Optimization and Contro of Network Duaity Mode of TCP/AQM Lijun Chen 02/08/2016
Agenda Utiity maimization and dua decompoition An introduction to TCP congetion contro A genera dynamica mode of TCP/AQM The duaity mode of TCP/AQM 2
Network mode A network modeed a a et L of ink with finite capacitie c { c, L} Shared by a et S of ource Each ource ue a ubet L L of ink, which define a routing matri 1 if L R 1 0 otherwie 110 R c 1 c 2 101 2 3 3
Utiity function Each ource attain a utiity U when tranmitting at rate q Non-decreaing function Given the et X of poibe aterna1ve, a func1on U : X R i a u1ity func1on repreen1ng preference rea1on among aterna1ve, if for a y, X, " i at eat a good a y" U U y To ue u1ity func1on to characterize preference i a fundamenta aump1on in economic 4
2 3 Reource aocation probem Each ource attain a utiity U when tranmitting at rate Utiity maimization Key 98 ma. t. U R c 1 1 + 2 c 1 1 + 3 c2 c 1 c 2 110 R 101 1 2 3 c c 1 2 5
Fairne For eatic traffic, U i aumed to be continuouy differentiabe, increaing and tricty concave q Diminihing return U Enure ome kind of fairne Eampe: U 1 α / 1 α, α > 0 q α 1, U og, proportiona fairne y / 0 q α, ma-min fairne 6
ma. t. U R c Poynomia-ovabe, if a the utiity and contraint information i provided. But impractica in rea network Have to eek decompoition to obtain ditributed agorithm 7
8 Lagrangian dua Conider the dua probem Low 99 q Congetion contro: given end-to-end price q Price update: given aggregate ource rate q Price can be updated and fed back to ource impicity c p p R U c R p U p D T c T o p + ma ma : min p R q 1 ' t q U t + + + ] [ 1 c t y t p t p γ R y
Agenda Utiity maimization and dua decompoition An introduction to TCP congetion contro A genera dynamic mode of TCP/AQM The duaity mode of TCP/AQM 9
TCP/IP protoco tack S D appication tranport network ink phyica Doe the part of tak pecific to the particuar appication Provide reiabe end-to-end tranmiion, congetion contro Provide end-to-end path between two end node routing Provide reiabe point-to-point tranmiion, channe acce Provide a ink for tranmitting bit between two node 10
Congetion contro Effect of congetion q Packet o, retranmiion, reduced throughput even congetion coape q Internet ha it firt congetion coape in Oct. 1986 throughput Congetion contro q Achieve high utiization q Avoid congetion q Fair bandwidth haring oad 11
Window-baed fow contro RTT Source 1 2 W 1 2 W time data ACK Detination 1 2 W 1 2 W time q ~ W packet per RTT round trip time q Lot packet detected by miing ACK q Source rate ~ W/RTT 12
TCP congetion contro Source cacuate cwnd from indication of network congetion q cwnd: congetion window ize Congetion indication q Packet oe q Deay q Packet mark Agorithm to cacuate cwnd q Tahoe, Reno, Vega, q DropTai, RED, REM, 13
TCP Reno Jacobon 90 cwnd SS CA time SS: Sow Start CA: Congetion Avoidance 14
Sow tart Start with cwnd 1 ow tart On each uccefu ACK increment cwnd cwnd cnwd + 1 Eponentia growth of cwnd each RTT: cwnd 2 cwnd Enter CA when cwnd > threh 15
Sow Start 1 RTT ender cwnd 1 2 data packet ACK receiver 3 4 5 6 7 8 cwnd cwnd + 1 for each ACK
Congetion Avoidance Start when cwnd threh On each uccefu ACK: cwnd cwnd + 1/cwnd Linear growth of cwnd each RTT: cwnd cwnd + 1 17
Congetion Avoidance ender cwnd 1 data packet receiver 2 ACK 1 RTT 3 4 cwnd cwnd + 1 for each cwnd ACKS
Packet Lo Aumption: o indicate congetion Packet o detected by q Retranmiion TimeOut RTO timer q Dupicate ACK at eat 3 Packet 1 2 3 4 5 6 7 Acknowedgement 1 2 3 3 3 3
