Métaroutage
[email protected]
L’école d’été RÉSCOM 2007
Calcotoggio, Corse, 21 Juin
Tutorial Outline
• Motivation : shortage of routing protocols
• Review of Metarouting paper [GS_MR]
• Open problems
–
–
–
–
–
Expressive power of “abstract metalanguage”
User-oriented languages
Compilation
Forwarding
Other applications? MANET routing.
Architecture of Dynamic Routing
IGP
EGP (= BGP)
AS 1
IGP = Interior Gateway Protocol
Metric based: OSPF, IS-IS, RIP,
EIGRP (cisco)
EGP = Exterior Gateway Protocol
IGP
AS 2
Policy based: BGP
The Routing Domain of BGP is the entire Internet
Technology of Distributed Routing
Link State
•
•
•
•
•
•
Topology information is flooded
within the routing domain
Best end-to-end paths are
computed locally at each router.
Best end-to-end paths
determine next-hops.
Based on minimizing some
notion of distance
Works only if policy is shared
and uniform
Examples: OSPF, IS-IS
Vectoring
•
•
•
•
•
•
Each router knows little about
network topology
Only best next-hops are chosen
by each router for each
destination network.
Best end-to-end paths result
from composition of all next-hop
choices
Does not require any notion of
distance
Does not require uniform
policies at all routers
Examples: RIP, BGP
The Gang of Four
Link State
IGP
EGP
OSPF
IS-IS
Vectoring
RIP
BGP !!
BGP
The Joy of Interdomain Routing
RBNet C
B
A
B
201 ms
4 ms
A = HP Palo Alto
B =Intel Berkeley
C =Moscow State U
A
257 ms
C
http://www.larrysface.com/
The Problem
• Small number of routing protocols
• Design, implementation, deployment,
standardization  long, slow process
• BGP is being pressed into service as an IGP
– No convergence guarantees
– BGP Wedgies (RFC 4264)
• Endless stream of BGP extensions
– Cost Communities
– Use of BGP for VPN routing (RFC 2547)
What is a BGP Wedgie? [RFC 4264]
The
half
wedgie
The
full
wedgie
• BGP policies make sense locally
• Interaction of local policies allows
multiple stable routings
• Some routings are consistent with
intended policies, and some are not
– If an unintended routing is installed (BGP is
“wedged”), then manual intervention is
needed to change to an intended routing
• When an unintended routing is
installed, no single group of network
operators has enough knowledge to
debug the problem
Half Wedgie Example
AS 3
peer
peer
provider
AS 4
provider
customer
AS 2
provider
primary link
backup link
customer
customer
AS 1
• AS 1 implements backup
link by sending AS 2 a
“depref me” community.
• AS 2 implements this
community so that the
resulting local pref is
below that of routes from
it’s upstream provider (AS
3 routes)
And the Routings are…
AS 3
AS 4
AS 2
AS 3
AS 4
AS 2
AS 1
Intended Routing
Note: this would be the ONLY
routing if AS2 translated its
“depref me” community to a
“depref me” community of AS 3
AS 1
Unintended Routing
Note: This is easy to reach from
the intended routing just by “bouncing”
the BGP session on the primary link.
Recovery
AS 3
AS 4
AS 2
AS 3
AS 4
AS 2
AS 1
Bring down AS 1-2 session
AS 3
AS 4
AS 2
AS 1
AS 1
Bring it back up!
• Requires manual intervention
• Can be done in AS 1 or AS 2
What the heck is going on?
• There is no guarantee that a BGP configuration has a
unique routing solution.
– When multiple solutions exist, the (unpredictable) order of updates
will determine which one is wins.
• There is no guarantee that a BGP configuration has any
solution!
– And checking configurations NP-Complete
– Lab demonstrations of BGP configs never converging
• Complex policies (weights, communities setting
preferences, and so on) increase chances of routing
anomalies.
– … yet this is the current trend!
Load Balancing Example
AS 3
peer
provider
peer
AS 4
provider
customer
customer
AS 2
AS 5
primary link for prefix P2
backup link for prefix P1
primary link for prefix P1
backup link for prefix P2
AS 1
Simple session reset my not work!!
Can’t un-wedge with session resets!
3
4
2
5
3
all up
4
BOTH
P1 & P2
wedged
2
all up
5
3
4
2
5
1
1
1
3
2
1—2 & 1—5
down
P2
wedged
4
5
Note that when bringing
all up we could actually land
the system in any one of the
4 stable states --- depends
on message order….
3
2
