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Traffic Engineering

- configuring routes to traffic demands so as to
- improve user performance
- use network resources more efficiently
- operates at coarse timescales
- not for failures, sudden traffic changes
- uses shortest path computations
- OSPF, MPLS
- Q how to set link weights?

Effect of link weights

- unit link weights
- local change to congested link
- global optimization
- to balance link utilizations

Traffic Engineering Framework

- knowledge of topology
- traffic matrix
- K set of origin destination flows
- k ?K, dk demand, sk source, tk destination
- how to get traffic matrix?
- SNMP
- edge measurements routing tables
- network tomography
- packet sampling
- optimization criteria
- minimize maximum utilization
- keep utilizations below 60

How does one set link weights?

Digression linear programming

Linear program

- polynomial time solution in n, m

Slack variables

Surplus variables

Free variables

Example optimal routes

- topology G (V,E)
- K set of origin destination flows
- k ?K, dk demand, sk source, tk destination
- set of given link weights wij (i,j) ?E
- fraction of flow k going over (i,j) ?E

Example

- decomposes into separate problems per flow k ?K

Interpretation

- let be optimal solutions
- if takes values 0 and 1, corresponds to

shortest paths - if takes other values, there exist

multiple shortest paths.

Linear Program

?

- x0 is feasible if Ax0 b and x0 gt 0

Basic solutions

Theorem of LP

Dual problem.

Primal

Dual

Dual problem properties.

- if x, y feasible, then cTx gt yT b
- if x, y feasible and if cTx yT b, then x

and y are optimal - if either problem has finite solution, so does

other, if either has unbounded solution, so does

other

Complementary slackness.

- Let x and y be feasible solutions. A necessary

and sufficient condition for them to be optimal

is that for all i - xi gt 0 ? yT Ai ci
- xi 0 ? yT Ai lt ci
- Here Ai is i-th column of A

Example primal (P-SP)

Example dual (D-SP)

Example

- optimal solution to dual problem
- length

of shortest path from sk to j - length of shortest path from sk to tk

How does one set link weights for OSPF?

Linear programming problem

Primal

Dual

Complementary slackness.

- Let x and y be feasible solutions. A necessary

and sufficient condition for them to be optimal

is that for all i - xi gt 0 ? yT Ai ci
- xi 0 ? yT Ai lt ci
- Here Ai is i-th column of A

Example primal (P-SP)

- topology G (V,E), link weights wij (i,j) ?E

- K set of origin destination flows
- k ?K, dk demand, sk source, tk destination
- fraction of flow k going over (i,j) ?E
- for k ? K

Interpretation

- let be optimal solutions
- if takes values 0 and 1, corresponds to

shortest paths - if takes other values, there exist

multiple shortest paths.

Example dual (D-SP)

Example

- optimal solution to dual problem
- length

of shortest path from sk to j - length of shortest path from sk to tk

Traffic engineering problem minimize maximum

link utilization

- topology G (V,E)
- cij capacity of link (i,j) ? E
- K set of origin destination flows
- k ? K, dk demand, sk source, tk destination
- a maximum link utilization

LP formulation

LP formulation

LP formulation

- can be many solutions with same a
- in case of tie, want solution with short paths
- ? add term
- with small r to cost
- use standard LP algorithms (Simplex) to solve
- Q can we find link weights so that soultion

comes from shortest path problem?

Duality revisited

Primal

Dual

- free variables in primal ? equality constraints

in dual

Dual formulation

- decision variables

Properties of primal-dual solutions

- optimal solution to primal problem
- dual problem
- if
- can think of as shortest path distance
- from sk to j when link weights are
- Therfore solution to TE problem is also solution

to shortest path problem with

Issues

- solutions are flow specific - need destination

specific solutions - not a big deal, can reformulate to account for

this - solutions may not support equal split rule of

OSPF - accounting for this yields NP-hard problem
- see heuristics in FT paper
- modify IP routing

One approach to overcome the splitting problem

- current routing tables have thousands of routing

prefixes - instead of routing each prefix on all equal cost

paths, selectively assign next hops to (each)

prefix - i.e., remove some equal cost next hops assigned

to prefixes - goal to approximate optimal link load

Example EQUAL-SUBSET-SPLIT

j

Prefixes D C

9

5 4 9

Prefix A 5

3

Prefix B 1

Prefixes A B

i

k

Prefix C 8

2.5 0.5 3

12

Prefix D 10

Prefixes D C B A

Prefix A Hops k,l Prefix B Hops k,l Prefix C

Hops j,l Prefix D Hops j,l

l

5 4 2.5 0.5 12

Advantages

- requires no change in data path
- can leverage existing routing protocols
- current routers have 10,000s of routes in routing

tables - provides large degree of flexibility in next hop

allocation to match optimal allocation

Performance

Summary

- can use OSPF/ISIS to support traffic

engineering objectives - performance objectives link weights
- equal splitting rule complicates problem
- heuristics provide good performance
- small changes to IP routing provide in better

performance - MPLS suffers none of these problems

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