Summary: Reno Baic idea q Genty probe network for pare capacity q Draticay reduce rate on congetion for every ACK { if W < threh then W++ ee W + 1/W } for every o { threh W/2 W threh } SS CA 20
TCP Vega Brakmo & Peteron 94 cwnd SS CA time for every RTT { if W/RTT min W/RTT < α then W ++ if W/RTT min W/RTT > α then W -- } for every o W : W/2 queue ize Congetion meaure: end-to-end queueing deay 21
Link agorithm AQM DropTai: drop coming packet when buffer i fu RED random eary detection: warn ource of incipient congetion by probabiiticay marking/ dropping packet q Probabiiticay drop packet q Probabiiticay mark packet marking 1 router B Avg queue 22
Agenda Utiity maimization and dua decompoition An introduction to TCP congetion contro A genera dynamica mode of TCP/AQM The duaity mode of TCP/AQM 23
TCP & AQM p t i t Two component q A ource agorithm: adjut the ending rate baed on congetion Impemented in TCP Tranmiion Contro Protoco q A ink agorithm: update a congetion meaure and end it back to the ource Congetion meaure: o probabiity and deay In form of o/mark or deay Carried out by AQM Active Queuing Management 24
Dynamic mode of TCP/AQM Notation q q q q t : ource rate at time t R : aggregate ource rate at ink t t : ink congetion meaure y p Source can oberve ony t and Link can oberve ony t and t q t R p t : end-to-end congetion meaure of ource q t p t y 25
p t i t q Dynamica mode p t t + 1 + 1 F G p t, t, q y t t q The eact form of F and G are determined by the pecific TCP/AQM protoco 26
Eampe: Vega D d + q for every RTT { if W/RTT min W/RTT < α then W ++ if W/RTT min W/RTT > α then W -- } for every o W : W/2 queue ize F: G: 1 t + t + if w t d t < α d 1 2 D 1 + 1 t 2 D if w t d t > α d t t + 1 t ee p t+1 [p t + y t/c - 1] + 27
Agenda Utiity maimization and dua decompoition An introduction to TCP congetion contro A genera dynamic mode of TCP/AQM The duaity mode of TCP/AQM 28
Duaity mode of TCP/AQM Denote by, p the equiibrium of the ytem p t t + 1 + 1 F G p t, t, q y t t The fied point equation define a reation q f q F > 0 i continuouy differentiabe, and Define a utiity function for each ource U f d, > q Uuay continuou, increaing and tricty concave q Ony determined by tcp agorithm F 0, q F / q 0 impicity 29
30 Eampe: Vega At equiibrium Utiity function d t d t w D t t < + + α if 1 1 2 ee 1 t t + d t d t w D t t > + α if 1 1 2 F: / d q d q d d D d d w α α α α d U og α
Define utiity maimization Dua probem min p o ma. t. R c Interpret ource rate a prima variabe and the congetion price p a dua variabe U D ma U R c p + p T c 31
32 The equiibrium ove the prima and dua, if it atifie KKT condition q The compementary ackne condition i atified by any AQM that tabiize the queue q AQM houd match input rate to capacity to maimize utiization at every botteneck ink, p 0 0 0 ' q U p c y p c y
Remark Revere engineering: the network a an optimization over, and different TCP/AQM protoco a ditributed prima-dua agorithm to ove the utiity maimization and it dua Forward engineering: guide new congetion contro deign q By carefuy chooing utiity function q By propoing better convergent agorithm 33
Can etend to provide a mathematica theory for network architecture and a genera approach to cro-ayer deign appication tranport network ink phyica Minimize repone time web ayout Maimize utiity TCP/AQM Minimize path cot IP Throughput-maima cheduing, Minimize SIR, ma capacitie, 34