1—2 & 1—5
down
P1
wedged
1
1
1—2 up
1—5 up
3
4
2
3
5
1
2
1—2 down
INTENDED
1
4
5
4
3
4
5
2
5
1—5 down
1
Recovery
3
2
4
P2
wedged
5
Temporarily
filter P2 from
1—5 session
Temporarily
filter P1 from
1—2 session
3
2
4
P1
wedged
1
1
1—2 up
1—5 up
3
4
2
3
5
1
2
1—2 down
INTENDED
1
5
4
3
4
5
2
5
1—5 down
1
Who among us could figure this one out?
When 1—2 is in New York and 1—5 is in Tokyo?
Full Wedgie Example
peer
•
peer
AS 3
AS 4
provider
provider
customer
customer
AS 2
peer
provider
•
peer
•
AS 5
backup links
primary link
customer
customer
AS 1
AS 1 implements backup
links by sending AS 2 and AS
5 a “depref me”
communities.
AS 2 implements its
community so that the
resulting local pref is below
that of its upstream providers
and it’s peers (AS 3 and AS
5 routes)
AS 5 implements its
community so that the
resulting local pref is below
its peers (AS 2) but above
that of its providers (AS 3)
And the Routings are…
AS 3
AS 4
AS 5
AS 2
AS 3
AS 4
AS 5
AS 2
AS 1
AS 1
Intended Routing
Unintended Routing
Resetting 1—2 does not help!!
AS 3
AS 4
AS 5
AS 2
AS 3
AS 4
AS 5
AS 2
AS 1
AS 1
Bring down AS 1-2 session
Bring up AS 1-2 session
Recovery
AS 3
AS 2
AS 4
AS 5
AS 3
AS 2
AS 1
Bring down AS 1-2 session
AND AS 1-5 session
AS 4
AS 5
AS 3
AS 2
AS 4
AS 5
AS 1
AS 1
Bring up AS 1-2 session
AND AS 1-5 session
A lot of “non-local” knowledge is required to arrive at
this recovery strategy!
Try to convince AS 5 and AS 1 that their session has be
reset (or filtered) even though it is not associated with an
active route!
That Can’t happen in MY network!!
NA
EMEA
LA
AP
AU++
An “normal” global global backbone (ISP or Corporate Intranet)
implemented with 5 regional ASes
The Full Wedgie Example, in a new Guise
NA
AP
LA
EMEA
Intended Routing for
some prefixes in AU,
implemented
with communities.
DOES THIS LOOK
FAMILIAR??
AU
Message: Same problems can arise
with “traffic engineering” across
regional networks.
The Problem
• Small number of routing protocols
• Design, implementation, deployment,
standardization  long, slow process
• BGP is being pressed into service as an IGP
– No convergence guarantees
– BGP Wedgies (RFC 4264)
• Endless stream of BGP extensions
– Cost Communities
– Use of BGP for VPN routing (RFC 2547)
Is there a Betterer way?
Metarouting
= Let Operators Decide
• We don't know how to define generic IGPs for every network ---let the operators decide.
• We don't know how to define IBGPs for every network --let the operators decide.
• We don't know how to fix EBGP or how to evolve it for changing
requirements --let the operators decide.
• Operators can decide, if only they are given the right tools.
Central Dogma
Routing Protocol
=
Routing language + Routing Algorithms +
• How routes are
described
• How routes are
compared
• How policy is
described
• How policy is
applied
• How routing solutions
are computed
• How adjacencies are
established and
maintained
• …
Proof
• Does the
protocol
converge?
• Is resulting
forwarding
loop-free?
• …
Basic Thesis
Routing languages should not be hard-coded
into protocols specifications and implementations.
• Allow the operator community to define
routing languages and routing protocols
that fit the needs of their networks (IGPs,
IBGPs).
• Allow the operator community to
standardize and evolve interdomain
routing languages.
How?
Define a metalanguage for the specification
of routing languages.
This language must be carefully constructed
to be highly expressiveness while at the same
time allowing the automatic derivation of properties
required for proofs.
Standardize the metalanguage (IETF?)
Standardize (IETF) and
implement a generic
(routing language Independent)
set of algorithms such as
BGP-like hard state path vector,
RIP-like soft-state path-vector,
OSPF-like link state
flooding and generalized Dijkstra.
Routing Protocol = Routing Language + Routing Algorithms + Proof
LIBERATE
NETWORK OPERATORS
FROM THE IETF
Proofs are automated: simply
match the derived properties
of the metalanguage
specification with
the required properties
of each algorithm used.
Routing Algebras [JS_Alg]
m+n
m
n
Generalize
Shortest Paths
 


