Flow%20Models,%20Optimal%20Routing,%20and%20Topological%20Design

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Section 5.4

• Flow Models, Optimal Routing, and Topological
  Design

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5.4.1 Optimal centralized Routing in Datagram
Network

• Diagraph G(V,A) is the model of a datagram
  network
• For each (i ,j ) ?A,let Cij be the capacity in
  data units/sec
• For each (i ,j ) ?A, let Fij be the flow in data
  units/sec
• For each origin i?V and destination j?V let w be
  the index for the O-D pair
• W be the set of O-D pairs

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5.4.1 Optimal centralized Routing in Datagram
Network

• Pw be the set of directed path from origin to
  destination of O-D pair w
• rw input rate , in data units/sec at the origin
  for OD pair w

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5.4.1 Optimal centralized Routing in Datagram
Network

• Let Xp be the flow on path p , ?p ?Pw and ?w ?W

r1
2
X4
X5
X1
X6
X7
3
1
r1
X2
X3
4
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5.4.1 Optimal centralized Routing in Datagram
Network
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5.4.1 Optimal centralized Routing in Datagram
Network
Dij ( Fij )
Cij
Fij
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5.4.1 Optimal centralized Routing in Datagram
Network

• Optimal Centralized Routing
• Object function
• To minimize the average delay in the system
• Other possible objective min maximum traffic in
  system
• By littles formula

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5.4.1 Optimal centralized Routing in Datagram
Network
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5.4.1 Optimal centralized Routing in Datagram
Network

• Assume Dij(Fij) is monotone increasing, convex
  and continuously differential for all (i,j)? A
• If each link may be modeled as an M/M/1 queue
  using Klein rock's independence assumption, and
  Jacksons Theorem

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5.4.1 Optimal centralized Routing in Datagram
Network
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5.4.2 Capacity Assignment Problem
Given
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5.4.2 Capacity Assignment Problem
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5.4.2 Capacity Assignment Problem
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5.4.2 Capacity Assignment Problem

• Weakness
• Cost-Capacity function(pij) is linear(actually,
  not linear)
• Capacities assigned is continuous ( capacities
  are chosen from a discrete set)

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Section 5.5

• Characterization of Optimal Routing

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5.5 Characterization of Optimal Routing
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5.5 Characterization of Optimal Routing
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5.5 Characterization of Optimal Routing
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5.5 Characterization of Optimal Routing

• Example 5.7

High Capacity C1
r
x1
1
2
x2
Low Capacity C2
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5.5 Characterization of Optimal Routing

• To
• Min cost function D(x) D1 (x2) D2 (x2),based on
  M/M/1
• Constraints x1 x2r , x1?0, x2?0
• Assume C1? C2 ? x1?x2 from intuition

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5.5 Characterization of Optimal Routing

• Case 1
• x1r, x20

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5.5 Characterization of Optimal Routing

• Case 2
• x1gt0 ,and x2gt0

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5.5 Characterization of Optimal Routing
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5.5.1 Traffic Control in High-Speed Networks

• Traffic control
• Flow control
• Congestion Control
• Congestion Avoidance
• If ?demandgtResource ?traffic control
• Resource
• Buffer space
• Bandwidth
• Processing capability at a nodes

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5.5.1 Traffic Control in High-Speed Networks

• Flow control
• Agreement between a source and a destination.As
  long as there are enough resources at the
  destination, the need to invoke flow control does
  not arise
• Example window control

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5.5.1 Traffic Control in High-Speed Networks

• Congestion control
• Is concerned with the intermediate nodes
• ExampleON/OFF control

eliff
Throughput
Congestion Avoidance attempts to operate resource
at the knee
knee
breakdown
Offered load
delay
Offered load
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5.5.1 Traffic Control in High-Speed Networks

• High speed Network
• Why cant we use existing traffic control schemes
  in HS network?
• Propagation delay ?5?s/1km
• exfixed packets of length 500 bits
• Tx speed 1Mbps
• one packets tx time 500/106500 ?s
• one packets in transit between AB
• Tx speed 1Gbps
• one packets tx time 500/1090.5 ?s
• 500/0.5 1000 packets

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5.5.1 Traffic Control in High-Speed Networks

• Feedback schemes relatively ineffective
• Processing is a bottleneck
• ATM technology is a candidate transfer technology
• Packet switching
• Fixed packet length(cells)
• Slotted system
• Virtual circuit based connections
• Enforcement schemes

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5.5.1 Traffic Control in High-Speed Networks
Leaky Bucket scheme
arrivals
Departure packet
Threshold
Token Pool
Token generator
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5.5.1 Traffic Control in High-Speed Networks

• Space priorities
• Push ort mechanism
• At a full buffer, high-priority pushes ort
  low-priority packet
• Partial buffer sharing
• If number packets in bufferltThreshold admin both
  kinds of packets, otherwise admit only class 1