Traffic Engineering for ISP NetworksTraffic Engineering for ISP Networks

Jennifer RexfordComputer Science Department

Princeton Universityhttp://www.cs.princeton.edu/~jrex

OutlineOutline

Internet routing– Overview of the Internet routing architecture

– Shortest-path link-state routing between edge routers

Optimization: Tune routing to the traffic– Optimizing routing given a topology and traffic matrix

– Local search to select the integer link weights

Design for optimizability: Design routing protocol– Optimal traffic engineering with link-state routing

Tomography: Infer the traffic matrix– Estimating traffic matrix from routing and link load

Internet RoutingInternet Routing

Autonomous Systems (ASes)Autonomous Systems (ASes)

Internet is divided into Autonomous Systems– Distinct regions of administrative control

– Routers/links managed by a single “institution”

– Service provider, company, university, …

Hierarchy of Autonomous Systems– Large, tier-1 provider with a nationwide backbone

– Medium-sized regional provider with smaller backbone

– Small network run by a single company or university

Cooperate to ensure end-to-end reachability

Interdomain RoutingInterdomain Routing

AS-level topology– Destinations are IP prefixes (e.g., 12.0.0.0/8)

– Nodes are Autonomous Systems (ASes)

– Edges are links and business relationships

1

2

34

5

67

ClientWeb server

Example Backbone: Abilene Internet2 NewtorkExample Backbone: Abilene Internet2 Newtork

Points-of-Presence (PoPs)Points-of-Presence (PoPs)

Inter-PoP links– Long distances

– High bandwidth

Intra-PoP links– Short cables between

racks or floors

– Aggregated bandwidth

Links to other networks– Wide range of media

and bandwidth

Intra-PoP

Other networks

Inter-PoP

Intradomain Routing: Shortest-Path RoutingIntradomain Routing: Shortest-Path Routing

Path-selection model– Destination-based

– Load-insensitive (e.g., static link weights)

– Minimum hop count or sum of link weights

32

2

1

14

1

4

5

3

Computing Shortest Paths: Link-State RoutingComputing Shortest Paths: Link-State Routing

Topology discovery– Routers flood information to learn the topology

– Each router constructs a link-state database

32

2

1

13

1

4

5

3

Computing Shortest Paths: Link-State RoutingComputing Shortest Paths: Link-State Routing

Shortest-path computation– Each router runs Dijkstra’s shortest-path algorithm

– Computes the “next hop” to reach other routers

32

2

1

13

1

4

5

3

Computing Shortest Paths: Link-State RoutingComputing Shortest Paths: Link-State Routing

Packet forwarding– Each router maintains a forwarding table

– To forward incoming packets to the right next-hop link

32

2

1

13

1

4

5

3

Our Focus: Traffic Engineering (TE)Our Focus: Traffic Engineering (TE)

Adjusting routing to the flow of traffic– How should network administrators run their networks?

– Specifically, how should they set the link weights?

Designing protocols for better traffic engineering– How should future routing protocols be designed?

– Specifically, how to make TE efficient and easy?

Collecting measurements of the offered traffic– How should administrators learn the traffic matrix?

– Specifically, how to infer the matrix from link loads?

Optimization: Tuning Routing to the TrafficOptimization: Tuning Routing to the Traffic

Joint work with Bernard Fortz and Mikkel Thorup

http://www.cs.princeton.edu/~jrex/papers/ieeecomm02.pdfhttp://www.cs.princeton.edu/~jrex/papers/opthand04.pdf

Link Weights Control the Flow of TrafficLink Weights Control the Flow of Traffic

32

2

1

13

1

4

5

3

Routers compute paths– Shortest paths as sum of link weights

Operators set the link weights– To control where the traffic goes

3

Heuristics for Setting the Link WeightsHeuristics for Setting the Link Weights

Proportional to physical distance– Cross-country links have higher weights than local ones

– Minimizes end-to-end propagation delay

Inversely proportional to link capacity– Smaller weights for higher-bandwidth links

– Attracts more traffic to links with more capacity

Tuned based on the offered traffic– Network-wide optimization of weights based on traffic

– Directly minimizes key metrics like max link utilization

Why Are the Link Weights Static?Why Are the Link Weights Static?

Strawman alternative: load-sensitive routing– Link metrics based on traffic load

– Flood dynamic metrics as they change

– Adapt automatically to changes in offered load

Reasons why this is typically not done– Delay-based routing unsuccessful in the early days

– Oscillation as routers adapt to out-of-date information

– Most Internet transfers are very short-lived

Research and standards work continues…– … but operators have to do what they can today

Big Picture: Measure, Model, and ControlBig Picture: Measure, Model, and Control

Topology/Configuratio

n

Offeredtraffic

Changes tothe network

Operational network

Network-wide“what if”

model

measure

control

Traffic Engineering in an ISP BackboneTraffic Engineering in an ISP Backbone

Topology– Connectivity and capacity of routers and links

Traffic matrix– Offered load between points in the network

Link weights– Configurable parameters for Interior Gateway Protocol

Performance objective– Balanced load, low latency, service level agreements …

Question: Given the topology and traffic matrix in an IP network, which link weights should be used?