Routing Algebras
S  (, )
An ordered set of signatures
A  ( S , ,  )

    (   )

is a set of policy labels
Is the policy application
function
     ( )( )
Note : the notations in this tutorial differ a bit from those in [JS_Alg, GS_MR].
Important Properties
   
   
Non-decreasing
(ND)
Increasing
(IN)
Monotonicity
(M)
         
(SI)
         
Strict Monotonicity
(  )
What makes these algorithms work?
• Generalized Dijkstra (Think Link State)
– Correctness proof uses M,
– Loop-freedom for hop-by-hop forwarding uses
IN.
• Generalized Bellman-Ford (Vectoring)
– Convergence proof uses IN,
– Loop-freedom for hop-by-hop forwarding uses
strict IN
An algebra for OSPF?
(hand-coded from careful reading of RFC 2328
I’m not sure that it is correct, but that’s not the point….)

(1, )
e
(1, e , 
(1, (1, v), )
(1, e, )
e)
(1, e , 
)
(1, (1, v), 
(1, (2, v), )
)
(1, (2, v), 
(2, (1, v), )
(2, e, )
)
(2, e , 
)
(2, (1, v), 
(2, (2, v), )
)
(2, (2, v), 
(1, (1, v), )
(1, (1, v), 
e)
f
f
f
f
f
f
(1, (2, v), )
(1, (2, v), 
e)
f
f
f
f
f
f
f
f
(2, )
(2, e , 
e)
(2, e , 
)
(2, (1, v), 
)
(2, (2, v), 
)
f
(2, (1, v), )
(2, (1, v), 
e)
f
f
f
f
f
f
(2, (2, v), )
(2, (2, v), 
e)
f
f
f
f
f
f
<1, …> = intra-area route
<2, …> = inter-area route
<{1,2}, <1, v>, > = type I external
)
<{1,2}, > = “normal” route
<{1,2}, <2, v>, > = type II external
Routing Algebras are a good start, but…
• The algebraic framework does not, by
itself, provide a way of constructing new
and complex algebras.
– Algebra definition is hard…
– Proofs are tedious…
– Modifications to an algebra’s definitions are
difficult to manage…
Routing Algebra Meta-Language
A ::= B
| Op(A)
| A Op A
(base algebras)
(unary operator)
(binary operators)
• “Abstract syntax” for generating new Algebras
• Key innovation: automatically derive properties (ND, IN, …) of
the algebra represented by an expression from properties of
base algebras and preservation properties of operators
• Other goals
– Simplicity
– Expressiveness
Some Examples:
Lexicographic Product


( S A ,  A ,  A)  ( S B ,  B ,  B )  ( S A  S A ,  A   B ,  A   B )
(1, 1 )  ( 2 , 2 )  (1  A  2 )  ((1  A  2 )  (1 B 2 ))
( ,  )

(A , B ) (A A  , B B  )
Property Preservation with Lex Product
A

B A B
ND
ND
IN
ND
IN
A

B A B
ND
EQ,SM
M
M
IN
EQ,SM
SM
SM
IN
A design pattern:
EQ
EQ
EQ
( EQ             )
IN
  
