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Section 5.4

Section 5.4. Flow Models, Optimal Routing, and Topological Design. 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 C ij be the capacity in data units/sec

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Section 5.4

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  1. Section 5.4 Flow Models, Optimal Routing, and Topological Design

  2. 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

  3. 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

  4. 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 r1 1 X2 X3 4

  5. 5.4.1 Optimal centralized Routing in Datagram Network

  6. 5.4.1 Optimal centralized Routing in Datagram Network Dij ( Fij ) Cij Fij

  7. 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 little’s formula

  8. 5.4.1 Optimal centralized Routing in Datagram Network

  9. 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 Jackson’s Theorem:

  10. 5.4.1 Optimal centralized Routing in Datagram Network

  11. 5.4.2 Capacity Assignment Problem Given

  12. 5.4.2 Capacity Assignment Problem

  13. 5.4.2 Capacity Assignment Problem

  14. 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)

  15. Section 5.5 Characterization of Optimal Routing

  16. 5.5 Characterization of Optimal Routing

  17. 5.5 Characterization of Optimal Routing

  18. 5.5 Characterization of Optimal Routing

  19. 5.5 Characterization of Optimal Routing • Example 5.7 High Capacity C1 r x1 1 2 x2 Low Capacity C2

  20. 5.5 Characterization of Optimal Routing • To: • Min cost function D(x)= D1 (x2)+ D2 (x2),based on M/M/1 • Constraints: x1*+ x2*=r , x1*0, x2*0 • Assume C1 C2  x1*x2* from intuition

  21. 5.5 Characterization of Optimal Routing • Case 1: • x1*=r, x2*=0

  22. 5.5 Characterization of Optimal Routing • Case 2: • x1*>0 ,and x2*>0

  23. 5.5 Characterization of Optimal Routing

  24. 5.5.1 Traffic Control in High-Speed Networks • Traffic control • Flow control • Congestion Control • Congestion Avoidance • If demand>Resource traffic control • Resource • Buffer space • Bandwidth • Processing capability at a nodes

  25. 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

  26. 5.5.1 Traffic Control in High-Speed Networks • Congestion control • Is concerned with the intermediate nodes • Example:ON/OFF control eliff Throughput Congestion Avoidance attempts to operate resource at the “knee” knee breakdown Offered load delay Offered load

  27. 5.5.1 Traffic Control in High-Speed Networks • High speed Network • Why can’t we use existing traffic control schemes in HS network? • Propagation delay 5s/1km ex:fixed packets of length 500 bits • Tx speed : 1Mbps one packets tx time = 500/106=500 s one packets in transit between A&B • Tx speed : 1Gbps one packets tx time = 500/109=0.5 s 500/0.5 = 1000 packets

  28. 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

  29. 5.5.1 Traffic Control in High-Speed Networks Leaky Bucket scheme arrivals Departure packet Threshold Token Pool Token generator

  30. 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 buffer<Threshold admin both kinds of packets, otherwise admit only class 1

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