Outline. 1 Introduction. 2 The problem of assigning PCUs in GERAN. 3 Other hierarchical structuring problems in cellular networks.

Transcription

1 Optimisation of cellular network structure by graph partitioning techniques Matías Toril, Volker Wille () (2) () Communications Engineering Dept., University of Málaga, Spain (2) Performance Services, Nokia Siemens Networks, Huntingdon, UK 24/0/2005 Rome, 29 October 2007 (COST 293 Discussion Workshop)

2 Outline duction 2 The problem of assigning s in GERAN 3 hierarchical structuring problems in cellular networks 4 usions

3 duction duction The network management problem The network structuring problem 2 The problem of assigning s in GERAN 3 clustering problems in cellular networks 4 usions HO Sum

4 The network management problem Services CS-Voice CS- VoIP PTT Gaming Web Streaming Voice Features DR HR POC DTX FH RAN parameters P-GSM KPIs E-GSM RATs UTRAN WIFI Operators Subscribers

5 The network structuring problem GERAN architecture BSC LA BSC LA Site MSC/SGSN LA LA BSC BSC BSC Site Site Site Site Site Site

6 The assignment of s in GERAN duction 2 The problem of assigning s in GERAN Problem formulation Solution method Analysis over measurement-based network model 3 clustering problems in cellular networks 4 usions

7 Problem formulation The cell re-selection process in GERAN Purpose Algorithm Problem Solution Terminals in idle/packet-transfer mode camp on the strongest cell C = RLA_C RxLevAccessMin i i i C2 i= Ci - CellReselectOffseti CRS delay severely affects performance of RT packet-data services ) Network features (P-BCCH, Network Assisted Cell Change, Packet-data HO) 2) Optimisation of the assignment base stations to s in each BSC a) Connect adjacent cells to the same b) Keep the load of all s within given limits BSC

8 Problem formulation The assignment of s as a graph partitioning problem Classical model 2 ω ω 5 Cell 5 γ 5 Cell γ 2 ω 2 Cell 2 γ 4 Network model γ 45 ω 4 Cell 4 γ 34 ω 3 Cell 3 γ 23 (CPAP) Minimise Optimisation model subject to

9 Solution method The assignment of s as a graph partitioning problem Adaptation to the cellular environment ) Spatially consistent solutions Connectedness/site constraints [no fragmentation/no overlap] 2) Minimum number of network changes Re-labelling subdomains [maximum service availability] Disconnected solution Cell resolution Connected solution Site resolution

10 Formulación del problema The assignment of s as a graph partitioning problem Minimise subject to # users changing capacity Load imbalance between S V, V 2,,V k i, j = :N sites are connected Connectivity Site resolution Spatial consistency

11 Solution method Classical graph partitioning methods a) Exact methods Pure brute-force [T=O(k V )] Goldschmidt and Hochbaum [T=O( V k )] Branch-and-cut algorithm over ILP model [T=O(2 V + E )] b) Heuristic methods Geometric methods [T=O( V ) or O( E )] Structural methods [T=O( V ) or O( E )] Geometrical method Structural method

12 Solution method a) Exact method General Integer Linear Programming Model (GM)

13 Solution method a) Exact method Compact Integer Linear Programming Model (CM)

14 Solution method a) Exact method Compact Integer Linear Programming Model with Less Symmetry (CMS)

15 Solution method a) Exact method Classical method Branch-and-Cut = Branch-and-Bound + Cutting Planes planes ( IP) Min f ( X) ( IP) Min s.t. gf ( j( X) 0 s.t. gj X) 0 cn ( X) 0 xi i { 0, 0, } Bounding ( LP LP ) Min Min f f ( ( X ) ) s.t. s.t. g j j ( X ) 0 c ( X) 0 n Branching ( IP ) Min f ( X ) s.t. g ( X ) 0 xc j n i = ( X) 0 0 x = x i { 0 } { } 0, i 0, i ( IP ) Min f ( X ) s.t. Pruning g j ( X ) 0 cx ( = X) 0 n x = x i i { } { } 0, i 0, i ( LP ) Min f f( ( X) ) s.t. gg ( ( X) ) 0 0 j j xc n= ( X) 0 0 Bounding x = 0 Branching ( IP) Min f ( X) s.t. g ( X) 0 c ( X) 0 n x = 0 j { } x 0, i i ( IP) Min f ( X) s.t. g ( X) 0 c ( X) 0 n x = 0 j { } x 0, i i

