Scalable Methods for Provisioning and Restoration of QoS Paths and Trees

1
Scalable Methods for Provisioning and Restoration
of QoS Paths and Trees

• Alex Sprintson
• Advisor Prof. Ariel Orda

2
Motivation

• Networks grow in size at a rapid pace
• Emergence of new applications
• e.g., voice over IP, multimedia streaming
• Requirements
• Support for Quality of Service (QoS)
• Resilience to failures
• Network mechanisms must be scalable
• We investigate scalable network mechanisms for
  the support of QoS and failure resilience

3
Mechanisms

• We focus on two major network mechanisms
• Provisioning establishing a suitable routing
  topology (paths or trees)
• Restoration establishing a restoration
  topology, i.e., a set of restoration paths or
  trees, each protecting part of the primary path

4
QoS constraints

• Imposed by applications
• e.g., voice over IP, requires
• bandwidth 16 - 64 Kbs
• delay 100 and 300 ms
• Can be divided into
• bottleneck constraints - e.g., bandwidth
• additive constraints - e.g., delay and jitter
• Both primary and restoration topologies must
  satisfy QoS constraints

5
Models

• Basic model
• Each link can provide a certain QoS guarantee at
  certain cost
• Extended model
• Each link can provide several QoS guarantees at
  different costs
• Link is associated with a cost function that
  assigns a cost to each QoS value
• The cost estimates the amount of resources
  consumed in order to provide the QoS guarantee

6
Extended Model

• How to allocate resources in order to provide
  the required QoS?

• Each link is a provider's network

• Cost per delay is given by Service Level
  Agreements (SLAs)
• Less delay for more cost

7
Extended Model
8
Methods

• Scalability is achieved in two ways
• We establish algorithmic solutions that are
  considerably less dependent on the size of
  network
• We employ a precomputation approach
• reduce the time required for computing a path by
  performing computations in advance

9
Precomputation
The main loop of a network element
Idea Reduce the time required to identify a
solution by precomputing solutions for each
possible delay value
10
Problems considered
?-precomputation methods
We provide rigorous solutions, with proven
performance guarantees
11
Practical Applications

• ATM PNNI recommendations
• Need to find paths and trees that satisfy QoS
  constraints
• Bandwidth is reserved for a long period of time
• IntServ/RSVP
• Unsuitable paths and trees incur major overhead
• DiffServ
• Identify paths and trees that satisfy SLA
  (service level agreements
• MPLS
• Level-switched paths

12
Model

• Directed Graph G(V,E)
• Undirected for symmetric networks
• For each link l? E
• dl- the delay of link l
• cl - the cost of link l
• Path (P) Sequence of distinct nodes v0, v1, ,vn
• Tree (T) - A subgraph of G with a source node s
  such that each node is reached from s by a unique
  path

13
Provisioning of QoS paths

• Example find a path that satisfies delay
  constraint D6

(2,6)
u
v
1
2
(2,5)
(2,2)
(1,5)
t
s
(1,4)
(5,4)
(1,2)
(2,3)
(2,4)
(2,4)
v
u
1
2
14
Provisioning of QoS paths

• Find a minimum cost path between s and t that
  satisfies QoS constraint D

• Can be efficiently solved for bottleneck
  constraints
• For additive constraints, the problem is NP-hard
• Approximation schemes (PTAS) H92, LR01
• ?-approximate solutions
• O(E?V ?(1/?loglogV))

15
Provisioning of QoS Trees

• Example find a tree that satisfies delay
  constraint D6

16
Provisioning of QoS trees

• Find a minimum cost tree T that connects source
  s to each terminal tj?X and satisfies the delay
  constraint D
• Related problems
• Directed Steiner Tree (DST)
• Special case with no QoS constraints
• Extensively investigated for undirected networks
• Directed Networks Algorithm by Charikar et
  al.,99
• Restricted Shortest Path (RST)
• Special case for unicast

17
Provisioning of QoS trees

• Problem has attracted a large body of research
• Most studies proposed heuristic solutions
• often based on restricting assumptions such as a
  symmetry of link delays
• Probable solutions available only for special
  cases
• E.g., identical link delays
• Or incurred large violation of QoS constraint,
• e.g, an O(Log N, log N) solution
• No solution of provable performance has been
  established for general networks and no violation
  of QoS constraints.

18
Our Results
19
Solution methodology

• Reduction to problem DST

20
Solution to DST problem

• Procedure Ai(K,s,Y)
• T??
• while Kgt0
• Tbest?? Kbest?0
• for each link (r,v)?G and each 1?K'?K do
• T'?Ai-1(K,v,Y)?(r,v)
• if then
• Tbest?T' Kbest?K'
• Y'?tj tj ?Y ? tj ? Tbest
• T?T ? Tbest
• Y ?Y/Y'
• K ?Y
• return T

Approximation ratio
Complexity
21
Preliminaries - Graph Unfolding
22
T1-reduction
23
T1-reduction

• Build a Layers Graph which allows to distinguish
  between trees that satisfy QoS constraint D and
  all other trees

24
T1-reduction

• Any approximation scheme for problem DST can be
  employed in order to obtain an approximate
  solution for problem RST
• E.g., Feldman Ruhl, 99 presents an optimal
  solution for problem DST for a small number of
  terminals
• Computation complexity
• Depends on the delay constraint D

25
Lemma Zelicovsky,97

• Let G' be a transitive closure of graph G. Then,
  for each tree T?G' that connects source s with a
  group X of terminals and for each i, 1 ? i? log
  X there exists an i-level tree T' in G' that
  connects s with X such that

We identify trees with small number of layers
26
T2-reduction

• Efficient, but violates the delay constraint
• We look for a tree that includes at most i layers
• Delay scaling

27
T2-reduction

• Example

28
T2-reduction
29
T2-reduction

• Computational complexity
• May violate the delay constraint by a factor of
• Returns a solution whose cost is at most
• higher than the optimum

30
T3-reduction

• Employs several techniques
• Graph Unfolding
• Layers Graphs
• Cost Scaling
• Path Aggregation

31
Graph Unfolding
32
Layers Graph
33
(No Transcript)
34
Cost Scaling
B is an estimate of the optimum cost
35
Path aggregation

• reduces the size of the auxiliary graph
• represent large number of paths by a small subset
  S

36
T3-reduction

• Construct a layers graph in which the outdegree
  of each node is S

37
T3-reduction

• Begin with initial Lower and Upper bounds on B,
  which are iteratively improved
• Computational complexity
• Does not violates the delay constraint
• The first solution

38
Conclusions

• We focused on the fundamental problems in
  provisioning and restoration of QoS paths and
  trees
• Considered generic models, that capture most
  practical settings of networks
• Practical applications IntServ, DiffServ, MPLS,
  VPN, overlay networks

39
What we did and what is tbd
40
Future work

• Sharing of backup paths
• Topology aggregation
• Reducing complexity of network mechanisms
• End system multicast
• Investigate trade-off between complexity and
  performance
• Monitoring and enforcement of network protocols
• Similar to the enforcement of social laws