Internet Traffic Policies and Routing

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Internet TrafficPolicies and Routing

• Vic Grout
• Centre for Applied Internet Research (CAIR)
• University of Wales
• NEWI Plas Coch Campus, Mold Road
• Wrexham, LL11 2AW, UK
• v.grout_at_newi.ac.uk
• http//www.newi.ac.uk/Computing/Research

NEWI North East Wales Institute of Higher
Education - Centre for Applied Internet Research
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Introduction and Overview

• Optimisation of network traffic requires care.
  Without it
• An unrealistically simplified problem may be
  considered
• The wrong problem may be solved entirely
• This presentation considers three examples
• (Very briefly) Access control lists (ACLs)
  (again!)
• Cost minimisation in wireless networks
  (straightforward)
• Routing protocols (more serious?)
• The first two (simple) examples point the way to
  the third

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Example 1Access Control Lists (ACLs)
Routers
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Example 1Access Control Lists (ACLs)
Rules
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Example 1Access Control Lists (ACLs)
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Example 1Access Control Lists (ACLs)
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Example 1Access Control Lists (ACLs)
Optimal? No
considerable duplication
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Example 1Access Control Lists (ACLs)
True optimum can only come from taking a global
view
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Example 2Traffic Routing in Wireless Networks
Wireless nodes Feasible links
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Traffic Routing in Wireless NetworksEdge/Node
(Add) Constraints

• Distance matrix, D (dij i,j?V)
• Maximum distance, dmax
• Line-of-sight matrix, ? (?ij i,j?V)
• Edge viability matrix, V (vij i,j?V)
• Node viability vector, v (vi i?V)
• Boolean
• relay permitted/not permitted
• fixed
• (equipment already installed)
• or
• integer
• maximum degree

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Traffic Routing in Wireless NetworksPath/Load
(Drop) Constraints

• Path length matrix, P (pij i,j?V)
• maximum number of links between i and j
• Minimal degree vector, ? (?i i ?V)
• number of (other) nodes to which i must be
  connected
• Traffic matrix
• Load matrix (N)
• Load limit matrix (edges)
• Load limit vector (nodes)
• For any (valid) N

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Traffic Routing in Wireless NetworksFeasible
Links
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Traffic Routing in Wireless NetworksMST Solution
Number of switches
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Traffic Routing in Wireless NetworksMST
Formulation

• Graph, G (V, E)
• vertices (nodes), edges
• Cost matrix, C (cij)
• 1?i,j?n, n ?V?
• Tree, T ? E
• Link matrix,
• Find T such that

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Traffic Routing in Wireless NetworksMRP
Formulation

• Minimal Relay Problem
• Network, N ? E. Link matrix, ?N, as before
• Relay vector,
• Find Nsuch that

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Traffic Routing in Wireless NetworksMDRP
Formulation

• Minimal Degree Relay Problem
• Network degree vector,
• Find Nsuch that
• (
  )

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Traffic Routing in Wireless NetworksMRP/MDRP
Algorithms

• MRP and both MDRP NP-complete
• (minimal vertex cover)
• Add algorithm
• Edge matrix,
• Valency vector
• Drop algorithm

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Traffic Routing in Wireless NetworksAdd
Algorithm

• for all i ? V do siN 0
• for all i, j ? V do ?ijN 0
• find i such that vi max j vj
• siN 1
• while there exists j such that sjN 0 do
• for all? j ? V
• such that eij 1 and sjN 0 do
• ?ijN 1
• sjN 1
• find i such that
• vi-?iN max j (vj-?jN) where sjN 1

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Traffic Routing in Wireless NetworksDrop
Algorithm

• Initialization
• for all? i, j ? V do ?ijN 1
• Reduction
• while there exists i, j
• such that ?iN gt ?i and ?jN gt ?j do
• find? i, j such that ?iN-?i min k (?kN-?k)
• ?ijN 0

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Traffic Routing in Wireless NetworksMST Solution
Number of switches
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Traffic Routing in Wireless NetworksAdd Solution
Number of switches
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Traffic Routing in Wireless NetworksDrop
Solution
Heavily loaded links
Number of switches
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Example 3Routing Algorithms
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Example 3Routing Algorithms
Routers exchange link status information
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Example 3Routing Algorithms
Routers exchange link status information
?
?
?
?
?
?
?
?
to build a complete knowledge of the current
network topology.
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Example 3Routing Algorithms
Then each router
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Example 3Routing Algorithms
Then each router
calculates the shortest path to each of the
others in turn
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Example 3Routing Algorithms
Is this optimal?
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Example 3Routing Algorithms
Is this optimal?
No!
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Routing AlgorithmsLevels of Optimality

