Resource sharing optimality in WiFi infrastructure networks

Transcription

1 Resource sharing optimality in WiFi infrastructure networks Ilenia Tinnirello 1, Laura Giarré 1, Giovanni Neglia 2 1 Università di Palermo, Italy, 2 INRIA, France (giarre@unipa.it) November 2009 MIT 1

2 Summary In WiFi networks nodes compete for accessing a shared channel (random access protocol - Distributed Coordination Function) DCF is in principle fair -> unfair behaviors emerge (nonstandard configurations, term performance) critical network topology, short Infrastructure Network: assuming that a station can dynamically change its strategy by tuning his contention parameters based on channel observation -> access strategies are able to reach NE equilibrium conditions, which are PO The station strategies converge toward values maximizing a per-node utility function, maintaining performance fairness DCF extension: Design, Implementation and Run-time performance analysis November 2009 MIT 2

3 Motivation -Despite of the Wi-Fi certification, several cards exhibit very heterogeneous performance, due to arbitrary protocol implementations Experimental Assessment of the Backoff Behavior of Commercial IEEE b Network Cards, G Bianchi et al, INFOCOM Proliferation of open-source drivers encouraged users to modify transmission power, routing schemes, protocol operation.. Lynksis Dlink 122 Dlink 650 Realtek Centrino Ralink Linux Windows Mbps Payload =1470 byte, Expected Throughput= 6.1Mbps -Is it possible to exploit AP central role for correcting/discouraging selfish behaviors? November 2009 MIT 3

4 Cooperation in WLAN WLAN operation intrinsically assumes different forms of cooperation among nodes, including: Forwarding frames belonging to other nodes Consuming energy for other nodes, for improving network connectivity Controlling transmission power for improving spatial reuse Arbitrating the access to the same shared medium Listen before talk principle, for avoiding interference with other nodes A B B waits until the medium is idle + a random backoff delay Shared channel Are nodes always available for cooperation??? November 2009 MIT 4

5 Wi-Fi Networks IEEE Technology defines both the PHY and the MAC Layer: several modulation/coding schemes have been standardized for coping with different channel Layer: a random access protocol (named Distributed Coordination Function) has been standardized based on the CSMA paradigm Sense channel before transmit; Send explicit ACK Backoff to avoid station synchronization and channel capture Simultaneous transmissions interfere: loss of the transmitted frames. November 2009 MIT 5

6 802.11DCF Each station is CONTENDING the channel: a station with a new packet to be transmitted monitors channel activity. If the channel is idle for the Distributed InterFrame Space (DIFS), the station transmits. The receiving station signals the successful reception with an acknowledgment frame (ACK). The ACK is transmitted at the end of reception within a time: Short InterFrame Space (SIFS). collision avoidance (avoid synchronized accesses to the channel): random deferments of packet transmissions (DCF) November 2009 MIT 6

7 Collision Avoidance DCF employs the collision avoidance to reduce the probability that two or more competing stations simultaneously transmit causing packet corruption The station monitors the channel until it is idle for a DIFS, then the station schedules the packet transmission after a random time interval: backoff. The backoff interval is an integer number of backoff slots. The number of waiting slots is called backoff counter in the range (0, w-1), where w is the contention window. DCF: binary contention signal - each node doubles its CW upon a collision and sets it to its base value upon a successful transmission November 2009 MIT 7

8 DCF as a Slotted Access Protocol (1) Model Time Actual Time -Carrier sense synchronizes transmissions of waiting stations and protocol operations can be summarized in terms of average access probability -In each system slot, each station accesses with probability access with probability 1- ) (Does not - depends on the collision probability p and on the average CW (Contention Window) value. -For a given p, it can be increased by using non-standard CW values! -Station strategy can be represented by the tuning of the transmission probability November 2009 MIT. 8

9 DCF as a Slotted Access Protocol (2) Model Time. Actual Time Is the probability that a tagged station accesses the channel during the slot Is the average backoff interval, depending on the collision probability p November 2009 MIT 9

10 DCF as a Slotted Access Protocol (3) Model Time. Actual Time -Uneven slot duration (empty slot), T (busy slot) -Assuming fixed length packets (P bits), each station gets: ( 1 p)p (1 p) P p) [1 (1 )(1 bits/slot or bits/sec (1 )(1 p)] T November 2009 MIT 10

