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Intuitions on Proportional Fairness

Intuitions on Proportional Fairness. Proportional fair rate. Proportional fair rate per unit charge. Relation between these two: replace users r by Wr identical sub-users, construct the proportionally fair allocation over all sub-users, and then provide to user r the aggregate rate

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Intuitions on Proportional Fairness

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  1. Intuitions on Proportional Fairness Proportional fair rate Proportional fair rate per unit charge Relation between these two: replace users r by Wr identical sub-users, construct the proportionally fair allocation over all sub-users, and then provide to user r the aggregate rate allocated to its sub-users. then the resulting rates are proportional fair per unit charge. ECE department, Rice University Jingpu Shi

  2. Intuitions on Proportional Fairness Definition: A vector of rates x is proportionally fair if it is feasible and if for any other feasible vector x*, the aggregate of proportional changes is zero or negative P3: maximum aggregate throughput Aggregate change: P2: x2 = 3x1 x2 P1: maximum throughput P2: proportional fairness P3: equal throughput x2 + 3x1 = 0 P1: x2 = x1 , Max-min fairness x1 ECE department, Rice University Jingpu Shi

  3. Maximizer of aggregate log utility is the maximizer ECE department, Rice University Jingpu Shi

  4. A a B b Proportional Fairness In CSMA networks: the case of two contending flows. T(Bb) T(Aa) = T(Bb) P1 P2 P3 D C T(Aa) (1) Achievable log utility is bounded by P1. (2) If T(Aa)+T(Bb) = constant, P2 achieves maximum utility. (3) For achievable throughput, maximum is achieved around P3. ECE department, Rice University Jingpu Shi

  5. Packet Decoding Channel Error Probability 100% Transmission range Distance ECE department, Rice University Jingpu Shi

  6. Carrier Sensing Probability Carrier is sensed 100% Interference range Distance ECE department, Rice University Jingpu Shi

  7. AIS in real networks A a B b ECE department, Rice University Jingpu Shi

  8. X = two-way handshake = four-way handshake Simulations with 802.11 protocol Measurements every 400 ms Fair ! Short term Unfair ! Long term unfair ! ECE department, Rice University Jingpu Shi

  9. Modeling AIS (general equations) ECE department, Rice University Jingpu Shi

  10. Modeling AIS (Non-backlogged case) e is the probability that the transmission queue is empty. ECE department, Rice University Jingpu Shi

  11. Validation – Model vs Simulation With RTS/CTS Without RTS/CTS ns - Flow B 1000 1000 model - Flow B ns - Flow B TFA model - Flow B 800 800 TFA Packet Throughput (pkt/s) 600 600 400 400 ns - Flow A ns - Flow A model - Flow A model - Flow A TFA 200 200 TFA 0 0 200 400 600 800 1000 1200 1400 200 400 600 800 1000 1200 1400 Data Payload Size (bytes) ECE department, Rice University Jingpu Shi

  12. Analysis of AIS A a B b B b B b A a B b B b B b A a B b B b B b • The collision probability of flow A a can be accurately computed assuming that the first packet arrives at a random point in time • The collision probability of flow B  b is zero ECE department, Rice University Jingpu Shi

  13. Occurrence Probability • We compute the occurrence probability of each scenario • Random throw two flows, given they are connected, what are the probability that each of these scenarios occurs. ECE department, Rice University Jingpu Shi

  14. Probabilities of 3 groups of scenarios • Problematic scenarios are highly likely to occur ! 1 SC 0.9 AIS 0.8 SIS 0.7 Probability (conditioned) 0.6 0.5 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Normalized distance (sender-receiver distance/ transmission range) ECE department, Rice University Jingpu Shi

  15. 0.5 Most of actively used hops are close to the maximum TX range ! 0.4 0.3 Probability 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Hop distance / TX range Hop distance distribution in a multi-hop network 300 nodes - 2000 m x 2000 m – Random waypoint – DSDV ECE department, Rice University Jingpu Shi

  16. Transition probability for SIS class ECE department, Rice University Jingpu Shi

  17. 0.16 0.14 0.12 Probability 0.1 0.08 0.06 0.04 0.02 0 0 1 2 0 3 1 4 2 stage B 3 5 4 5 6 stage A 6 Model Vs. Simulation System’s bi-stability, with large probability, the system is in one of the two stable states. ECE department, Rice University Jingpu Shi

  18. First time segment is transmitted TCP retransmissions A B GW Two-hop Node’s severe TCP Penalty TCP DATA TCP ACK TCP ACK received (Accumulated ACK) 335 TCP Congestion Window 330 MAC Packet drop (Max Retry Limit reached) 325 320 TCP sequence number [kB] 315 TCP Timeouts TCP penalty 310 305 300 295 80 85 90 95 100 105 Time [sec] ECE department, Rice University Jingpu Shi

