# 01/16/2007ECE department, Rice University Jingpu Shi 1 Intuitions on Proportional Fairness Proportional fair rate per unit charge Proportional fair rate.

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01/16/2007ECE department, Rice University Jingpu Shi 1 Intuitions on Proportional Fairness Proportional fair rate per unit charge Proportional fair rate 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.

01/16/2007ECE 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 x2 x1 P1: x2 = x1, Max-min fairness P2: x2 = 3x1 P3: maximum aggregate throughput Aggregate change: P1: maximum throughput P2: proportional fairness P3: equal throughput x2 + 3x1 = 0

01/16/2007ECE department, Rice University Jingpu Shi 3 Maximizer of aggregate log utility is the maximizer

01/16/2007ECE department, Rice University Jingpu Shi 4 Proportional Fairness In CSMA networks: the case of two contending flows. A a Bb (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. T(Aa) T(Bb) C P1 P2 P3 T(Aa) = T(Bb) D

01/16/2007ECE department, Rice University Jingpu Shi 5 Packet Decoding Distance Channel Error Probability 100% Transmission range

01/16/2007ECE department, Rice University Jingpu Shi 6 Carrier Sensing Distance Probability Carrier is sensed 100% Interference range

01/16/2007ECE department, Rice University Jingpu Shi 7 AIS in real networks B b Aa

01/16/2007ECE department, Rice University Jingpu Shi 8 Simulations with 802.11 protocol Measurements every 400 ms X = two-way handshake = four-way handshake Long term unfair ! Fair ! Short term Unfair !

01/16/2007ECE department, Rice University Jingpu Shi 9 Modeling AIS (general equations)

01/16/2007ECE department, Rice University Jingpu Shi 10 Modeling AIS (Non-backlogged case) e is the probability that the transmission queue is empty.

01/16/2007ECE department, Rice University Jingpu Shi 11 Validation – Model vs Simulation 0 200 400 600 800 1000 200400600800100012001400 Packet Throughput (pkt/s) Data Payload Size (bytes) 0 200 400 600 800 1000 200400600800100012001400 ns - Flow B model - Flow B ns - Flow A model - Flow A With RTS/CTSWithout RTS/CTS TFA ns - Flow A model - Flow A TFA ns - Flow B model - Flow B TFA

01/16/2007ECE department, Rice University Jingpu Shi 12 Analysis of AIS B  b A  a B  b A  a B  b A  a 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

01/16/2007ECE 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.

01/16/2007ECE department, Rice University Jingpu Shi 14 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.10.20.30.40.50.60.70.80.91 Probability (conditioned) Normalized distance (sender-receiver distance/ transmission range) SC AIS SIS Probabilities of 3 groups of scenarios Problematic scenarios are highly likely to occur !

01/16/2007ECE department, Rice University Jingpu Shi 15 Hop distance distribution in a multi-hop network 300 nodes - 2000 m x 2000 m – Random waypoint – DSDV 0 0.1 0.2 0.3 0.4 0.5 00.10.20.30.40.50.60.70.80.91 Probability Hop distance / TX range Most of actively used hops are close to the maximum TX range !

01/16/2007ECE department, Rice University Jingpu Shi 16 Transition probability for SIS class

01/16/2007ECE department, Rice University Jingpu Shi 17 Model Vs. Simulation System’s bi-stability, with large probability, the system is in one of the two stable states.

01/16/2007ECE department, Rice University Jingpu Shi 18 Two-hop Node’s severe TCP Penalty First time segment is transmitted TCP retransmissions TCP Congestion Window TCP Timeouts TCP ACK received (Accumulated ACK) MAC Packet drop (Max Retry Limit reached) 295 300 305 310 315 320 325 330 335 80859095100105 Time [sec] TCP sequence number [kB] ABGW TCP DATA TCP ACK TCP penalty

01/16/2007ECE 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

01/16/2007ECE department, Rice University Jingpu Shi 20 TCP throughput J. Padhye, V. Firoiu, D. Towsley, and J. Kurose. Modeling TCP throughput: a simple model and its empirical validation. ACMSIGCOMM, September 1998.

