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Topological design of telecommunication networks

Topological design of telecommunication networks Michał Pióro a,b , Alpar Jüttner c , Janos Harmatos c , Áron Szentesi c , Piotr Gajowniczek b , Andrzej Mysłek b a Lund University, Sweden b Warsaw University of Technology, Poland c Ericsson Traffic Laboratory, Budapest, Hungary Outline

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Topological design of telecommunication networks

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  1. Topological design of telecommunication networks Michał Pióroa,b, Alpar Jüttnerc, Janos Harmatosc, Áron Szentesic, Piotr Gajowniczekb, Andrzej Mysłekb a Lund University, Sweden b Warsaw University of Technology, Poland c Ericsson Traffic Laboratory, Budapest, Hungary

  2. Outline • Background • Network model and problem formulation • Solution methods • Exact (Branch and Bound) and the lower bound problem • Minoux heuristic and its extensions • Other methods (SAN and SAL) • Comparison of results • Conclusions

  3. Background of Topological Design problem: localize links (nodes) with simultaneous routing of given demands, minimizing the cost of links selected literature: Boyce et al1973 - branch-and-bound (B&B) algorithms Dionne/Florian1979 – B&B with lower bounds for link localization with direct demands Minoux1989 - problems’ classification and a descent method with flow reallocation to indirect paths for link localization

  4. Transit Nodes’ and Links’ Localization– problem formulation Given • a set of access nodes with geographical locations • traffic demand between each access node pair • potential locations of transit nodes find • the number and locations of the transit nodes • links connecting access nodes to transit nodes • links connecting transit nodes to each other • routing (flows) minimizing the total network cost

  5. Symbols used constants hd volume of demand d aedj=1 if link e belongs to path j of demand d, 0 otherwise cecost of one capacity unit installed on link e ke fixed cost of installing link e B budget constraint Me upper bound for the capacity of link e variables xdj flow realizing demand d allocated to path j (continuous) ye capacity of link e (continuous) se =1 if link e is provided, 0 otherwise (binary)

  6. LER L1 LSR L3 L2 LSP LSR LSR L4 LER LSR L4 Network model adequate for IP/MPLS • LER  access node • LSR  transit node • LSP  demand flow

  7. BCP minimize C = Se ce ye constraints Se keseŁ B Sj xdj = hd SdSjaedj xdj = ye yeŁMese Optimal Network Design Problemand Budget Constrained Problem ONDP minimize C = Se ce ye + Se kese constraints Sj xdj = hd SdSjaedj xdj = ye yeŁMese

  8. Solution methods • Specialized heuristics • Simulated Allocation (SAL) • Simulated Annealing (SAN) • Exact algorithms: branch and bound (cutting planes)

  9. 1 0 1 Branch and Bound method • advantages • exact solution • heuristics’ results verification • disadvantages • exponential increase of computational complexity • solving many “unnecessary” sub-problems

  10. Branch and Bound - lower bound • LB proposed by Dionne/Florian1979 is not suitable for our network model – with non-direct demands it gives no gain • We propose another LB – modified problem with fixed cost transformed into variable cost: minimizeC = Se xeye+ Seke where xe = ce + ke /Me

  11. elimination Minoux heuristics The original Minoux algorithm: step 0 (greedy) allocate demands in the random order to the shortest paths: if a link was already used for allocation of another demand use only variable cost, otherwise use variable and installation cost of the link 1 calculate the cost gain of reallocating the demands fromeach link to other allocated links (the shortest alternative path is chosen) 2 select the link, whose elimination results in the greatest gain 3 reallocate flows going throughthe link being eliminated 4 if improvement possiblego to step 2

  12. Minoux heuristics’ extensions • individual flow shifting (H1) • individual flow shifting with cost smoothing (H2) Ce(y) =cey + ke·{1 - (1-)/[(y-1) +1]} if y > 0 = 0 otherwise. • bulk flow shifting (H3) • for the first positive gain (H3F) • for the best gain (H3B) • bulk flow shifting with cost smoothing (H4) • two versions (H4F and H4B)

  13. Other methods • Simulated Allocation (SAL) in each step chooses, with probability q(x), between: • allocate(x) – adding one demand flow to the current state x • disconnect(x) – removing one or more demand flows from current x • Simulated Annealing (SAN) starts from an initial solution and selects neighboring state: • changing the node or link status • switching on/off a node • switching on/off a transit or access link

  14. Comparison - objective

  15. Comparison - running time

  16. Conclusions • proposed modification of Minoux algorithm can efficiently solve TNLLP, especially H4B • Simulated Allocation seems to be the best heuristics • proposed lower bound can be used to construct branch-and-bound implementations • need for diverse methods - hybrids of the best shown here, e.g. Greedy Randomized Adaptive Search Procedure using SAL seems to be a good solution

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