  19. Some Model Details Occurrence probability. Markov stable state probability. Binary transmission matrix. Transition matrix. Throughput Average channel state duration State duration ECE department, Rice University Jingpu Shi

  20. TCP throughput • J. Padhye, V. Firoiu, D. Towsley, and J. Kurose. ModelingTCPthroughput: a simplemodel and its empirical validation. ACMSIGCOMM, September 1998. ECE department, Rice University Jingpu Shi

  21. CWmin at 1st hop nodes A B GW Basic Topology RTS/CTS On Increase CWmin • Severe unfairness with Default CWmin, log utility = -0.6931 • Improved fairness with increased CWmin at B, log utility = 0.6523 • Log utility upper bound = 3.2917 ECE department, Rice University Jingpu Shi

  22. A->GW B->GW C->GW CWmin at 1st hop nodes Two Branches RTS/CTS ON Increase CWmin Increase CWmin • Severe unfairness with default CWmin, log utility = -3.8 • Improved fairness with larger CWmin at 1st hop nodes, log utility = -1.23 • Bounding log utility = 3.2 ECE department, Rice University Jingpu Shi

  23. Large Topologies: Long Hop Chain 1st hop CWmin = 128 • Severe unfairness with default CWmin, log utility = -11.9763 • Improved fairness with larger CWmin, log utility = -6.1721 • Log utility is bounded by 3.6931 ECE department, Rice University Jingpu Shi

  24. Large Topologies: Long Hop Chain (one queue) 1st hop CWmin = 128 • Severe unfairness with Default CWmin, log utility = -14.0015 • Improved fairness with larger CWmin, log utility = -6.1415 • Log utility is bounded by 3.6931 ECE department, Rice University Jingpu Shi

  25. TFA Network • 802.11 access and backhaul serving tier. • Wireless card: • SMC 2532-b 802.11b 200 mW power • Antenna: • 15 dBi omni-directional • Iperf ECE department, Rice University Jingpu Shi

  26. Unfair Contention in Mesh Two TCP flows contend. B A GW TCP traffic using Iperf v.1.7.0 ECE department, Rice University Jingpu Shi

  27. Prior Work Related to Unfairness Analysis • Two classes of prior work related to our analysis on unfairness: • Studies on fairness with perfect, TDMA or Slotted Aloha MAC: • [Radunovic TMC 04 ] [Huang MobiHoc 01 ] [Chen Infocom 06] [Chen Infocom 05] [Tan IEEE Comm. Letters 06] [Tassiulas INFOCOM 02] [Kar IEEE Transactions on Automatic Control 04]. • Studies on fairness with CSMA or IEEE 802.11 MAC. • Papers reporting poor performance of IEEE 802.11. • [Sundaresan, Ad Hoc Networks Journal 04] [Nandagopal MOBICOM 00] [Chen MOBICOM 06] [Luo MOBICOM 00] [Karn ARRL/CRRL ARCNC 90] [Bharghavan SIGCOMM 94] [Kanodia MobiHoc 02] [Wang INFOCOM 05] [Carvalho,MOBICOM 04] • We systematically study all possible two-flow scenarios, and analytically capture unfairness contention between the two flows. • Papers reporting poor performance of TCP. • [Gerla, WMCSA 99] [Tang MMTWCW 99] [Raniwala INFOCOM 07] [Xu IEEE Communications Magazine, 01] [Xu WOWMOM 02] [Xu MOBICOM 03] [Holland MOBICOM 99] [Fu INFOCOM 03] [Yu MOBICOM 04] [Gambiroza MOBICOM 04] • We identify unfair contention in the basic scenario, and develop analytical models to study two flow contention. ECE department, Rice University Jingpu Shi

  28. Prior Work Related to Our Solution • Prior work on the use of multiple channels. • [Adya Broadnets 04] [ Bahl MobiCom04] [Jain IC3N01] [Nasipuri 99] [So MobiHoc 04] [Wu I-SPAN 00] • All these protocols are designed to improve fairness, and do not provided any sort of lower throughput bound for individual flows. • Prior work on contention window policy. • [Cali TON 00] [Kuo INFOCOM’ 03] [Chen INFOCOM 2001] [Nafaa WCNC 05] [Romdhani WCNC 03] • None of these identified the role of 1st-hop contention window in shifting queuing of mesh network and improving fairness. ECE department, Rice University Jingpu Shi

  29. Multi-hop flow topology IEEE 802.11 networks, Ns 2, 50 nodes, 10 flows, 1m/s, 1000x1000m UDP load: 30 pkts/s ECE department, Rice University Jingpu Shi

