Link State Routing - UCL Systems and Networks Researchnrg.cs.ucl.ac.uk/mjh/gz01/lectures/gz01-lecture13-lsrouting.pdf · • Link State routing protocols instruct routers to ... •

Link State Routing

Stefano VissicchioUCL Computer Science

CS 3035/GZ01

Shortest paths problem:– What path between two vertices offers minimal sum of

edge weights?

•  Classic graph algorithms find single-source shortest paths when the entire graph is known centrally– Dijkstra’s Algorithm, Bellman-Ford Algorithm

•  Typically, no central knowledge of entire graph–  Each router only knows its own interfaces’ addresses

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Reminder: Intra-domain Routing Problem


edge weights?



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Reminder: Distance Vector (DV) Approach

…but turned into a distributed algorithm


edge weights?



4

Link State (LS) Approach

unmodified, but run on every router

Link State Approach: Share the Map!

•  Dijkstra’s algorithm takes a weighted graph as input–  it is a centralized algorithm

•  Link State routing protocols instruct routers to collectively build a map of the whole network– each router shares its local information– each router stores the map in a link state database– each router runs Dijkstra’s algorithm locally

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Comparison between LS and DV principles

•  Distance Vector principle: “tell everything you know to your neighbours”– dump routing tables to neighbours

•  Link State principle: “tell everybody what you know about your neighbourhood”– flood local information network-wide

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Agenda

•  We deepen how Link State routing protocols work

1.  Sharing the map•  Finding links: Hello protocol•  Building the map: Flooding protocol• Dealing with failures and partitions

2.  Computing paths

3.  Properties of Link State Routing

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Routers periodically say hello

•  Each router runs a Hello Protocol–  transmits a hello packet on each interface, every

time period P

•  A hello packet contains:–  sender ID– a list of neighbours from which sender has heard

hello on that interface during period D > P •  e.g., D=3P

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Routers establish adjacencies

•  Routers need to know who to share the map with–  they establish logical links called adjacencies•  used to exchange LS messages

•  Hello messages enable adjacencies to be built between neighbouring routers–  the adjacency is up if each of the two routers has

received a hello message with its own ID, in the last period D

–  the adjacency is down otherwise 9

Routers spread news on their neighbourhood

•  Goal: build a map and keep it updated– whenever a link in the LS map comes up or goes

down, the map should be changed

•  To this end, information is flooded– LS routers run a Flooding Protocol– a router detecting a topology change sends a link

state advertisement (LSA) to all its neighbours• over the established adjacencies

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Flooding enables to build the network map

•  An LSA contains:–  ID of the advertising router– a sequence number–  information on every local link, including router ID

of the other endpoint and link metric– message parameters: LS age, type, etc.

•  Routers store received LSAs in a link-state database–  the LSDB keeps all the most recent LSAs–  routers flood new LSAs in the database

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Routers flood information about adjacencies

If link was not previously in database or LSA seq. no. > stored seq. no then:

1. store the LSA in the database2. send the LSA out of all interfaces except the one it arrived on

else if LSA seq. no. < stored seq. no then:send the stored LSA back to that neighbour (it’s out of date)

else ignore the LSA (we’ve already heard it).

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Agenda





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LS: No bouncing after link failures

•  LS distributes complete information on the network– no ambiguity on valid paths à no bouncing

•  When a link fails, the network map is updated– flood that link is down, everyone recalculates paths

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A BC

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LS: No count to infinity

Flooding also implies no count to infinity

When the network partitions, each router will end up with a map of its connected component•  computes paths on that sub-map

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Can LS always heal partitions efficiently?

Consider flooding behavior when partition heals•  Link D-E is restored•  Link C-E fails nearly at the same time

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•  D detects link (D, E) is now up, and floods LSAs to A– but A and D may still think link (C, E) exists!

•  If this is the first time link (D, E) comes up, how will A and D learn about links (B, E) and (B, C)?

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Some cases seem tricky…

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•  OSPF sends new LSAs every 30 mins, even for unmodified links–  sent often à too much overhead–  sent not so often à too slow

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Periodic state refreshes are inadequate

•  Problem: A, D do not know the state of remote links–  think about (B,C)

•  Root cause: flooding news for neighbouring links is not always sufficient

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Let’s think about the real problem

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•  Solution: Routers exchange LS database summaries when they form new adjacencies– upon new adjacency, routers exchange lists of (link

endpoints, sequence numbers)•  LS databases contain much more information à

summaries save bandwidth– each router then requests missing or newer entries– anything new is flooded to all the other neighbours

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Routers briefly sync on new adjacencies!

