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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

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

outline
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
background of topological design
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

transit nodes and links localization problem formulation
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

symbols used
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)

network model adequate for ip mpls

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
optimal network design problem and budget constrained problem
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

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

1

0

1

Branch and Bound method
  • advantages
    • exact solution
    • heuristics’ results verification
  • disadvantages
    • exponential increase of computational complexity
    • solving many “unnecessary” sub-problems
branch and bound lower bound
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

minoux heuristics

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

minoux heuristics extensions
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)
other methods
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
conclusions
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