  
A1  A2  Ai 1  Ai  An
All at least ND
IN
Don’t care!
Disjoint Label Union
(S ,  A , A)  L (S , B , B)  (S ,  A  B , A  L B)
Same order Structure


left (A )
A  A 
right (B )
B B 
Disjoint Union : Property Preservation
A
B A L B
A
B A L B
ND
ND
ND
M
M
M
IN
ND
ND
SI
M
M
ND
IN
ND
M
SM
M
IN
IN
IN
SM
SM
SM
Local Preference, Origin Preference
S A  ( A ,  A )
A  (S A ,  A , A)
LP( A)  (S A ,  A ,l )
 l   
OP( A)  (S A ,{},r )
 r   
(NOT NICE!)
(Always ND, M)
BGP-like Partition
A
B
internal
B
external
internal
BGP  EBGPIBGP
Scoped Product


AB  ( A LP( B))  L (OP( A)  B)

( ,  )
left (A ,  )
(A A  ,  )
right ( , B )
( , B B  )
Scoped Product : Property Preservation
A
B
AB
IN
ND
ND
IN
IN
IN
These rules can be automatically derived
Area Product


AB  ( A  OP( B))  L (OP( A)  B)

( ,  )
left (A ,  )
(A A  ,  )
right ( , B )
( , B B  )
OSPF  InterAreaIntraArea
Area Product : Property Preservation
A
B
ND
ND
ND
IN
IN
IN
AB
These rules can be automatically derived
Current work and Open Problems
• Current prototype implemented in Ocaml
– Compilation : generating C code implementation
– using Quagga and XORP code base
• Modeling
–
–
–
–
Forwarding, tunneling
Administrative distance
Protocol interaction
Protocol migration
• Design and implementation of routing metalanguage
– Relational algebra vs. SQL
• Novel IGP design and testing
• What is the right mathematical setting for the
metalanguage?
Quadrants Model of
Algebraic Routing
[email protected]
[email protected]
WORK IN PROGRESS
Languages for defining Languages
A space of Routing Languages
Routing Languages
that can be expressed
in a fixed meta-language
Question: What is a good formalism for the space of routing languages?
Mind the Gap
Metarouting.
tgg & Sobrinho (2005)
Sobrinho’s Routing
Algebra (2003)
Semiring routing (1970’s …)
Shortest paths (1950’s)
Maze Solving (1800’s)
Sobrinho’s QoS
Algebra (2002)
BGP analysis
(mid 1990’s  present)
3 Basic Structures
O  pre - ordered set
O  ( ,  )
Blue = optional properties
Antisymmetric
Total
Bounded
…
S  semigroup
S  (,)
commutative
selective
has identity element
has absorbtive element
…
F 
T  (, F )
has identity
closed under composition
idempotent
…
Two Approaches to Path Weight
path p  i1 , i2, , ik , ik 1
Algebraic
w(i1 , i2 )
i1
w(i2 , i3 )
i3
i2
…
w(ik , ik 1 )
ik
ik 1
w( p)  w(i1 , i2 )  w(i2 , i3 )    w(ik , ik 1 )
f i1 ,i2
a
i1
Functional
f i2 ,i3
i2
i3
…
f ik ,ik 1
ik
w( p)  f ik ,ik 1 ( ( f i2 ,i3 ( f i1 ,i2 (a))) )
ik 1
Two Approaches to Path “Selection”
p
i
j
q
Ordered weights
w( p)  w(q) ?
Algebraic
w( p)  w(q)
Quadrants Model
Bisemigoup
Order Semigroup
(S , S )
(O, S )
Semigroup Transforms
(S , T )
Order Trasforms
(O, T )
Coverage
Bisemigroup
Vast literature on semiring
routing, starting in 1970’s
Order Semigroup
Sobrinho QoS Algebras.
ToN 2002.
Ordered Semigroups
Non-commutative structures
Semigroup Tranforms
Monoid endomporphisms
M. Minoux (1976)
Order Transforms
Sobrinho Routing Algebras.
SIGCOMM 2003.
CRASH COURSE in Semigroups

a nonempty set
 : (   )  
a binary operation
This operation must be associative:
a, b, c   : (a  b)  c  a  (b  c)
S  (,)
is a semigroup
Semigroup Examples
Boolean :
Powerset :
B  ({T , F},)

P ()  (2 ,)

Free semigroup:
free ()  ( ,)
Projections:
left ()  (, left )
a left b  a
B  ({T , F},)