11 Motivation for GT analysis Extensions of DCF (EDCA) allow the AP to set heterogeneous contention windows -> we assume that nodes are able to adapt their contention windows according to rational strategies Techniques to estimate the network status and develop monitoring functionalities are now available in literature Repartition between uplink and downlink (Kim et al.) resources (not only maximizing) November 2009 MIT 11

12 DCF as a non-cooperative game -Contending stations = players -Channel access probability τ = player strategy Game definition: N players, [0,1] N set of strategies, node payoff (J1, J2,, JN) -Payoff perceived by each station depends on the whole set of probability ( 1, 2, n) chosen by all the stations ( 1, 2, n)->( i, pi) with pi = - pi collision probability -> aggregated information on other stations 1 (1 j i j ) November 2009 MIT 12

13 Previous results Access to shared wireless channel has been modeled considering an ad hoc mode operation Utility function used combines throughput and cost related to collision rates [Cagaly et al.], [Chen et al] or energy consumptions [Zhang et al.] In infrastructure networks individual performance may be easily related to overall network performance: (artificial -> induced by punishment) or intrinsic in the traffic scenario. November 2009 MIT 13

14 Previous results: Node Payoff -Which performance metric has to be optimized?? -Throughput: for a given pi, station i best response leads to i = 1 J i S i (1 )(1 i p i i(1 pi ) P ) [1 (1 )(1 i p )] T i S i max (1 p T i ) P If exists j=1 (pi=1)->resource collapse Equilibria with 0 payoff! - Improvement : other choice of payoff with a penalty (Cagaly et al) : J ( ) (Zhang et al): energy consumption cost i S i c i i November 2009 MIT 14

15 Previous results: Node Payoff With these different costs Results: Non-zero payoff at equilibrium states, but arbitrary cost definitions or penalty functions (i.e. energy consumption is not always an objective for the stations) -Our idea: consider jointly transmission and reception process!! Nodes belonging to a network are usually interested not only in transmitting, but also in receiving packets! November 2009 MIT 15

16 Reference Scenario 1) AP as referee for detecting and punishing cheaters by dropping ACK frames! Mechanism design for forcing desired equilibria, by setting the ACK dropping rate and the punishment thresholds 2) User applications involved in both uplink/downlink data throughput S: J i =min{s up, k S down } (we assume AP equally shares downlink bandwidth among all the stations, i.e. S down = 1/N S AP ) τ=1 is no more a best response, since it corresponds to S down = 0! November 2009 MIT 16

17 Unidirectional case - NEs Defining as payoff the uplink throughput for the i-th station (Cagaly et al) proved that The Nash equilibria are all and only the vectors of strategies such that - > two different set of NEs: or -> very poor performance -> throughput is zero November 2009 MIT 17

18 Unidirectional case - Results We prove that there is a unique outcome maximizing the social cost Such outcome is homogeneous and Pareto optimal. Where November 2009 MIT 18

19 Unidirectional case - Results Sketch of the proof- 1) We observe that the social utility is null for the sets of strategies while it is strictly positive otherwise, for the set of strategies (every player has a positive uploading rate) 2) We prove that the social utility cannot be maximum for a non homogeneous outcome in A. 3) Focusing on homogeneous outcome, we can consider the single variable function. Studying the sign of its derivative we observe that there is a unique point of maximum: 4) Finally we prove Pareto optimality, taking a different with at least a player better of than in \n non-homogenous -> and proving that is November 2009 MIT 19

20 REMARKS: Unidirectional case - Results 1) The outcome is not a NE, in fact every player can increase its utility by increasing its own access probability. 2) Optimal value: (Bianchi et al.) We want to design a game so that is a NE This case requires some punishment policies in order to prevent that each station i accesses the channel with probability equal to 1. November 2009 MIT 20

21 Mechanism Design AP is the common receiver for all the stations Suppressing the ACK corresponds in triggering ACK timeouts at the station side which are interpreted as collisions (artificial) The punishment strategy is energy saving No jamming is introduced (as in Cagaly et al.) We use this mechanism to induce a NE. November 2009 MIT 21