Key Ingredients of Our ApproachKey Ingredients of Our Approach

Measurement– Topology: monitoring of the routing protocols

– Traffic matrix: widely deployed traffic measurement

Network-wide models– Representations of topology and traffic

– “What-if” models of shortest-path routing

Network optimization– Efficient algorithms to find good configurations

– Operational experience to identify key constraints

Formalizing the Optimization ProblemFormalizing the Optimization Problem

Input: graph G(R,L)– R is the set of routers

– L is the set of unidirectional links

– cl is the capacity of link l

Input: traffic matrix– Mi,j is traffic load from router i to j

Output: setting of the link weights– wl is weight on unidirectional link l

– Pi,j,l is fraction of traffic from i to j traversing link l

Multiple Shortest Paths With Even SplittingMultiple Shortest Paths With Even Splitting

0.5

0.5

0.5

0.5

0.250.25

0.250.251.0

1.0

Values of Pi,j,l

Defining the Objective FunctionDefining the Objective Function

Computing the link utilization

– Link load: ul = i,j Mi,j Pi,j,l

– Utilization: ul/clObjective functions

– min(maxl(ul/cl))

– min(lf(ul/cl))

f(x)

1x

Complexity of the Optimization ProblemComplexity of the Optimization Problem

NP-hard optimization problem– No efficient algorithm to find the link weights

– Even for the simple convex objective functions

Why can’t we just do multi-commodity flow?– E.g., solve the multi-commodity flow problem…

– … and the link weights pop out as the dual

– Because IP routers cannot split arbitrarily over ties

What are the implications?– Have to resort to searching through weight settings

Optimization Based on Local SearchOptimization Based on Local Search

Start with an initial setting of the link weights– E.g., same integer weight on every link

– E.g., weights inversely proportional to link capacity

– E.g., existing weights in the operational network

Compute the objective function– Compute the all-pairs shortest paths to get Pi,j,l

– Apply the traffic matrix Mi,j to get link loads ul

– Evaluate the objective function from the ul/cl

Generate a new setting of the link weights repeat

Making the Search EfficientMaking the Search Efficient

Avoid repeating the same weight setting– Keep track of past values of the weight setting

– … or keep a small signature (e.g., a hash) of past values

– Do not evaluate a weight setting if signatures match

Avoid computing the shortest paths from scratch– Explore weight settings that changes just one weight

– Apply fast incremental shortest-path algorithms

Limit the number of unique values of link weights– Do not explore all 216 possible values for each weight

Stop early, before exploring the whole search space

Incorporating Operational RealitiesIncorporating Operational Realities

Minimize number of changes to the network– Changing just 1 or 2 link weights is often enough

Tolerate failure of network equipment– Weights settings usually remain good after failure

– … or can be fixed by changing one or two weights

Limit dependence on measurement accuracy– Good weights remain good, despite random noise

Limit frequency of changes to the weights– Joint optimization for day and night traffic matrices

Application to AT&T’s Backbone NetworkApplication to AT&T’s Backbone Network

Performance of the optimized weights– Search finds a good solution within a few minutes

– Much better than link capacity or physical distance

– Competitive with multi-commodity flow solution

How AT&T changes the link weights– Maintenance done every night from midnight to 6am

– Predict effects of removing link(s) from the network

– Reoptimize the link weights to avoid congestion

– Configure new weights before disabling equipment

Example from My Visit to AT&T’s Operations CenterExample from My Visit to AT&T’s Operations Center

Amtrak repairing/moving part of the train track– Need to move some of the fiber optic cables

– Or, heightened risk of the cables being cut

– Amtrak notifies us of the time the work will be done

AT&T engineers model the effects– Determine which IP links go over the affected fiber

– Pretend the network no longer has these links

– Evaluate the new shortest paths and traffic flow

– Identify whether link loads will be too high

Example ContinuedExample Continued

If load will be too high– Reoptimize the weights on the remaining links

– Schedule the time for the new weights to be configured

– Roll back to the old weight setting after Amtrak is done

Same process applied to other cases– Assessing the network’s risk to possible failures

– Planning for maintenance of existing equipment

– Adapting the link weights to installation of new links

– Adapting the link weights in response to traffic shifts

Conclusions on Traffic EngineeringConclusions on Traffic Engineering

IP networks do not adapt on their own– Routers compute shortest paths based on static weights