P ()  (2 ,)

is concatenation
right ()  (, right )
a right b  b
Some (Optional) Properties
Commutative (comm):
a, b   : a  b  b  a
Idempotent (idem):
a   : a  a  a
Selective (sel):
a, b   : a  b {a, b}
Special Elements (Optional)
Neutral element
 
b   :   b  b   b
If it exist, then it is unique.
Absorbing element
 
b   :   b  b    
If it exist, then it is unique.
Note: if
 
, then the semigroup is trivial,
  {}
Examples revisited
Name
B
B
P ()
P ()
left ()
right ()
free ()

{T , F }
{T , F }

2

2









 
F
T
f

properties
T
comm
idem
sel
F
comm
idem
sel

comm
idem
f
comm
idem
left
idem
sel
right
idem
sel

More Examples!
  
Name

min( n)
{0...n}
min
n
0
comm
idem
sel
max( n)
{0...n}
max
0
n
comm
idem
sel

0

comm
plus ( n) {0...n}  {}
properties
min[ 0,1]
[0,1]
min
1
0
comm
idem
sel
max[ 0,1]
[0,1]
max
1
comm
idem
sel
 [0,1]
[0,1]

0
1
0
comm
Natural Orders
If S is a commutative and idempotent,
then
( a  b)  ( a  a  b)
L

(a  R b)  (b  a  b)
Examples revisited
Name
B
B
P ()
P ()


{T , F }
{T , F }

2

2




 
F
T
f
T


f
F
(a  R b)  (b  a  b)

R

F T
TF


examples
  
Name

min( n)
{0...n}
min
n
0
max( n)
{0...n}
max
0
n
min[ 0,1]
[0,1]
min
1
0
max[ 0,1]
[0,1]
max
0
1
(a  R b)  (b  a  b)





R

Special Elements
Neutral element:
Absorbing element:
b   :   b  b   b
b   :   b  b    
(a  b)  (b  a  b)
From
we get
R

(a  L b)  (a  a  b)
b   :   b  
R

R

b   :   b  
L

:L

Property Translations
(,   )
S  (,)
associative
transitive
reflexive
idempotent
reflexive

idempotent and commutative
anti-symmetric

bounded
selective
total
Cayley Maps
( , C )
L

S  (  , )
( , C )
R

CL  { f b | b  , a   : f b (a)  b  a}
C  {g b | b  , a   : g b (a)  a  b}
R

Include mappings in metalanguage …
S
S
O
(,,)
(,  L ,)
(,, CL )
(,  L , C L )
T
… and property mappings
S
S
a  a  (b  a)
O
a  L (b  a )
T
a  a  f (a )
a  L f (a)
Acknowledgements
•
•
•
•
•
John Billings
Alex Gurney
Samuel Hym
Peter Sewell
Joao Sobrinho
([email protected])
([email protected])
([email protected])
([email protected])
([email protected])
Financial support thanks to
HELP WANTED
• 1 Studentship.
3 year PhD.
• 2 Post Doc
Research
Positions.
Suggested Reading (1)
• [JS_QoS]
– "Algebra and Algorithms for QoS Path Computation and Hop-byHop Houting in the Internet," João L. Sobrinho. In Proc. IEEE
INFOCOM 2001
– "Algebra and Algorithms for QoS Path Computation and Hop-byHop Routing in the Internet," João L. Sobrinho. IEEE/ACM
Transactions on Networking , pp. 541-550, August 2002.
• [JS_Alg]
– “Network Routing with Path Vector Protocols: Theory and
Applications” João L. Sobrinho. SIGCOMM 2003
– "An Algebraic Theory of Dynamic Network Routing," João L.
Sobrinho. IEEE/ACM Transactions on Networking, pp. 11601173, October 2005.
• [GS_MR]
– Metarouting. Griffin & Sobrinho. SIGCOMM 2005.
Metarouting project page: http://www.cl.cam.ac.uk/~tgg22/metarouting
Suggested Reading (2)
• Chapitre 1: Pré-semi-anneaux,
semi-anneaux et dioïdes
• Chapitre 2: Propriétés
combinatoires des (pré-)semianneaux
• Chapitre 3: Topologies des
ensembles ordonnés
• Chapitre 4: Résolution de systèmes
linéaires dans les dioïdes
• Chapitre 8: Répertoire de (pré)semi-anneaux et dioïdes
END