1. 1 Bandwidth Allocation Planning in Communication Networks Christian Frei & Boi Faltings Globecom 1999 Ashok Janardhanan

2. 2 Outline RAIN Problem Definition as a CSP Need for abstractions Blocking Islands paradigm Mechanism for building them Properties Search Forward checking Value, variable ordering heuristics Conflict identification & resolution Evaluation by experiments Conclusion & future works

3. 3 Routing in networks Static traffic Demands are known in advance Dynamic: Cater to demands as and when they arrive

4. 4 Context Paper considers problem of allocating a set of demands between pairs of nodes in an offline manner for static traffic within the resource capacities of the network

5. 5 Routing From routing point of view what is the key resource to manage in networks? Bandwidth

6. 6 Resource Allocation in Networks (RAIN) Given: a network composed of nodes and bi-directional links of given bandwidth a set of communication demands between pairs of nodes Find: one and only one route for each demand that satisfies bandwidth requirements of the demands within the capacities of the links

7. 7 Routing Most commonly used routing algorithm Shortest path routing Good for a single demand [Wang & Crowcroft 96] showed it can lead to sub optimal routing or congested networks

8. 8 Solution Allow other routes than shortest path Problem: there exists an exponential number of acceptable paths Greedy algorithm yields incompleteness Solution: Backtrack to previous allocation in order to squeeze in new demands

9. 9 Algorithms to solve RAIN Incomplete: explores only partially the search space (i.e., subset of possible routes) E.g. shortest path Fast, but not guaranteed to find a solution when there is one

10. 10 Algorithms to solve RAIN Complete: performs exhaustive search and always finds a solution when one exists exponential number of possible routes for each demand  huge search space  exponential worst-case behavior To cope with complexity, guide search with heuristics

11. 11 RAIN as a CSP So you have routes (with capacity) communication requests (of given bandwidth) how would you model it as a CSP?

12. 12 Model RAIN as CSP Variables  demands Domain:  set of possible routes between endpoints Constraints  demand must not exceed any link capacity along route (min link capacity) Solution  select one route for each demand

13. 13 Problem Domains (i.e., the set of possible routes) have exponential size Authors’ contribution:  restrict domain using abstractions  propose Blocking Island paradigm

14. 14 What is abstraction is a mapping of a problem representation into a simpler one that satisfies some desirable properties in order to reduce complexity of reasoning. [Giunchiglia & Walsh 91]

15. 15 Motivating example Blackboard

16. 16 Blocking island paradigm  blocking island for a node x is a set of all nodes of the network that can be reached from x using links with at least  available resources

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18. 18 Properties of  -BIs  - BI is built according to communication requirements

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20. 20 New terms  - BI: blocking island for demand   - BIG: blocking island graph BIH: blocking island hierarchy Abstraction tree Critical link: max capacity link between 2 BIs at the same level

21. 21 Routing from BIH perspective Why shortest path doesn’t work? Considering route c  e Uses resources on two critical links in terms of bandwidth Route c, b, d, e uses only links clustered at the lowest level

22. 22 Routing heuristics Lowest Level (LL) choose the route in the lowest BI Minimal Splitting (MS) attempts to minimize splitting a route across branches in BIH Implementation: compute routes using LL then order them according to MS

23. 23 Lowest level (LL) Route a demand along links clustered in the lowest BI, between the endpoints of the demand Rationale: the lower the BI in BIH, the less critical are the links clustered in the BI ‘Overall load-balancing’

24. 24 Minimal splitting heuristic Select route that causes the fewest splitting of the BIs in the BIH Rationale: The more the splitting The more links become critical  increases allocation failures

25. 25 Solving the RAIN problem Equivalent to solving the CSP BIs are an abstraction that allow us to restrict the domain of variables to routes within a BI thus reducing the size of the CSP and the complexity of solving it

26. 26 Solving the RAIN problem When the endpoints of a demand are clustered in the same  -BI   at least one route satisfying the demand A route is a path in the abstraction tree There is a route satisfying a demand   path that does not traverse BIs of a higher level than its resource requirement

27. 27 Search Mapping of routes into BIH is used to formulate a new forward checking criterion dynamic value ordering shortest path heuristic lowest level heuristic (some kind of min-conflict) dynamic variable ordering heuristic DVO-HL DVO-NL

28. 28 Forward checking (FC) When endpoints of demand are in the same BI, then a route exists (can be computed easily) assign the route to demand (i.e., instantiate variable) update BIH check for future variables (demands) whether or not their endpoints remain in same BIs they do? this is FC they don’t? choose another possible route

29. 29 Dynamic value ordering we have seen it… shortest path heuristic lowest level heuristic (some kind of min- conflict)

30. 30 Dynamic variable ordering DVO-HL (highest level) lowest common father of demand’s endpoints is the highest in the BIH (low in resources) DVO-NL (number of levels) difference in  levels between the common father of its endpoints and its resource requirements is lowest

31. 31 Conflict identification and resolution Suppose we already have allocated some demands in the network Suppose the next demand is D n = (c, h, 64) Since c, h not in same BI it is impossible to satisfy D n without rerouting previously allocated demands

32. 32 Two cases Maybe the problem to allocate is unsolvable Rerouting earlier demands may resolve the problem

33. 33 Solving feasible RAIN Tightness: ratio of resources required for the best possible allocation (in terms of bandwidth) over the the total amount of resources available in the network

34. 34 Experiments 22,000 solvable instances of RAIN Each problem has a randomly generated network topology of 20 nodes and 38 links a random set of 80 demands, each demand characterized by two endpoints and a bandwidth Criteria: time, routes, #backtracks

35. 35 Six strategies 1. Basic shortest-path (basic SP) 2. Backtrack shortest-path (BT-SP) 3. Blocking island with LL & HL (BI-LL-HL) 4. Blocking island with LL & NL (BI-LL-NL) 5. Blocking island with BJ, LL & HL (BI-BJ- LL-HL) 6. Blocking island with BJ, LL & NL (BI-BJ- LL-NL)

36. 36 Tested strategies Basic SP: search using shortest path BT-SP: incorporates BT undo bad allocations BI-LL-HL: uses LL for route generations and DVO-HL for dynamic demand selection BI-LL-NLL: uses DVO-NL for choosing the next demand to allocate BI-BJ-LL-NL: uses LL and NL (to break ties) BI-BJ-NL-LL: uses NL and LL (to break ties)

37. 37 Results BJ-based strategies slightly better performance over pure BT-ones NL outperforms HL: better at choosing most difficult demand to assign  achieves a greater pruning effect Maintenance of the BIH is significant in easy problems

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39. 39 Summary & conclusion Current strategies used in networks lead to sub-optimal routing BIs coupled with CSP search complete algorithm for solving RAIN reasonable amount of time in many instances and yields better solutions Advantages of BI paradigm quickly identifies infeasible problems and constitutes powerful aid to the network operator

40. 40 Summary & conclusion The BI paradigm proves to be efficient in identifying infeasible problems quickly constitutes as a powerful aid to the network operator

41. 41 Questions?