Service providers need to adapt the weights– Due to failures, congestion, or planned maintenance

Leads to an interesting optimization problems– Optimize link weights based on topology and traffic

Optimization problem is computationally difficult– Forces the use of efficient local-search techniques

Results of the local search are pretty good– Near-optimal solutions that minimize disruptions

Ongoing WorkOngoing Work

Robust link-weight assignments– Link/node failures

– Range of traffic matrices

More complex routing models– Hot-potato routing

– BGP routing policies

Interaction between ASes– Inter-AS negotiation for joint optimization

– Grappling with scalability and trust issues

Design for Optimizability: Design for Optimizability: Optimal Link-State Routing ProtocolOptimal Link-State Routing Protocol

Joint work with Dahai Xu and Mung Chiang

http://www.cs.princeton.edu/~jrex/papers/pefti.pdf

Revisiting TE With Link-State Routing ProtocolsRevisiting TE With Link-State Routing Protocols

Advantages of link weights– One parameter for each unidirectional link

– Hop-by-hop forwarding (no tunneling, no per-flow state)

– New routes computed automatically after failure

– Changing just a few weights can alleviate congestion

Disadvantages of link weights– Computationally expensive optimization

– Suboptimal distribution of traffic

– (Disruptions when changing the link weights)

Example of Inefficient TEExample of Inefficient TE

Simple topology

Demand of 300 units:– All on top path: 300% utilization of top path

– All on bottom path: 150% utilization of bottom path

– Even splitting: 150% on top path, 75% on bottom

s t

c1 = 100

c2 = 200

Stepping Back: Design for OptimizabilityStepping Back: Design for Optimizability

Two research approaches– Bottom up: do the best with what you have

– Top down: design systems that are easier to manage

Design for manage-ability– “If you are both the professor and the student, you create

exam questions that are easy to answer.” – Mung Chiang

Knowing what we know now…– How should intradomain routing protocols work…

– … to make TE more efficient and hopefully easier?

Optimal TE With Multicommodity FlowOptimal TE With Multicommodity Flow

Problem with shortest-path routing– Inflexible even splitting over shortest paths

Optimal distribution of traffic– Send traffic over any paths in any proportions

– Using tunneling to force traffic on the paths

– Realizable with MultiProtocol Label Switching (MPLS)

Disadvantage of MPLS: high overhead– Large number of paths between pairs of routers

– Must adapt the splitting ratios after each failure

Can We Have Link-State Routing Can We Have Link-State Routing andand Optimal TE? Optimal TE?

Link-state routing and hop-by-hop forwarding– Single weight on each link

– Local rule to compute splitting over paths

– Each router forwards based only on the destination

Link-state routing != shortest-path routing– Routers could use other traffic-splitting rules

– … as long as they are locally computable

– … only from the link weights

Forward Packet Based on Link WeightsForward Packet Based on Link Weights

Available information at router u– wu,v :weights for all links

– dut : shortest distance from u to t

– hu,vt : distance gap (dv

t + wu,v – dut)

32

2

1

13

1

4

5

3distance gap of 0

distance gap of 1

Traffic-Splitting FunctionTraffic-Splitting Function

Relative flow distributed on outgoing links– G(hu,v

t): proportion sent out link v toward t

Split traffic to t in proportion

Even splitting– G(hu,v

t) is 1 if hu,vt = 0 (all traffic on shortest paths)

– G(hu,vt) is 0 if hu,v

t > 0 (no traffic on longer paths)

G(hu,vt)

G(hu,jt)

Exponential SplittingExponential Splitting

Exponentially diminishing traffic on longer paths– Proportion on path i proportional to exp(-pi)

– … where pi is the cost of path i

3

2

2

1

13

1

4

5

3

Optimal TEOptimal TE

A surprising result– This kind of link-state routing can achieve optimal TE

Optimality– Can realize the multicommodity flow traffic distribution

– Expressible in terms of settings of link weights

Efficient algorithm– Computationally tractable to compute optimal weights

– … for a given traffic matrix and capacitated topology

Intuition Behind the TheoryIntuition Behind the Theory

Feasible flow routing

Optimal flow routing

Realizable with link-state routing

Finding Link-State Protocols That Achieve Optimal TEFinding Link-State Protocols That Achieve Optimal TE

Need an additional objective function– To find solutions expressible in terms of link weights

But we already have an objective function– So, how can we add another one?

