1. Towards Communication Network Development (structural systems issues, combinatorial models) Mark Sh. Levin Inst. for Inform. Transmission Problems, Russian Acad. of Sci. Email: mslevin@acm.org Http://www.mslevin.iitp.ru/ SIBIRCON’2010, Irkutsk, Russia, 7/13, 2010 “Telecom.&commun.networks” 11:40 PLAN: 1.Systems development approaches (improvement/modification, extension) 2.Basic combinatorial models: ranking, clustering, assignment/allocation, multiple choice problem, 3.Illustrative examples: *network improvement/modification *network extension 4.Conclusion

2. Systems Development Approaches Additional system part: structure, components, component interconnection Basic system: *structure/hierarchy, *components, *component interconnections Two General System Development Approaches: 1.System improvement/ modification (by component, by interconnection, by structure) 2.System extension: *addition, *coordinated addition, *new generalized design

3. Network improvement/modification System operation Implementation Improvement of *Improvement of device/ component (e.g., node) management (models, software) *New device Improvement of *Improvement of two device interconnection (two sides) (e.g., link) *New two devices Improvement of system structure: (a)Topology *Additional links (by devices, etc., by new nodes) (it is extension) (b)Structure *New structure, e.g., hierarchy (e.g., hierarchy) (it is extension)

4. Illustrative Example (building extension) Addition Coordinated addition New generalized design

5. Basic network extension design problems Network layer Design problems System hubs *addition of hubs (centers) *addition of links (e.g., bridges) *redesign of topology Network over *addition of access points gateways *addition of links (e.g., bridges) *redesign of topology Access *addition of access points network *addition of links (e.g., bridges) *redesign of topology Distributed *addition of users network *addition of distribution network

6. Basic combinatorial optimization models/problems Problem Application Selection/ranking *selection of access point *selection of provider Knapsack, *design of a configuration Multiple choice problem (e.g., selection of access points, design of a system configuration (for a device) Assignment/ *connection of users to access points allocation *allocation of devices Clustering *grouping of users, etc. Spanning *topology design/redesign structures (trees) Covering *topology design, allocation

7. Example: Network Improvement (phone network in Moscow) Central A1 South A2 North A5 East A9 West A8 South-West A3 South-East A4 North-West A7 North-East A6 MOSCOW GROUPS (clustering by parameters, i.e, types of regions): Group 1 (G1): A1 Group 2 (G2): A2 Group 3 (G3): A3&A8 Group 4 (G4): A4 Group 5 (G5): A5&A7&A9 Group 6 (G6): A6 DEVELOPMENT ACTIONS: D1 None D2 New links D3 Reparation (upgrade) of links D4 Extension (new links and devices) D5 Deletion of old links

8. Example: Network Improvement (phone network in Moscow) Central A1 South A2 North A5 East A9 West A8 South-West A3 South-East A4 North-West A7 North-East A6 MOSCOW OUR SOLVING (SYSTEM DEVELOPMENT) SCHEME: 1.Clustering of regions (to decrease the problem dimension) 2.Selection of development action for each region group (while taking into account a total constraint - budget). This is muilticriteria multiple choice problem

9. Example: Network Improvement (phone network in Moscow) Criteria: C1 general profit of development action C2 complexity of development action C3 perspective profit C4 expenditure (by devices, by workers, etc.) C5 cost

10. Multicriteria Multiple Choice Problem (  m i=1  qi j=1 c 1 ij x ij, …,  m i=1  qi j=1 c p ij x ij, …,  m i=1  qi j=1 c k ij x ij ) -> Pareto-effective solutions s.t.  m i=1  qi j=1 a ij x ij  b  qi j=1 x ij  1, i = 1, …, m x ij  {0, 1}, i = 1, …, m, j = 1, …, qi... J 1 J i J m...  i | J i | = qi, j = 1, …, qi c ij => ( c 1 ij, …, c p ij, …, c k ij )

11. Algorithms for multiple choice problem 1.Ordering by decreasing of c ij / a ij ( heuristic ) 2.Branch-And-Bound method 3.Dynamic programming (exact solution) 4.Dynamic programming (approximate solving scheme) 5.Probabilistic methods 6.Hybrid schemes

