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

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 For each (i,j )  A, let F ij 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 p.2

5.4.1 Optimal centralized Routing in Datagram Network P w be the set of directed path from origin to destination of O-D pair w r w =input rate, in data units/sec at the origin for OD pair w p.3

5.4.1 Optimal centralized Routing in Datagram Network Let Xp be the flow on path p,  p  Pw and  w  W r1r1 r1r1 X4X4 X2X2 X5X5 X1X1 X3X3 X6X6 X7X7 p.4

5.4.1 Optimal centralized Routing in Datagram Network p.5

5.4.1 Optimal centralized Routing in Datagram Network D ij ( F ij ) F ij C ij p.6

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 p.7

5.4.1 Optimal centralized Routing in Datagram Network p.8

5.4.1 Optimal centralized Routing in Datagram Network Assume D ij (F ij ) 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: p.9

5.4.1 Optimal centralized Routing in Datagram Network p.10

5.4.2 Capacity Assignment Problem Given p.11

5.4.2 Capacity Assignment Problem p.12

5.4.2 Capacity Assignment Problem p.13

5.4.2 Capacity Assignment Problem Weakness Cost-Capacity function(p ij ) is linear(actually, not linear) Capacities assigned is continuous ( capacities are chosen from a discrete set) p.14

Section 5.5 Characterization of Optimal Routing p.15

5.5 Characterization of Optimal Routing p.16

5.5 Characterization of Optimal Routing p.17

5.5 Characterization of Optimal Routing p.18

5.5 Characterization of Optimal Routing Example High Capacity C 1 Low Capacity C 2 r x1x1 x2x2 p.19

5.5 Characterization of Optimal Routing To: Min cost function D(x)= D 1 (x 2 )+ D 2 (x 2 ),based on M/M/1 Constraints: x 1 *+ x 2 *=r, x 1 *  0, x 2 *  0 Assume C 1  C 2  x 1 *  x 2 * from intuition p.20

5.5 Characterization of Optimal Routing Case 1: x 1 *=r, x 2 *=0 p.21

5.5 Characterization of Optimal Routing Case 2: x 1 *>0,and x 2 *>0 p.22

5.5 Characterization of Optimal Routing p.23

p.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 p.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 p.26

5.5.1 Traffic Control in High- Speed Networks Congestion control Is concerned with the intermediate nodes Example:ON/OFF control Throughput delay knee eliff breakdown Offered load Congestion Avoidance attempts to operate resource at the “ knee ” p.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 = 500/10 6 =500  s one packets in transit between A&B Tx speed : 1Gbps one packets tx time = 500/10 9 =0.5  s 500/0.5 = 1000 packets p.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 p.29

5.5.1 Traffic Control in High- Speed Networks arrivalsDeparture packet ThresholdToken Pool Token generator Leaky Bucket scheme p.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 p.31