  30. Multi-channels to solve starvation, multi-hop flows • Multi-channel protocols do not necessarily address starvation. • Our objective: improves per-flow throughput ECE department, Rice University Jingpu Shi

  31. Challenges in solving starvation • Single channel starvation problem • Several transmissions can occur on one channel, thus inherit single-channel starvation problems. • Multi-channel coordination problem • Separate transmissions to reduce interference. • Coordinate their transmission. • How to achieve these two goals. ECE department, Rice University Jingpu Shi

  32. Multi-channel coordination:missed channel reservation • Channel reservation of one flow may not be heard by its neighbors on a different channel. Example A a B Bb x x x x Channel N Aa (First identified by Junmin So etc, Mobihoc 04) ECE department, Rice University Jingpu Shi

  33. Multi-channel coordination:receiver on different channel • Receiver is missing (on a different channel) Example A B C • Hard to synchronize channel hopping schedule. ECE department, Rice University Jingpu Shi

  34. Challenges in solving all the problems MMAC (Junmin So etc, Mobihoc 2004) Common time reference, infrastructure supported Flow 1 Flow 2 RTS/CTS/DATA/ACK (Channel 1) … … t RTS/CTS/DATA/ACK (Channel 2) Flow N RTS/CTS/DATA/ACK (Channel 3) Channel contention phase Data Transmission phase Problems 1) Duration of negotiation phase 2) Receiver missing 3) Single channel starvation problems ECE department, Rice University Jingpu Shi

  35. AMCP general description • Asynchronous Multi-channel Coordination Protocol • Asynchronous • One common control channel, multiple data channels. • Separate control exchange from data transmission. • Provide a common frequency reference for nodes. Data channel 3 DATA/ACK Data channel 2 DATA/ACK Data channel 1 DATA/ACK RTS/CTS Control channel RTS/CTS RTS/CTS ECE department, Rice University Jingpu Shi

  36. AMCP Principle 1 • Reserve common channel and data channel differently. • Improve efficiency, avoid collision on data channels. Data channel 2 Data + ACK Data channel 1 Control channel RTS/CTS Defer transmission on control channel Reserve Data 2 ECE department, Rice University Jingpu Shi

  37. AMCP Principle 2 t0 t1 Data channel 2 data + ACK Data channel 1 Control channel control Contend for 1, 2 Contend for 2 Max Tx time • Only contend for channels clear of traffic ECE department, Rice University Jingpu Shi

  38. AMCP Principle 3 success collision • Self-learning channel hopping • Stick to the channel given successful transmission • Contend for a different channel given collision ECE department, Rice University Jingpu Shi

  39. 1 2 A a … N Lower throughput bound analysis step 1 • Construct a worst-case low throughput scenario with N interferers: A cannot sense the activity of the interferers ECE department, Rice University Jingpu Shi

  40. Lower throughput bound analysisstep 2 • Assume aggregate transmission attempt distribution is Poisson. • Compute conditional collision probability perceived by this flow. ECE department, Rice University Jingpu Shi

  41. Lower throughput bound analysis step 3 • Use our single-channel CSMA analytical model to compute the (minimum) throughput of this flow. M. Garetto, J. Shi, and E. Knightly. Modeling Media Access in Embedded Two-Flow Topologies of Multi-hop Wireless Networks. In Proc. ACM MobiCom, Cologne, Germany, August 2005. ECE department, Rice University Jingpu Shi

  42. Protocol PerformanceSingle-hop flows, multi-hop topology 12 data channels, 100 nodes, 50 one-hop flows 1000mx1000m area Flows starve with 80211 Log U = -90.9 MMAC, Log U = -3.7 AMCP = 13.2 Maximum Log U = 34.65 ECE department, Rice University Jingpu Shi

  43. Protocol performance (multi-hop flows with mobility) 50 nodes, 10 flows, 1m/s, UDP traffic: 30 pkts/s AMCP outperforms 802.11 and MMAC Log: 802.11 = -24.2 MMAC = -21.05 AMCP = -15.3 Max = -10.2 ECE department, Rice University Jingpu Shi

  44. Protocol performance (multi-hop flows with mobility) AMCP outperforms 802.11 and MMAC Log: 802.11 = -56.2 MMAC = -74.3 AMCP = -54.5 Max = -32.4 Scenario: 20 nodes, gateway download to each node. Gateway is saturated. ECE department, Rice University Jingpu Shi

  45. Channel switching overhead ECE department, Rice University Jingpu Shi

  46. Inefficiency due to channel switching constraints Some packets may be stuck in the queue due to incapabilities of swift channel switching Example B A C C B C C ECE department, Rice University Jingpu Shi

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