12. Illustration for Development Plan G2G2 D41…D45D41…D45 G4G4 G5G5 D51…D55D51…D55 D21…D25D21…D25 System S = G 1 *...* G i *…* G 6 Example: P 1 = D 1 3 *…* D 3 2 *…* D 6 1 G1G1 D11…D15D11…D15 G6G6 D61…D65D61…D65 G3G3 D31…D35D31…D35

13. Example: Network Extension (assignment of users to access points) Basic problem: 1.Set of users 2.Set of access points Assign access point(s) for each user We use multicriteria assignment problem (or multicriteria generalized assignment problem, i.e., several access points for each user)

14. Assignment/Allocation problem Allocation (assignment, matching, location): matrix of weights c ij BIPARTITE GRAPH 1 2 3 4 5 6 7 8 a b c d e f g h........ a b c d e f g h 1234567812345678 Positions Set of elements

15. Assignment/allocation problem a3a3 a1a1 a2a2 anan b1b1 FORMULATION (algebraic): Set of elements: A = { a 1, …, a i, …, a n } Set of positions: B = { b 1, …, b j, …. b m } (now let n = m) Effectiveness of pair a i and b j is: c ( a i, b j ) x ij = 1 if a i is located into position b j and 0 otherwise ( x ij  { 0,1 } ) The problem is: max  n i=1  n j=1 c ij x ij s.t.  n i=1 x ij = 1  j  n j=1 x ij = 1  i b2b2 b3b3 bmbm... ELEMENTSPOSITIONS

16. Evolution chart of allocation-like problems Basic assignment problem Quadratic assignment problem PLUS: distance matrix for positions Generalized assignment problem PLUS: resource (s) for positions Generalized quadratic assignment problem Multicriteria quadratic assignment problem Multicriteria generalized assignment problem Multicriteria generalized quadratic assignment problem Multicriteria assignment problem PLUS: multicriteria description PLUS: distance matrix for positions PLUS: resource (s) for positions PLUS: multicriteria description

17. Example: Network Extension 1 3 2 1 6 9 2 4 3 5 11 12 13 8 7 10 Initial region

18. Example: Network Extension 1 3 2 1 6 9 2 4 3 5 11 12 13 8 7 10 Initial region 4 5 6 Additional region 15 14 16 17 25 18 19 20 21 22 23 24 SEPARATED ASSIGNMENT

19. Example: Network Extension 1 3 2 1 6 9 2 4 3 5 11 12 13 8 7 10 Initial region 4 5 6 Additional region 15 14 16 17 25 18 19 20 21 22 23 24 JOINT ASSIGNMENT

20. Some References (combinatorial problems & redesign methods) 1.C. Ahlund, A.B. Zaslavsky, Extending global IP connectivity for Ad Hoc networks. Telecommunication Systems, 24(2-4), 221-250, 2003. 2.H. Kellerer, U. Pferschy, D. Pisinger, Knapsack Problems, Springer, 2004. 3.M.Sh. Levin. Combinatorial Engineering of Decomposable Systems, Kluwer, 1998. 4.M.Sh. Levin, Composite Systems Decisions, Springer, 2006. 5.M.Sh. Levin, A.V. Safonov, Design and Redesign of Configuration for Facility in Communication Network. Inform. Technologies and Comp. Syst. (Russian Acad. of Sci.), Issue 4, 63-73, 2006 (in Russian). 6.M.Sh. Levin, Modular system synthesis: Example for composite packaged Software. IEEE Trans. on SMC - Part C, 35(4), 544-553, 2005. 7.M.Sh. Levin, M.A. Danieli, Hierarchical decision making framework for evaluation and improvement of composite systems. Informatica, 16(2), 213-240, 2005. 8.M.Sh. Levin, M.V. Petukhov, Multicriteria assignment problem (selection of access points), LNCS 6097, part II, Springer, 277-287, 2010. 9.H. Noltermeier, H.-C. Wirth, S.O. Krumke, Network design and improvement. ACM Comput. Surv., vol. 32(3es), Art. No. 2, Sept. 1999.

21. Conclusion 1.Examination of new applied examples 2.Usage of new redesign models, e.g., models of combinatorial synthesis, taking into account uncertainty (stochastic models, fuzzy set based models) 3.Examination of network topology development (includin multi-layered networks) 4.Design of a special computer environment for networks development/reengineering (i.e., modification, extension): database for networks, visualization part (data, graphs), typical development strategies and their design, models/algorithms, base of realistic examples

22. That’s All Gr8 Thanks! http://www.mslevin.iitp.ru/ Mark Sh. Levin