1 / 16

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.

anoush
Download Presentation

Topological design of telecommunication networks

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related