01/16/2007ECE department, Rice University Jingpu Shi 21 Basic Topology RTS/CTS On 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 Increase CWmin ABGW CWmin at 1 st hop nodes

01/16/2007ECE department, Rice University Jingpu Shi 22 Two Branches RTS/CTS ON Severe unfairness with default CWmin, log utility = -3.8 Improved fairness with larger CWmin at 1 st hop nodes, log utility = -1.23 Bounding log utility = 3.2 Increase CWmin B->GW A->GW C->GW CWmin at 1 st hop nodes

01/16/2007ECE department, Rice University Jingpu Shi 23 Large Topologies: Long Hop Chain 1 st 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

01/16/2007ECE department, Rice University Jingpu Shi 24 Large Topologies: Long Hop Chain (one queue) 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 1 st hop CWmin = 128

01/16/2007ECE 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

01/16/2007ECE department, Rice University Jingpu Shi 26 Unfair Contention in Mesh Two TCP flows contend. GW A B TCP traffic using Iperf v.1.7.0

01/16/2007ECE 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.

01/16/2007ECE 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.

01/16/2007ECE 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

01/16/2007ECE 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

01/16/2007ECE 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.

01/16/2007ECE 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. Aa Bb x xx x Channel N AaB (First identified by Junmin So etc, Mobihoc 04) Example

01/16/2007ECE department, Rice University Jingpu Shi 33 Multi-channel coordination: receiver on different channel Receiver is missing (on a different channel) AB C Example Hard to synchronize channel hopping schedule.

01/16/2007ECE department, Rice University Jingpu Shi 34 Challenges in solving all the problems MMAC (Junmin So etc, Mobihoc 2004) Common time reference, infrastructure supported t RTS/CTS/DATA/ACK (Channel 1) RTS/CTS/DATA/ACK (Channel 2) RTS/CTS/DATA/ACK (Channel 3) Channel contention phase Data Transmission phase Flow 1 … Flow 2 Flow N … Problems 1) Duration of negotiation phase 2) Receiver missing 3) Single channel starvation problems

01/16/2007ECE 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. Control channel Data channel 1 Data channel 2 Data channel 3 RTS/CTS DATA/ACK RTS/CTS DATA/ACK RTS/CTS DATA/ACK

01/16/2007ECE department, Rice University Jingpu Shi 36 AMCP Principle 1 –Reserve common channel and data channel differently. Improve efficiency, avoid collision on data channels. RTS/CTS Data + ACK Control channel Data channel 1 Data channel 2 Defer transmission on control channel Reserve Data 2

01/16/2007ECE department, Rice University Jingpu Shi 37 AMCP Principle 2 –Only contend for channels clear of traffic control data + ACK Control channel Data channel 1 Data channel 2 t0t1 Contend for 2 Contend for 1, 2 Max Tx time

01/16/2007ECE department, Rice University Jingpu Shi 38 AMCP Principle 3 –Self-learning channel hopping Stick to the channel given successful transmission Contend for a different channel given collision success collision

01/16/2007ECE department, Rice University Jingpu Shi 39 Lower throughput bound analysis step 1 Construct a worst-case low throughput scenario with N interferers: A cannot sense the activity of the interferers Aa 1 2 N …

01/16/2007ECE department, Rice University Jingpu Shi 40 Lower throughput bound analysis step 2 –Assume aggregate transmission attempt distribution is Poisson. –Compute conditional collision probability perceived by this flow.

01/16/2007ECE 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.

01/16/2007ECE department, Rice University Jingpu Shi 42 Protocol Performance Single-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

01/16/2007ECE 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

01/16/2007ECE 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.

01/16/2007ECE department, Rice University Jingpu Shi 45 Channel switching overhead

01/16/2007ECE 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 A BCC B C C Example

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