16 Solution method a) Exact method Refinements to classical method ) Initialization with a heuristic solution (i.e., multi-level refinement) 2) Use of exact method over a set of problem instances with loose runtime constraints Runtime sharing strategies among problem instances a) Size-based b) Edge-cut based

17 Solution method b) Heuristic method Classical method Multi-Level Clustered Refinement Adaptive (ML) Multi-Start (ML-CAMS) G (0) G (0) G () G () Sorted Heavy Edge Coarsening Matching G (2) G (2) Kernighan-Lin Uncoarsening and refinement G (m) Clustered Initial Adaptive partitioning Multi-Start

18 Solution method b) Heuristic method Classical method Multi-Level Clustered Adaptive Multi-Start (ML-CAMS) Stage 2) Initial partitioning by Clustered Adaptive Multi-Start (CAMS) Greedy Graph Growing Partitioning Random Greedy Graph Growing Partitioning Clustered Adaptive Multi-Start Edge-cut Distance from global optimum Minimum value Minimum value Optimal value Optimal value Edge-cut Edge-cut Edge-cut Floyd-Warshal Greedy Graph Growing Partitioning Nbr. of attempts Nbr. of attempts Single attempt Naive Multi-Start Adaptive Multi-Start

19 Solution method b) Heuristic method Classical method Multi-Level Clustered Adaptive Multi-Start (ML-CAMS) Stage 2) Initial partitioning by Clustered Adaptive Multi-Start (CAMS) Solution set: Solution set: Solution set: [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] Matching {{,5},2,3,4,6,7,8,{9,0,3},,2,4,5,6} Matching {{,5},2,3,4,6,7,8,{9,0,,3},,2,4,5,6} Matching {{,5},2,3,4,6,7,8,{9,0,,2,3,6},,{4,5}} Step Step Step Step N

20 Solution method b) Heuristic method Adaptation to the cellular environment ) Control of weight imbalance between subdomains 2) Enforcement of connected subdomains Connected FM refinement 3) Control of the granularity of the assignment Graphs of site resolution 4) Reduction of the number of changes in the network Re-labelling of subdomains Sorted Heavy Edge Matching -level graph Site-level graph # articulation vertices = 4 Site Matching Cell-level graph

21 Analysis over measurement-based network model Analysis setup Purpose Evaluate more sophisticated methods in a wider set of real graphs Scenario 6 BSCs (6 CPAP instances) Methodology Graph partitioning analysis based on HO stats in NMS ) Build problem instances HO statistics [γ ij ], GPRS config. (nºs/bsc, #GPRS TSLs/cell) [k, ω i ] Operator s constraints [B aw =256, B rw =2] 2) Evaluate CPAP optimisation surface by R-GGGP in isolated instances Build a distributional model for the local minima values Prove the correlation between the best local minima 3) Compare proposed and classical methods over the entire instance set Branch-and-cut in CPLEX, heuristic methods built from scratch Criteria Total edge-cut ( Total nbr. of inter-s CRs) Avg. weight imbalance ratio ( Avg. load imbalance ratio between s) Total execution time

22 Analysis over measurement-based network model Analysis setup -level Site-level δ = V E k E V ( V -) 2 max( E( i) ) max( E( i) ) min( E( i) ) max( ωi ) min( ωi ) V k Example of BSC Graph

23 Analysis over measurement-based network model Analysis results ) Optimisation surface Nbr. of attempts Nbr. of samples Edge-cut Edge-cut E E+05.3E+06 Edge-cut 4.0E Avg. Avg. distance to other local local minima minima 3.0E-06 Gumbel distribution a= b= Prob Prob 2.0E-06.0E-06 Edge-cut 0.0E E E+05.0E+06.5E E+06 Edge-cut Edge-cut Distance from global optimum

24 Analysis over measurement-based network model Analysis results 2) Exact methods 34 IO BC-SS BC-ES R-GGGP (non-conn.) Edge-cut ratio [%] Runtime [h]