First, solve the original optimization problem– To determine the load on each link at optimality

– … i.e., the “necessary capacity” of each link

Then, solve a second optimization problem– On this new topology, with our new objective

TE Optimization Problem: Compute Necessary CapacityTE Optimization Problem: Compute Necessary Capacity

Convex objective– Min sum f() over all links

Constraints– Flow conservation: must carry the traffic matrix

– Capacity constraint: cannot exceed link capacity

Variables– Flow along each path

Given– Traffic matrix and link capacities

New Optimization ProblemNew Optimization Problem

Necessary link capacity– Flow on link u,v in the multicommdity-flow solution

– … becomes the capacity of the link in the new problem

In the new optimization problem– Any feasible solution is “optimal”

– … relative to the original optimization problem

So, now we can pick a new objective– Key intuition: maximizing “entropy”

Entropy MaximizationEntropy Maximization

Assume we could enumerate all paths from s to t– (Though in practice this wouldn’t be practical)

Entropy– xk

s,t : fraction of traffic from s to t put on path k

– z(x) = - x * log(x): entropy function

New objective: maximize entropy

– Mi,j (z(xks,t))

High-Level Overview of the DetailsHigh-Level Overview of the Details

NEM problem always has a solution– Earlier multicommodity flow solution

Solving directly is not efficient– Need to avoid enumerating all the paths

Solving with dual decomposition– Derivation leads to the exponential function

– … for splitting traffic over the multiple paths

Derivation also leads to weight-setting algorithm– Computationally efficient, better than local search

ConclusionsConclusions

Protocols induce optimization problems– E.g., setting link weights to do traffic engineering

Complexity of the optimization problems– A symptom that the protocol is not quite right

– E.g., NP-hard problem and suboptimal traffic flow

Design for optimizability– Design the protocol to be easy to optimize

– … using optimization theory as a protocol design tool

Tomography: Inferring the Traffic MatrixTomography: Inferring the Traffic Matrix

Work by Yin Zhang, Matthew Roughan, Nick Duffield, and Albert Greenberg

http://www.cs.utexas.edu/~yzhang/papers/tomogravity-sigm03.pdf

Computing the Traffic Matrix Computing the Traffic Matrix MMi,ji,j

Hard to measure the traffic matrix– IP networks transmit data as individual packets

– Routers do not keep traffic statistics, except link utilization on (say) a five-minute time scale

Need to infer the traffic matrix Mi,j from

– Current topology G(R,L)

– Current routing Pi,j,l

– Current link load ul

– Link capacity cl

4Mbps 4Mbps

3Mbps5Mbps

Inference: Network TomographyInference: Network Tomography

Sources

Destinations

From link counts to the traffic matrix

Tomography: Formalizing the ProblemTomography: Formalizing the Problem

Ingress-egress pairs – p is a ingress-egress pair of nodes (i,j)

– xp is the (unknown) traffic volume for this pair Mi,j

Routing– Plp is proportion of p’s traffic that traverses l

Links in the network– l is a unidirectional edge

– ul is the observed traffic volume on this link

Relationship: u = Px (work backwards to get x)

Tomography: One Observation Not EnoughTomography: One Observation Not Enough

Linear system of n nodes is underdetermined– Number of links e is around O(n)

– Number of ingress-egress pairs c is O(n2)

– Dimension of solution sub-space at least c - e

Multiple observations are needed– k independent observations (over time)

– Stochastic model with Poisson iid counts

– Maximum likelihood estimation to infer matrix

Doesn’t work all that well in practice…

Approach Used at AT&T: Tomo-gravityApproach Used at AT&T: Tomo-gravity

Gravitational assumption– Ingress point a has traffic vi

a

– Egress point b has traffic veb

– Pair (a,b) has traffic proportional to via * ve

b

9 20

10

6

3

21

147

Approach Used at AT&T: Tomo-gravityApproach Used at AT&T: Tomo-gravity

Problem with gravity model– Gravity model ignores the load on the inside links

– Gravity assumption isn’t always 100% correct

– Resulting traffic matrix might not satisfy the link loadsCombining the two techniques

– Gravity: find a traffic matrix using the gravity model

– Tomography: find the family of traffic matrices consistent with all link load statistics

– Tomo-gravity: find the tomography solution that is closest to the output of the gravity model

Works extremely well (and fast) in practice

Conclusions on TomographyConclusions on Tomography

Routers don’t reveal much information about traffic– Measurement provides a network-wide view

– E.g., network topology and traffic matrix

Available data induces a tomography problem– Input: network topology, routing, and link loads

– Output: inferred traffic matrix

Design for tomography?– Design future monitoring systems to induce easier-to-

solve tomography problems?

ConclusionsConclusions

Internet routing is a rich problem space– Designed incrementally as Internet evolved

– Not designed with network management in mind

Network management: bottom up– Working with what you have

– Tuning link weights, and inferring traffic matrices

Exciting new area: design for manageability– Protocols that are easy to tune

– Measurements that make inference easy