1

Bandwidth Allocation Planning in

Communication Networks

Christian Frei & Boi FaltingsGlobecom 1999

Ashok Janardhanan

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

Routing in networks

Static traffic Demands are known in advance

Dynamic: Cater to demands as and when they arrive

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

Routing From routing point of view what is

the key resource to manage in networks?

Bandwidth

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

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

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

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

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

RAIN as a CSP So you have

routes (with capacity) communication requests (of given

bandwidth)

how would you model it as a CSP?

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

Problem Domains (i.e., the set of possible

routes) have exponential size

Authors’ contribution: restrict domain using abstractions

propose Blocking Island paradigm

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

Motivating example Blackboard

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

17

18

Properties of -BIs -BI is built according to

communication requirements

19

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

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

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

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

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

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

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

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

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

Dynamic value ordering

we have seen it…

shortest path heuristic lowest level heuristic (some kind of

min-conflict)

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

Conflict identification and resolution Suppose we already have allocated

some demands in the network Suppose the next demand is

Dn = (c, h, 64)

Since c, h not in same BI it is impossible to satisfy Dn without rerouting previously allocated demands

32

Two cases Maybe the problem to allocate is

unsolvable Rerouting earlier demands may

resolve the problem

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

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

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

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

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

38

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

Summary & conclusion The BI paradigm proves to be

efficient in identifying infeasible problems quickly

constitutes as a powerful aid to the network operator

41

Questions?