25 Analysis over measurement-based network model Analysis results 3) Heuristic methods a) Edgecut-runtime tradeoff Normalised Normalized edge-cut, Qρ edgecut RO RO FW-GGGP R-GGGP CAMS ML ML ML-CAMS Normalised Normalized edge-cut, edgecut Qρ 2.5 R-GGGP CAMS ML-CAMS Normalised runtime, T ρ Normalised runtime, T ρ

26 Analysis over measurement-based network model Analysis results 3) Heuristic methods b) Influence of optimisation constraints Network performance 3.50E+07 Total edge-cut 3.00E E E+07.50E+07.00E+07 ML ML-CAMS R-GGGP 5.00E E Max. Max. weight weight imbalance imbalance ratio, ratiob rw Weight imbalance ratio

27 Analysis over measurement-based network model Analysis results 3) Heuristic methods b) Influence of optimisation constraints Network performance 2.50E+07 Total edge-cut 2.00E+07.50E+07.00E E E+00 Nbr. of disconnected subdomains Connected Non-connected ML ML-CAMS R-GGGP BC-ES Connected Non-connected Total edge-cut 3.50E E E E+07.50E+07.00E E E+00 Cell Site ML-CAMS R-GGGP 0 ML ML-CAMS R-GGGP BC-ES Connectedness Site granularity

28 Analysis over measurement-based network model Analysis results 3) Heuristic methods b) Influence of optimisation constraints Ease of management Initial operator ML-CAMS with non-connected refinement and cell resolution ML-CAMS with connected refinement and cell resolution ML-CAMS with connected refinement and site resolution

29 clustering problems in cellular networks duction 2 The problem of assigning s in GERAN 3 clustering problems in cellular networks Site re-parenting problem Location area planning problem 4 usions

30 Site re-parenting problem Problem formulation BSC MSC/SGSN LA LA BSC BSC BSC BSC Site Site Site Site Site Site

31 Site re-parenting problem Problem formulation Minimise # users changing BSC subject to BSC capacity Load imbalance between BSCs V, V 2,,V k i, j = :N sites are connected Connectivity Site resolution Spatial consistency d(π*, Π 0 ) B ch # site re-allocations

32 Site re-parenting problem Problem formulation ILP model

33 Location areas planning problem Problem formulation BSC LA LA MSC/SGSN LA BSC LA BSC BSC BSC Site Site Site Site Site Site

34 LA planning problem Problem formulation Minimise subject to # users changing LA LA paging capacity k {,, V }

35 LA planning problem Problem formulation ILP model k =,, V

36 Instance size comparison Instance statistics planning Site re-parenting LA planning V E k # ILP var # ILP const # ILP non-zeros Runtime [s] 56 [Cplex0.] [GLPK] - [GLPK] [SCIP/Cplex] [LPSOLVE*] - [LPSOLVE] - [GLPK]

37 usiones duction 2 Optimisation of the assignment of s in GERAN 3 clustering problems in cellular networks 4 usions Main results Open issues

38 Main results Hierarchical network structuring of a cellular network gives rise to different clustering problems that can be solved by graph partitioning techniques Resulting graphs are smaller but more irregular and dense than in other applications domains, which suggests the use of more sophisticated methods Most graph partitioning packages in the public domain do not consider peculiarities of the cellular environment Even the simplest heuristic achieves a significant gain in network performance and operational efficiency due to the current manual approach followed by operators When formulated as an ILP model, state-of-the-art solvers find difficulties to prove optimality in some instances of the planning, site re-parenting and LA planning problems Sum

39 Open issues Formulation Include connectedness constraint in ILP model Find new constraints to tighten the ILP model Solution technique Find best LP/ILP solver in the public domain Find best default settings for standard solvers (or systematic methodology) Dual-Primal/Primal-Dual, Ceiling/Floor, st /PseudoNonInt/Pseudocost, basis crash, Estimate time to prove optimality (or find a solution of reasonable quality) Design solution method from scratch HO Branch-and-price, branch-and-cut based on cover inequalities, rounding heuristic Dissemination of results Sum Find journals in computer science/applied OR Find network operator/partners

40 Optimisation of cellular network structure by graph partitioning techniques Matías Toril (), Volker Wille(2) () Communications Engineering Dpt., University of Málaga, Spain (2) Performance Services, Nokia Siemens Networks, Huntingdon, UK 24/0/2005 Rome, 29 October 2007 (COST 293 Discussion Workshop)