22 Payoff with AP dropping ACK Utility function of a given station i: where we recall that the AP drops an ACK frame transmission with probability November 2009 MIT 22

23 Proposition The outcome is a Pareto optimal Nash equilibrium of the game, when the ACK suppression scheme is implemented with November 2009 MIT 23

24 Bidirectional Traffic We assume that the AP equally shares the downlink throughput among the stations For the i-station Uplink throughput: Downlink throughput: The utility function November 2009 MIT 24

25 Bidirectional Payoff Function S up =S down k=1 (τ, p) outcome br k AP n ( n k) AP S up <S down S up >S down where: τ AP =f(p AP )= f(1-(1- τ)(1-p )) in turns is function of the strategy set (τ,p) November 2009 MIT 25

26 Looking for NEs Remark 1: from is a monotonic increasing function starting is a monotonic decreasing function starting from Remark 2: is not monotonic and has a single maximum value with November 2009 MIT 26

27 Bidirectional Payoff Function with homogeneous outcomes S up =S down k=1, (τ, τ,, τ ) outcome Single homogeneous outcome S up <S down S up >S down perceived by each station Note that is not fixed (NON UNILATERAL STRATEGY) November 2009 MIT 27

28 Non unilateral Strategy The intersection of the two curves depends on k. Let kx be the value of k for which The limit condition is reached for kx=20 (n=2) or kx=11 (n=10) For smaller k, the NE is PO. For larger k, stations are mainly interested to the uplink bandwidth and the system tends to the unidirectional case (where the NE is not PO) November 2009 MIT 28

29 Best Response Player utility Ji is maximized for such that is the solution of the following implicit equation: November 2009 MIT 29

30 Nash Equilibrium and Pareto Optimality Proposition: The homogeneous strategy vector (τ *, τ *, τ * ) such that * * n kf(1 (1 ) ) * n ( n k) f (1 (1 ) is the only Nash equilibrium in [0,1) n of the game with non-null utility. Proposition: If the solution for of the Best Response equation is lower or equal to the homogeneous NE (τ +, τ +, τ + ) is Pareto optimal. n ) November 2009 MIT 30

31 Non unilateral Strategy The intersection of the two curves depends on k. Let kx be the value of k for which The limit condition is reached for kx=20 (n=2) or kx=11 (n=10) For smaller k, the NE is PO. For larger k, stations are mainly interested to the uplink bandwidth and the system tends to the unidirectional case (where the NE is not PO) November 2009 MIT 31

32 AP Optimal Strategy The system performance could be further improved by also tuning the AP CW to a fixed value? The best response for all the stations is equal to the NE For, maximinzing the NE utility, a single optimal τ* AP can be found, that can be approximated for as November 2009 MIT 32

33 Heterogeneous applications among nodes Utility function: Uniqueness of the solution only experimentally found Best Response: Approximating solution: November 2009 MIT 33

34 Design of DCF extension Stations motivated in tuning their contention windows as a function of the AP channel access probability. Current selfish cards try to maximize their own throughput using fixed CW SMALLER We design some DCF extensions, in order to enable each contending station to dynamically tune its contention windows according to a best response strategy. November 2009 MIT 34

35 Implementation issues -Let each station dynamically change the CW according to the best response strategy at regular time intervals t -Best response adjustments in CW (i.e. in τ) for a generic station require two preliminary estimators: -the number of contenting stations n By filtering the number of different source headers in a given time window -the AP channel access probability τ AP By filtering the number of AP transmissions in a given time window br ( t 1) n( t) AP ( n( t) ( t) k) AP ( t) November 2009 MIT 35

36 Newtwork status Estimators: contending stations B = observation window Different stations: cyan, red, green the : the measured number of different stations during B (in the above example is equal to 3) The estimated number of contenting stations is obtained via an AR(1): November 2009 MIT 36

37 AutoTuning the observation time window B The observation time window B has to be carefully tuned, in order to guarantee a reasonable probability to catch all the contending stations in each measurement interval. To this purpose, we propose to run two different n estimators in parallel, based on two different measurement intervals (e.g. B and 2B) To adaptively increase or decrease the B value according to the comparison between the two estimates November 2009 MIT 37

