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Bandwidth Allocation Planning in
Communication Networks
Christian Frei & Boi FaltingsGlobecom 1999
Ashok Janardhanan
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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
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Routing in networks
Static traffic Demands are known in advance
Dynamic: Cater to demands as and when they arrive
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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
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Routing From routing point of view what is
the key resource to manage in networks?
Bandwidth
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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
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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
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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
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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
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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
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RAIN as a CSP So you have
routes (with capacity) communication requests (of given
bandwidth)
how would you model it as a CSP?
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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
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Problem Domains (i.e., the set of possible
routes) have exponential size
Authors’ contribution: restrict domain using abstractions
propose Blocking Island paradigm
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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]
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Motivating example Blackboard
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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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Properties of -BIs -BI is built according to
communication requirements
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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
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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
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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
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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’
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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
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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
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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
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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
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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
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Dynamic value ordering
we have seen it…
shortest path heuristic lowest level heuristic (some kind of
min-conflict)
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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
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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
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Two cases Maybe the problem to allocate is
unsolvable Rerouting earlier demands may
resolve the problem
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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
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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
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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)
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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)
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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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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
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Summary & conclusion The BI paradigm proves to be
efficient in identifying infeasible problems quickly
constitutes as a powerful aid to the network operator
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Questions?