Agenda





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Link State Database à Routing Table

•  After flooding, routers need to transform their map into a routing table

How?•  Single-source shortest paths algorithm

– Given a graph, the algorithm computes path with least cost from s to all other vertices

–  In LS, each router views itself as source s, and all other routers as destinations

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Shortest Paths: Definitions

•  Each router is a vertex, v ∈ V •  Each link is an edge, e ∈ E, also written (u, v) •  Each link metric maps to an edge weight, w(u, v) •  A path is a sequence of edges •  Path cost is sum of edges’ weights

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Shortest Paths: Definitions

Data structures:

π[v] is predecessor of v: π[v] is vertex before v along current shortest path from s to v

d[v] is shortest path estimate:

least cost found from s to v so far

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Shortest Paths: Initialization

When we start, we know little:•  no cost estimate for any path from s to any other vertex•  no predecessor of v along shortest path from s to any v

ini#alize-single-source(V,s)foreachvertexv∈Vdo

d[v]ß∞π[v]ßNULL

d[s]=0

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Shortest Paths Building Block: Relaxation

Relaxation of an edge:•  Suppose we have current estimates d[u], d[v] of

shortest path cost from s to u and v •  Does it reduce the cost of the shortest path from s to

v to reach v via edge (u, v) ?

relax(u,v,w)ifd[v]>d[u]+w(u,v):

d[v]ßd[u]+w(u,v)π[v]ßu

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Relaxation: Example

•  Suppose–  d[u] = 5 –  d[v] = 9 – w(u, v) = 2

•  relax(u,v,w)computes:–  is d[v] > d[u] + w(u, v)? –  is 9 > 5 + 2 ? •  Yes, so reaching v via (u, v) reduces path cost

–  d[v] ß d[u] + w(u, v) –  π[v] ß u

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5 9

u v

relax(u, v)

5 7

u v

2

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Dijkstra’s Algorithm: Overall Strategy

1.  Maintain running estimates of costs of shortest paths to all vertices (initially all infinity)

2.  Keep a set S of vertices that are “finished”; shortest paths to these vertices already found (initially empty)

3.  Pick the unfinished vertex v with smallest shortest path cost estimate

4.  Add v to set S 5.  Relax all edges leaving v 6.  Repeat from 3.

[Note: only correct for graphs where edge weights are not negative!]

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Dijkstra’s Algorithm: Pseudocode

Dijkstra(V,E,w,s)ini#alize-single-source(V,s)Sß∅QßVwhileQ≠∅do

ußextract-min(Q)SßS∪{u}foreachvertexvthatneighborsu

relax(u,v,w)

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extract-min(Q):return vertex v from Q that has minimal shortest-path estimate d[v]; remove v from Q

Dijkstra’s Algorithm: Example

s: sourced[i]: number inside of vertex i π[b]: if (a, b) is red, then π[b] = a members of set S: blue verticesmembers of priority queue Q: grey vertices

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∞∞

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Dijkstra’s Algorithm Example (cont’d)

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Dijkstra’s Algorithm Example (cont’d)

•  At termination, we know shortest-path routes from s to all other routers

•  Shortest-path tree, rooted at s

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0

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Dijkstra’s Algorithm: Pseudocode

Dijkstra(V,E,w,s)ini#alize-single-source(V,s)Sß∅QßVwhileQ≠∅do

ußextract-min(Q)SßS∪{u}foreachvertexvthatneighborsu

relax(u,v,w)

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extract-min(Q):return vertex v from Q that has minimal shortest-path estimate d[v]; remove v from Q

Dijkstra’s Algorithm: Efficiency

•  Implement Q with binary heap–  total cost to insert |V| entries into Q: O(V)

•  Cost of all extract-min()calls is O(V log2 V)–  cost of single call: O(log2 N), if N items in Q –  |V| calls, since the initial size of Q is |V|

•  Cost of all relax()isO(E log2 V)–  cost of single call: O(log2 V) •  each call reduces d[] value for one vertex in Q

–  at most |E| calls

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Dijkstra’s Algorithm: Efficiency (cont’d)

•  Total algorithm cost: O((V + E) log2 V) – or O(E log2 V) when all vertices are reachable from

the source

•  Dijsktra runs in POLYNOMIAL time!–  fast in practice

•  Also, note that most networks are sparse graphs– E << V2 à Dijkstra algorithm is almost linear

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Agenda





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Link State Routing: Properties

•  At first glance, flooding status of all links seems costly–  cost reasonable for hundreds of routers–  vanilla LS doesn’t scale indefinitely •  e.g., for thousands of nodes

–  yet, scalability can be improved with hierarchy

•  In practice, LS has won over DV–  LS is more commonly used, especially in large (ISP)

networks, where routing is critical– DV rarely used except in small networks •  e.g., enterprise ones

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Performance Comparison with Distance Vector

•  LS has more guarantees and better performance than DV–  no loops after flooding, provided all nodes have

consistent link state databases–  flooding à faster convergence after topology changes

•  However, LS is also more complex to implement than DV–  sequence numbers crucial to protect against stale

announcements–  adjacencies have to be established and maintained–  link state database is needed

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Disclaimer: The real world is more complex

•  Yet, LS does not solve all problems–  e.g., transient loops during convergence

•  Such problems are relevant in practice –  connectivity is of utmost relevance: £££ –  99.999% uptime à max downtime: 5.26 minutes / year

•  They attracted many industrial and research efforts–  Loop Free Alternate (LFA) and all its variants–  progressive metric increment– …

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Disclaimer: The real world is more complex

•  Also, network operators face more requirements–  avoid congestion, enforce firewall traversal, …

•  Routers’ primitives and Traffic Engineering (TE) techniques enable routing on non-shortest paths

•  Big players started to develop their own routing systems–  even centralized: Google B4 [2013], Microsoft SWAN

[2013], Google BwE [2015], …

•  … and this seems just an interesting beginning!

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Link State Routing - UCL Systems and Networks Researchnrg.cs.ucl.ac.uk/mjh/gz01/lectures/gz01-lecture13-lsrouting.pdf · • Link State routing protocols instruct routers to ... •

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