comparisons between Push-Pull, Hop- Tuning an Replanning techniques for Simple network D=30 an S=15 Table 1: Results of Push-Pull, Hop-Tuning an Replanning techniques consiering result from ILP- RSA-2 as initial state Cenario RSA-2 Push-Pull Hop-Tuning Replanning Network D S F N of iseble emans T[s] FT T[s] FT T[s] FT Simple Simple Simple Simple Simple Simple Simple Simple Simple Simple Simple Simple Cost Cost Cost Cost Figure 4: Comparisons between Push-Pull, Hop- Tuning an Replanning techniques for Cost239 network D=110 an S=5 5

6 It was also consiere as initial state the results from ILP-RSA-1, because their results reprouce immeiately a fragmente optical network since their results occupies almost the entire capacity of spectral slots efine at input algorithm (see initial state in figure 7). The result of ILP-RSA-1 occupies almost the entire capacity of spectral slots because its objective function is not to minimize the number of spectral slots in network but to minimize the number of spectral slots in the most loae link in network. Table 2 shows the results of ILP Push- Pull, Hop-Tuning an Replanning using as initial state the result from ILP-RSA-1. Table 2: Results of Push-Pull, Hop-Tuning an Replanning technique consiering result from ILP- RSA-1 as initial state Cenario RSA-1 Push-Pull Hop-Tuning Replanning Network D S F T[s] F T T[s] F T T[s] F T Simple Simple Simple Simple Cost The next figures show the comparisons between Push-Pull, Hop-Tuning an Replanning techniques for networks scenarios exhibite in table 2. Figure 5: Evolution of F T in function of number of emans to Push-Pull, Hop-Tuning an Replanning techniques for Simple network S =5 the computational time is the highest in this networks scenarios The main isavantage common to the three mathematical formulation is the simulation time because the simulation time set at input may not be the optimal, i.e. at time T, the algorithm may have unrealize all eman s reallocations that coul have one, because the ILP imposes that only one ligthpath may be rerouting per time perio. Ieally we shoul aapt the simulation time to the number of emans consiering at input but there is a commitment between simulation time an computation time, e.g. if we consier a simple network with 60 emans, we shoul consier a simulation time equal to 60 (it give the opportunity to all emans being relocate), but if we consier a simulation time equal to 60 the computational time increases exceeing the time limit of 48 hours. Due to this limitation it was implemente a heuristic algorithm for Push-Pull an Hop-Tuning techniques. It was not implemente a heuristic for a Replanning technique because if the main cause of fragmentation is ynamic network evolution ue to come-an-go nature of connection, we can use the heuristic implemente for RSA to Replanning technique if we upate traffic matrix by aing emans or elete emans accoring to the network evolution. The next figure illustrates the initial state F 0 (result of ILP-RSA-1) an the state F T after applying the replanning technique for Simple network with D=30, in orer to specify the movements of emans in frequency spectrum from t=0 to t=10. The vertical axis represents the links of simple network an horizontal axis represents the number of spectral slots available at input of algorithm. Figure 6: Evolution of F T in function of the maximum number of spectral slots that is assigne to a eman, S, to Push-Pull, Hop-Tuning an Replanning techniques for Simple network D=30 Base on the figures presente above, the Replanning technique provies the best results for almost all networks scenarios, but we have to consier that Figure 7: State of frequency spectrum before an after applie Replanning Defragmentation Technique 3.2. Performance of Push-Pull an Hop-Tuning heuristics To evaluate the performance of heuristics evelope for the Push-Pull an Hop-Tuning techniques, it was compare the performance of the propose algorithms to the ILP Hop-Tuning an ILP Push-Pull for Simple network. 6

7 Figure 8 represents the comparison between ILP Hop-Tuning an Hop-Tuning Heuristic for Simple network. In ILP Hop-Tuning it was consiere at input T=30 an as initial state the result from ILP- RSA-2. esignate Segmentation of Simulation Time (SST metho). Table 3 escribes the results of Push-Pull heuristic an SST metho for Simple network in orer to compare the results with each other. In SST metho for Simple network with D=30 scenario was consiere a total simulation time of 50 an for Simple network with D=60 scenario was consiere a total simulation time of 100. Figure 8: Comparison between ILP Hop-Tuning an Hop-Tuning Heuristic for Simple Network Figure 9 illustrates the comparison between ILP Push-Pull an Push-Pull Heuristic for Simple network. In ILP Push-Pull it was consiere at input T=40 an as initial state the result from ILP-RSA- 2. In ILP Push-Pull, the simulation time is higher than the simulation time in ILP Hop-Tuning because in ILP Push-Pull apart from just one eman may be reallocate per time perio, also emans can only be relocate to a lower or a higher unit in the frequency spectrum per time perio, so ILP Push-Pull will take longer time to achieve the optimal result. Figure 9: Comparison between ILP Push-Pull an Push-Pull Heuristic for Simple Network Another alternative to overcome the limitations associate to computation time in ILP is the use of the simulation time fragmente into an instalments, e.g. in ILP Push-Pull, if we have to consier a simulation time equal to 50 we can simulate the ILP Push-Pull with T=10 to get the result an re-simulate the ILP Push-Pull with T=10 consiering as initial state the result from previous ILP an so on until complete the total simulation time. The result may not be the optimal since it can make a ecision in the first simulation that may not be reversible in the other simulations, but it can be a goo alternative for larger networks scenarios when the mathematical formulations are unfeasible in terms of computational time. This metho was Table 3: Results of Push-Pull heuristic an SST metho with ILP Push-Pull Cenario RSA-2 SST metho Push-Pull Heuristic Network D S F Number of isable emans T [s] FT FT Simple Simple Simple Simple Simple Simple Simple Simple Base on the results in table 3 we can conclue that SST metho presents a smaller computational time than the computational time of the ILP Push-Pull an in general it has better results than the Push-Pull heuristic, so it can be a goo alternative. 4. Conclusions In this work, we propose a mathematical formulation ILP for Push-Pull, Hop-Tuning an Replanning efragmentation techniques for Elastic Optical Networks. It was also propose a heuristic for Push-Pull an Hop-Tuning techniques an an alternative metho(sst ) to apply when the ILP is unfeasible in terms of computational time. Simulation results inicate that the ILP of Replanning technique achieve better performance. As note throughout this work, the essential limitation in the ILP implemente to the Push-Pull, Hop- Tuning an Replanning techniques is associate to simulation time T, so an essential evolution of this work is aapt the three ILP techniques in orer that all emans coul be relocate per time perio requiring only two time perios, the first time t=0 to set the initial state of emans an the secon time perio allowe to perform the necessary relocations for all emans. References [1] F.Cugini, M.Seconini, N.Sambo, G.Bottari, G.Bruno, P.Iovanna, an P.Castoli. Pushpull technique for efragmentation in flexible optical networks. In National Fiber Optic Engineers Conference, Los Angeles, California Unite States, [2] I. Gurobi Optimization. Gurobi optimizer reference manual,

8 [3] M. Klinkowski an K. Walkowiak. Routing an spectrum assignment in spectrum slice elastic optical path network. IEEE Communucations Letters, 15(8): , August [4] J. H. Siregar, H. Takagi, an Y. Zhang. Routing an wavelength assignment in wavelengthroute optical networks. In Proc. 7th Asia- Pacific Network Oper. an Mgmt Symposium,