8th International Conference on Decision Support for Telecommunications and Information Society

Transcription

1 A bi-objective approach for routing and wavelength assignment in multi-fibre WDM networks Carlos Simões 1,4, Teresa Gomes 2,4, José Craveirinha 2,4 and João Clímaco 3,4 1 Polytechnic Institute of Viseu, Portugal 2 Dept. of Electrical and Computers Engineering University of Coimbra, Portugal 3 Faculty of Economics, University of Coimbra, Portugal 4 INESC Coimbra csimoes@ipv.pt, teresa@deec.uc.pt, jcrav@deec.uc.pt, jclimaco@inescc.pt 8th International Conference on Decision Support for Telecommunications and Information Society September 4-7, 2009, Coimbra, Portugal

2 Plan Introduction - The RWA Problem SLE; DLE; Routing subproblem Wavelength assignment Problem Definition Network - Notation Bicriteria Approach Resolution Method Results Model Extension to Resilient Routing Survivable Mechanisms/Dedicated Protection Bicriteria Approach/Resolution Method Results Conclusions and Future Work 2

3 Introduction RWA Problem Wavelength Division Multiplexing Network: Connection oriented Network Lightpaths RWA problem: Without wavelength converters the wavelength continuity constraint. With wavelength converters. A C D E A C D E λ1 λ2 λ3 B F B λ Converter F connection A-B blocked Successful A-B connection 3

4 RWA Problem 3 types of connection requests: Static - the entire set of connections is known beforehand; Incremental - connection requests arrive based on some stochastic process, and the lightpaths remain in network indefinitely (infinite duration); Dynamic - connection requests arrive based on some stochastic process, and the lightpath is released after some amount of time. Static Lightpath Establishment (SLE) - The objective is to set up lightpaths for all required connections, minimising the used resources. Dynamic Lightpath Establishment (DLE) - The objective is to minimise the number of blocked connections or the maximisation of number of connections in the network. 4

5 RWA Problem SLE can be formulated as an Integer Linear Program (ILP), which is NP-complete. Because of the stochastic nature of requests, which have to be answered in real time, the DLE problem is more difficult to solve. Strategy - The RWA problem can be partitioned into two sub-problems: Routing and Wavelength Assignment solved separately. The performance of approaches for solving the RWA depends more on the routing algorithm than on the wavelength selection method. 5

6 RWA Problem Wavelength Assignment Static Lightpath Establishment (SLE) Graph colouring: NP-Complete problem (but there are efficient sequential algorithms). Dynamic Lightpath Establishment (DLE) Heuristics seeks to preserve capacity to ensure the establishment of future requests R (Random) FF (First Fit) LU (Least Used)! MU (Most Used, pack)... MP (Min-Product) LL (Least-Loaded) M (Max-Sum) Relative Capacity Loss... 6

7 Network Characteristics Large WDM Network with: Multiple wavelegths per fibre; Multiple fibres per link; Nodes with total, limited range or no wavelength conversion; Traffic: Incremental Traffic; Unidirectional and bidirectional (symmetric) connections; For obtaining solutions in a very short time: the routing and wavelength assignment problems were separated; a flow oriented approach was used. 7

8 Notation Let R={N,L,C,T N } represent the WDM network, where: N is the set of nodes, N = {v 1, v 2,..., v n }, n = #N. L is the set of directed arcs, L = {l 1, l 2,..., l m }, m = #L. Set of wavelengths Λ = = {λ 1, λ 2,..., λ w }, w = #Λ. Set of fibres, F = {f 1, f 2,..., f k }, k = #F. C is the arc capacity, C(l i ) = (n li, b li ), with n li = (n li1, n li2,..., n liw ) and b li = (b li1, b li2,..., b liw ) where n li j is the total number of fibres in arc l i with wavelength j and b li j is the number of fibres where that wavelength is free in arc l i. T N represents the wavelength conversion capability of the nodes: T N (v i ) = [t uv ], v i N, u,v = 1, 2,..., w 8

9 Notation A topological path, p in R, will be described by: the source and destination nodes v s, v t. the ordered sequence of arcs (or nodes) in the path. A lightpath, p λ, is the sequence of arcs of the topological path, using a particular wavelength on a given fibre: * p λ = l * c,..., l d = ( v ) ( ) s, vu, fi, λ α,..., vx, vt, f j, λ β where f i,,f j F, λ α,,λ β Λ represent fibres and wavelengths. A bidirectional lightpath, p λ =(p st λ,p ts λ ), is supported by a bidirectional topological path p=(p st, p ts ), which is a pair of symmetrical topological paths. 9