38 Newtwork status Estimators: AP access probability Let the cyan be the AP For measuring the AP access probability, if B is the observation window, counting tx transmissions of the AP during B, and a total number of collisions C we get (in the example: B= 21, C=1, tx=3, then the measured probability is 3/(21-1)) Then,the estimated number of the AP channel access probability is obtained with an AR(1): November 2009 MIT 38

39 Numerical Example: Resource Repartition -Custom-made simulation platform; -Interval update:0.5 seconds; b; P=1500 bytes Best Response Scheme Standard DCF November 2009 MIT 39

40 Numerical Example: Aggregated Throughput for various k November 2009 MIT 40

41 Run-time Performances To assess our scheme effectiveness in time-varying load conditions -> several simulation experiments on a custom-made C++ simulation platform g physical rate, with data rate 6Mbps The contention windows used by the AP have been set to the legacy values CWmin=16 and CWmax=1024 All the experiments have been obtained by averaging 10 different simulation lasting 10s The measurement interval has been set to 500 channel slots (in average 300ms) The contending stations may activate and de-activate dynamically November 2009 MIT 41

42 Numerical Example: Resource Repartition in Time-varying Load conditions AP aggregated downlink throughput almost independent on n! throughput 1/n downlink November 2009 MIT 42

43 Numerical Example: Resource Repartition in Time-varying Load conditions STANDARD DCF Short term unfaindrness AP and reference station: identical behavior November 2009 MIT 43

44 Numerical Example: Effects of best response strategies on AP aggregated throughput and a given node throughput (K=0.2) the average AP throughput remains approximately constant during the whole experiment station 1 throughput obeys the desired repartition November 2009 MIT 44

45 Conclusions -Greedy behaviors of current users /cards are due to myopic definitions of node utility functions! -In infrastructure networks, the node strategies converge to Nash equilibria with non-zero payoff, by considering both uplink and downlink bandwidth requirements of user applications -Best response strategies can be easily implemented in current open-source cards, by using network state estimators based on channel monitoring November 2009 MIT 45

46 Final Comments on Interdisciplinarity Start with seminars to build a common language Exchange some tools (GT) Discuss some open problems (Selfish nodes on wifi) Together, find solutions Talk, discuss, be open minded November 2009 MIT 46

47 Related Literature S.W. Kim, B.S. Kim, Y. Fang, ``Downlink and uplink resource allocation in IEEE wireless LANs'',Proc. of IEEE Conf. on Vehicular Technology, Jan. 2005, Dallas, vol. 54, pp M. Cagalj, S. Ganeriwal, I. Aad, J.P. Hubaux, ``On selfish behavior in CSMA/CA networks'', Proc. of IEEE Infocom, March 2005, Miami, vol. 4, pp L. Chen, S.H. Low, J. Doyle, ``Contention Control: A Game- Theoretic Approach'', Proc. of IEEE Conf. On Decision and Control, Dec. 2007, New Orleans, pp G. Zhang, H. Zhang, ``Modelling IEEE DCF in wireless LANs as a dynamic game with incompletely information'', Proc. of Conf. on Wireless, Mobile and Multimedia Networks, Jan. 2008, Mumbai, pp G. Bianchi, ``Performance analysis of the IEEE DCF, IEEE JSAC, 2000, pp November 2009 MIT 47

48 Our contributes GIARRE' L., NEGLIA G., TINNIRELLO I. (2009). Medium Access in WiFi Networks: Strategies of Selfish Nodes. IEEE SIGNAL PROCESSING MAGAZINE, September 2009 GIARRE' L., NEGLIA G., TINNIRELLO I. (2009). Performance Analysis of Selfish Access Strategies on WiFi Infrastructure Networks. In: Proceedings of IEEE GLOBECOM. Honolulu, Hawaii, November 2009 GIARRE' L., NEGLIA G., TINNIRELLO I. (2009). Resource sharing optimality in WiFi infrastructure networks. In: Proceedings of IEEE CDC, Shangai, December 2009 TINNIRELLO I., GIARRE' L., NEGLIA G. (2009). The Role of the Access Point in Wi-Fi Networks with Selfish Nodes. In: Proceedings of GameNets09, Istanbul, may 2009 November 2009 MIT 48

49 Invitation to come to Palermo: Game theory meeting November 2009 MIT 49