Embed Size (px)
Citation preview
Towards Communication Network Development (structural systems issues, combinatorial models)
Mark Sh. LevinInst. for Inform. Transmission Problems, Russian Acad. of Sci.
Email: [email protected] 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 extension4.Conclusion
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
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 deviceinterconnection (two sides)(e.g., link) *New two devices
Improvement ofsystem 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)
Illustrative Example (building extension)
Addition
Coordinatedaddition
Newgeneralizeddesign
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 pointsgateways *addition of links (e.g., bridges) *redesign of topology
Access *addition of access pointsnetwork *addition of links (e.g., bridges) *redesign of topology
Distributed *addition of usersnetwork *addition of distribution network
Basic combinatorial optimization models/problems
Problem Application
Selection/ranking *selection of access point *selection of provider
Knapsack, *design of a configurationMultiple choice problem (e.g., selection of access points, design of a system configuration (for a device)
Assignment/ *connection of users to access pointsallocation *allocation of devices
Clustering *grouping of users, etc.
Spanning *topology design/redesignstructures (trees)
Covering *topology design, allocation
Example: Network Improvement (phone network in Moscow)
CentralA1
SouthA2
NorthA5
EastA9
WestA8
South-WestA3
South-EastA4
North-WestA7
North-EastA6
MOSCOW
GROUPS (clustering by parameters, i.e, types of regions): Group 1 (G1): A1Group 2 (G2): A2Group 3 (G3): A3&A8Group 4 (G4): A4Group 5 (G5): A5&A7&A9Group 6 (G6): A6
DEVELOPMENT ACTIONS:D1 NoneD2 New linksD3 Reparation (upgrade) of linksD4 Extension (new links and devices)D5 Deletion of old links
Example: Network Improvement (phone network in Moscow)
CentralA1
SouthA2
NorthA5
EastA9
WestA8
South-WestA3
South-EastA4
North-WestA7
North-EastA6
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
Example: Network Improvement (phone network in Moscow)
Criteria:C1 general profit of development actionC2 complexity of development actionC3 perspective profitC4 expenditure (by devices, by workers, etc.)C5 cost
Multicriteria Multiple Choice Problem
( mi=1 qi
j=1 c1ij xij , … , m
i=1 qij=1 cp
ij xij , … , mi=1 qi
j=1 ckij xij ) -> Pareto-
effective solutions s.t. m
i=1 qij=1 aij xij b
qij=1 xij 1 , i = 1, …, m
xij {0, 1}, i = 1, … , m , j = 1, …, qi
. . . . . .
J1 Ji Jm
. . . . . .
. . .
i | Ji | = qi , j = 1, … , qi
cij => ( c1ij , … , cp
ij , … , ckij )
Algorithms for multiple choice problem
1.Ordering by decreasing of cij / aij (heuristic)
2.Branch-And-Bound method
3.Dynamic programming (exact solution)
4.Dynamic programming (approximate solving scheme)
5.Probabilistic methods
6.Hybrid schemes
Illustration for Development Plan
G2
D41
…
D45
G4 G5
D51
…
D55
D21
…
D25
System S = G1 *...* Gi *…* G6
Example: P1 = D13 *…* D3
2 *…* D61
G1
D11
…
D15
G6
D61
…
D65
G3
D31
…
D35
Example: Network Extension (assignment of users to access points)
Basic problem: 1.Set of users2.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)
Assignment/Allocation problem
Allocation (assignment, matching, location):
matrix of weights cij
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
1
2
3
4
5
6
7
8
Positions
Set of elements
Assignment/allocation problem
a3
a1
a2
an
b1
FORMULATION (algebraic):Set of elements: A = { a1 , … , ai , … , an }Set of positions: B = { b1 , … , bj , … . bm } (now let n = m)Effectiveness of pair ai and bj is: c ( ai , bj )
xij = 1 if ai is located into position bj and 0 otherwise ( xij { 0,1 } )
The problem is: max ni=1 n
j=1 cij xij
s.t. ni=1 xij = 1 j
nj=1 xij = 1 i
b2
b3
bm
. . . . . .
ELEMENTS POSITIONS
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 quadraticassignment problem
Multicriteriaquadratic assignment
problem
Multicriteriageneralized assignment
problem
Multicriteria generalized quadratic assignment problem
Multicriteria assignment problem
PLUS: multicriteriadescription
PLUS: distance matrix for positions
PLUS: resource (s) for positions
PLUS: multicriteriadescription
Example: Network Extension
1
3
2
1
6
9
2
4
3
5
1112
13
8
7
10
Initial region
Example: Network Extension
1
3
2
1
6
9
2
4
3
5
1112
13
8
7
10
Initial region
4
5
6
Additional region
1514
16
17
25
18 19
20
21
22
23
24
SEPARATED ASSIGNMENT
Example: Network Extension
1
3
2
1
6
9
2
4
3
5
1112
13
8
7
10
Initial region
4
5
6
Additional region
1514
16
17
25
18 19
20
21
22
23
24
JOINT ASSIGNMENT
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 packagedSoftware. 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.
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
That’s All
Gr8 Thanks!
http://www.mslevin.iitp.ru/
Mark Sh. Levin