• Possible to attempt optimisation on three levels
• Path-optimal
• The shortest path is calculated independently
  between each pair of routers
• Network-optimal
• For each router, paths are chosen to optimise the
  combined routing for that router
• Domain-optimal
• For all routers, paths are chosen to optimise
  routing across the entire domain
• Increasingly difficult by level
• complexity
• distributed knowledge

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Routing AlgorithmsRouters and Networks
Network
Network
Network
Network
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Routing AlgorithmsPrinciples of Optimal Routing

• In what follows, the notation i?j is used to
  represent the single link from i to j and a?b for
  the path between end points a and b. a?b i?j
  means that traffic from a to b is carried by the
  link i?j. ? is used as shorthand for for all
  or for every and ? for there is or there
  exists.
•  
• Define a domain D (N, T) by a set of n networks
  N 1,2,..,n and a traffic matrix T (tab
  a,b?N) where tab represents the traffic
  requirement from a to b. (In situations in which
  traffic cannot be measured or predicted, we can
  set T (1), that is tab 1 ? a,b?N.)
•  
• A protocol P (M, c), acting on a domain D, is
  defined by a metric matrix M (mij i,j?N) and a
  cost function c(t,m). mij specifies the measure
  of i?j used by P and c(t,m) the cost of carrying
  traffic t on a link of metric m.

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Routing AlgorithmsDistributions and Routings

• A distribution X ( a,b,i,j ? N), acting on a
  domain D, is defined as
•  
•  
• Define a path-routing Pab ( i,j? N) for
  a?b as ? i,j?N.
• Define a network-routing Qa ( b,i,j? N)
  for a as ? b,i,j?N.
• Define a domain-routing R ( a,b,i,j? N) as
  ? a,b,i,j?N.

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Routing AlgorithmsPath Optimality

• The cost of i?j under a path-routing Pab is
• The path-cost of Pab is then given by
• If Pab minimises Cab, Pab is said to be
  path-optimal for a?b. X is path-optimal if Pab
  minimises Cab ? a,b?N. If X is path-optimal then
• is minimised.
• Easy Dijkstras algorithm (OSPF)

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Routing AlgorithmsNetwork Optimality

• The (known) traffic on i?j under a
  network-routing Qa is
• and its cost given by .
  The network-cost
• of Qa is then
• If Qa minimises Ca, Qa is said to be
  network-optimal for a. X is network-optimal if
  Qa minimises Ca ? b?N. If X is network-optimal
  then
• is minimised.
• k-shortest paths NP-complete
• distributed ?

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Routing AlgorithmsDomain Optimality

• The traffic on i?j under a domain-routing R is
  and
• its cost given by . The
  domain-cost of R is then
• If R minimises C, R is said to be domain-optimal.
  X (R) is domain-optimal if R is domain-optimal.
  If X is domain-optimal then
• is minimised.
• (k-shortest paths)2 NP-complete?
• centralised? ?

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Routing AlgorithmsNetwork Routing Heuristics

• Example Local search starting from Dijkstra SPA
• for y 1 to m do
• find R(x) ((x)yrij) such that Cxy
  minxyCxy using DSPA
• repeat
• MaxGain 0
• for y 1 to m do
• for i 1 to n do
• for j 1 to n do
• if Cx Cx(i?jy) gt MaxGain then
• MaxGain Cx Cx(i?jy)
• y y i i j j
• if MaxGain gt 0 then
• R(x) R(x)(i?jy)
• until
• MaxGain 0

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Routing AlgorithmsDomain Routing Heuristics

• Simple to apply heuristics
• example local search
• example starting from DSPA
• But how do we implement a centralised algorithm
  on a distributed basis?
• Agents?
• Ants?
• Some very preliminary work currently being
  pursued
• generally on a small scale
• But early days

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Concluding Remarks

• Traffic flows in internets are large and complex
• Difficult to
• model
• simulate
• optimise
• And thats assuming were dealing with the right
  problem in the first place!
• At present, we may not be getting the most from
  our systems
• Fresh thinking required?
• There is a lot of work to do

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Any questions?
Thank you

• Vic Grout
• Centre for Applied Internet Research (CAIR)
• University of Wales
• NEWI Plas Coch Campus, Mold Road
• Wrexham, LL11 2AW, UK
• v.grout_at_newi.ac.uk
• http//www.newi.ac.uk/Computing/Research

NEWI North East Wales Institute of Higher
Education - Centre for Applied Internet Research