10 Bicriteria Approach Routing subproblem First criteria is related to bandwidth usage, and seeks to spread traffic over all links (seeks to select arcs with more free capacity): min c 1 p D ( p) = l p 1 b D Set of possible lightpaths beteween s and t T l b l T Total available capacity in arc l (number of free wavelengths). Second criteria seeks to avoid long paths (minimising used resources): { c ( p) = h( )} min 2 p p D h(p) number of arcs in p. 10

11 Bicriteria Approach Wavelength Selection Seeks to maximise the Wavelength Bottleneck Bandwidth, b j (p): max b λ Λ ( p) Λ Set of wavelengths; b lj number of fibres in arc l where λ j is free. = min j j l p blj > 0 b lj In each arc, the method selects the fibre with lowest id where λ j is free. 11

12 Bicriteria Approach bidirectional lightpath Routing Subproblem (pair of symmetrical topological paths) min 1 pst, pts ) D First criteria is : c ( p) p= ( 1 1 = + T b b l p st l l p ts T l Second criteria is: p= ( p min 2 st, p ts ) D { c ( p) = h( p) } where h ( p) = h( pst ) + h( pts ) = 2h( pst ) = 2h( pts ) Topologically Symetrical Paths 12

13 Bicriteria Approach Resolution Method The candidate solutions are non-dominated topological paths, such that a lightpath can be constructed along that path, i.e., there exists a free and usable wavelength (according to T N ) in every arc of the path. Solutions are searched using a k-shortest algorithm, adapted from MPS algorithm, applied to a convex combination of the two objective functions ( p) c ( p) ( 1 α ) + α c1 2 The value of α is not relevant and only defines the order by which solutions will be obtained by the algorithm for ranking paths by cost. 13

14 Bicriteria Approach Resolution Method The limits for the solution space are defined by the optimal solutions of each objective function: c ( ) 1 c p1 = min c p 1 (p) (c 1M,h m ) 1 c p D c min{ ( ) ( )} 1M c2 p 2 1 p 1 = c 2 p = h p c1 p D p 1 c 1m I.O. (c 1m,h M ) h c 2 (p)=h(p) m h M In order to establish priority regions {A,B,C,D}, preference thresholds are defined: c < 1 m < c1 req < c1m and hm < c2req h M c 1 (p) c 1M c 1req (c 1M,h m ) B A D C c 1m I.O. hm c2req hm (c 1m,h M ) c 2 (p)=h(p) 14

15 Bicriteria Approach Resolution Method The final solution is choosed among non dominated solutions in the highest priority region S {A,B,C,D}, according to a weighted Chebysheb distance to a reference point in S: min max w f ( p) f p S i= 1,2 { } i where f 1 (p)=c 1 (p), f 2 (p)=c 2 (p)=h(p), f, f ) = ( c, ) is the left down corner ( h1 of S and the weights are given by: 1 1 w1 =, w2 = c c h h 2 1 (c 2,h 2 ) is the right upper corner of S. i i 2 1 c 1 (p) 3 (c 1,h 1 ) 2 1 B (c 2,h 2 ) A h(p) 15

16 Experimental Results Several multi-fibre WDM networks were considered, with 16 wavelengths per fibre; Incremental traffic model is used; Experiments considered 1200 requests with infinite duration. Experiments were made considering 2 situations: 100% bidirectional requests and 5% unidirectionai requests. Two scenarios: No wavelength conversion capability and 5 nodes with total wavelength conversion capability; Results of the Bicriteria Approach will be compared with the ones of the two corresponding single objective models for the same objective functions; 16

17 Experimental Results Selected Networks Net 1 - NSFNET 14 nodes; 21 links Net 2 - COST 266 BT 28 nodes; 41 links Net 3 - COST 266 TT 28 nodes; 61 links 17

18 Experimental Results Selected Networks Net 4 15 nodes; 28 links Net 5 18 nodes; 30 links Network # nodes # links Nodal degree NSFNET COST266BT COST266TT Net Net

19 Experimental Results Global Blocking (%) Global Blocking Network 1 - NSFNET BiC - No Conversion BiC - 5 Converters SPh (hops) - No Conversion SPh (hops) - 5 Converters SPc (1/freeBW) - No Conversion SPc (1/freeBW) - 5 Converters Global Blocking (%) Network 4 Global Blocking (%) Number of requests Network 2 - COST 266 BT Global Blocking (%) Number of requests Network 3 - COST 266 TT Number of requests Number of requests 19

20 Experimental Results Number successful connections/used BW/Mean Hop Count Accepted requests Used BW (%) Mean hop count BiC - No Conversion SPh (hops) - No Conversion SPc (1/freeBW) - No Conversion Network

21 Experimental Results computation time for each request (ms) computation time for each request (ms) CPU time per connection request Network 1 - NSFNET Number of requests Network 2 - COST 266 BT Number of requests computation time for each request (ms) computation time for each request (ms) Network BiC - No Conversion Number of requests Network 3 - COST 266 TT SPh (hops) - No Conversion SPc (1/freeBW) - No Conversion Number of requests 21

22 Experimental Results % non-optimal solutions Non-dominated non-optimal solutions (%) Non-dominated non-optimal solutions (%) Network 1 - NSFNET Number of requests Network 2 - COST 266 BT Number of requests Non-dominated non-optimal solutions (%) Non-dominated non-optimal solutions (%) Network Number of requests Network 3 - COST 266 TT BiC - No Conversion BiC - 5 Converters Number of requests 22

23 Survivable WDM Networks Resilient Routing Given the high capacity of the links in a WDM network, the traffic loss and service disruption resulting from failures have to be minimised. This can be achieved with dedicated path protection where a disjoint path (protection path) is needed as the backup path to reroute the traffic if a failure occurs. An extension of the Bicriteria model for obtaining a topological pair of node disjoint paths for each lightpath request in a WDM network, ensuring dedicated path protection against node failure, will be presented. 23

24 Survivable WDM Networks Resolution Approach Given an origin-destination node pair s-t, the algorithm starts by making a network topology modification, where all nodes and links of the graph, (N,L), representing the network topology are duplicated and a new link, of null cost, is added by linking node t to node s' (the duplicate of s): N' = N {v i ': v i N} and L' = L {(v i ',v j '):(v i,v j ) L} {(t,s')} s 1 2 s t 3 4 t 24

25 Survivable WDM Networks Resolution Approach Each path z from s to t in this augmented graph (N,L ) will correspond to a pair of paths from s to t in (N,L). z = p (t,s') q where p is a path from s to t and q is a path from s to t. We use the same two objective functions: min{c 1 (z)} and min{c 2 (z)=h(z)} Finally, an adapted version of the MPS algorithm, proposed by Clímaco&Pascoal2007, is used for ranking by non-decreasing order of cost the paths z, such that p and q are node disjoint. We use the path cost: ( 1 α ) z + αc z ( ) ( ) c1 2 α only defines the order by which solutions will be obtained. 25

26 Survivable WDM Networks Resolution Approach Only the generated solutions that correspond to viable lightpahs and are non-dominated with respect to previously generated solutions are stored. The final solution is choosed among non dominated solutions in the highest priority region S {A,B,C,D}, according to a weighted Chebysheb distance to the reference point in S (left down corner of S). The algorithm selects the wavelength that maximises the Wavelength Bottleneck Bandwidth in path p, and the same procedure is used on path q (or in each of the four paths which define a protected bidirectional lightpath). 26

27 Experimental Results Several multi-fibre WDM networks were considered, with incremental traffic. Network # nodes # links Nodal degree NSFNET COST266BT COST266TT Net Net Experiments were made considering 2 situations: 100% bidirectional requests and 5% unidirectionai requests. Two scenarios: No wavelength conversion capability and 5 nodes with total wavelength conversion capability; 27

28 Experimental Results Global Blocking (%) Global Blocking Network 1 - NSFNET BiC - No Conversion BiC - 5 Converters SPh (hops) - No Conversion SPh (hops) - 5 Converters SPc (1/freeBW) - No Conversion SPc (1/freeBW) - 5 Converters Global Blocking (%) Network 4 Global Blocking (%) Number of requests Network 2 - COST 266 BT Global Blocking (%) Number of requests Network Number of requests Number of requests 28

29 Experimental Results Number successful connections/used BW/Mean Hop Count Accepted requests Used BW (%) Mean hop count BiC - No Conversion SPh (hops) - No Conversion SPc (1/freeBW) - No Conversion Network

30 Experimental Results Number successful connections/used BW/Mean Hop Count Accepted requests Used BW (%) Mean hop count BiC - No Conversion 5.45 SPh (hops) - No Conversion SPc (1/freeBW) - No Conversion NSFNET

31 Conclusions No Protection Approach The Bicriteria Approach leads to a lower Blocking Probability, due to an initial better choice of paths; Network load has a more balanced distribution; At moderate load, although the Bicriteria Approach accepts more requests, the total used BW is lower than SPc. SPh uses less BW than the BiC approach, but it leads to a significant lower number of successful connections... The impact of having five nodes with wavelength conversion capability was negligible in most cases. 31

32 Conclusions Dedicated Protection Model The Bicriteria Approach leads to a better performance than the Monocriteria SPh (hop count metric); Contrary to what happens without protection, with dedicated protection the BiC and SPc approachs have similar performance, so A Bicriteria Approach (with these two criteria) for dedicated path protection do not provide additional benefits... 32

33 Future Work Specification and Analysis of new metrics for the link costs, taking into account power considerations and transmission impairments (Impairment Aware Routing), and evaluation of its effect on network performance. Definition of new criteria in order to make an efficient use of network resources, but also ensuring fairness in connections between different node pairs. 33

34 Thank You!... Questions?... 34