Resource Allocation in Contention-Based Infrastructured and Ad-hoc Wireless Networks

Transcription

1 Resource Allocation in Contention-Based Infrastructured and Ad-hoc Wireless Networks Laura Giarré Universita di Palermo Joint works with I. Tinnirello (Università di Palermo), G. Neglia (Inria - France), R. Pesenti (Università di Venezia) and my students R. Badalamenti and F. G.La Rosa

2 A poet The breeze started cleansing their thoughts, joined their souls in an intertwined moment, a moment of pure joy and serenity to let them descend to their own pathways each one to its own harbor bringing with them a clearer vision on what's next 2

3 A writer From The dance of the two child souls: My name is Gabriel and I am a child soul who does not know how to pilot his host, who is looking from his treasure chest and, in this life, has brighten only few times, but those times were so beautiful that I would only talk about that. Let me tell you the story of this child soul and the years that, while watching others fighting for the possession of the host, was just basking in those moments of pure joy, waiting for the next opportunity to come. 3

4 A scientist Resource allocation in Contention-based networks Analysis with rational nodes: Infrastructured IEEE Networks Achieving distributed fair bandwith among nodes in non homogeneous bidirectional traffic to optimize throughput Game theoretical analysis and design Schemes for multi-hop topologies Wireless Ad-Hoc Networks Grouping contending nodes (TDMA approach) in combination with Carrier Sense to access the channel (CSMA/CA) Graph coloring solution to assign slots and game theoretical analysis 4

5 Infrastructured Networks Infrastructured Networks AP AP X X If station X tries to get all wireless resources no space for the other stations, including the AP! If station X leaves spaces to the AP also the other stations able to transmit. ki - desired up/down ratio for each station 5

6 Infrastructured Networks IEEE DCF as a Slotted Access protocol Distributed Coordination Function (DCF) regulates access to the shared medium: - dynamic adaptation of the contention windows (short term unfairness) - use of homogeneous contention parameters among the contending nodes Protocol operations summarized in terms of average access probability in a slotted channel (with uneven or even slot size) In each system slot, each station accesses with probability (and does not access with probability 1-). Most protocols make depending on the collision probability p, =f(p), as a tradeoff between channel wastes due to collisions and idle slots. Model Time. Actual Time 6

7 Infrastructured Networks Game Theoretic Approach Thanks to open source drivers and programmable cards, we propose a dynamic tuning of the contention parameters used by the nodes via a game-theoretic approach. AIM: To guarantee a fair resource sharing among the nodes, while optimizing the per-node uploading and downloading bandwidth. SOLUTION: Some DCF protocol EXTENSIONS able to cope with current resource sharing problems. A non cooperative game where the contending stations act as the players The stations works in saturated conditions and DCF can be modeled as a slotted access protocol while the station behavior is summarized in terms of per slot access probability 7

8 Infrastructured Networks Contention-based access 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) background STA -Payoff perceived by each station depends on the whole set of probability ( 1, 2, n ) chosen by all the stations ( 1, 2, n )->( i, p i ) with pi = 1(1 j ) ji Tagged STA i τ i AP Finite number N-1 of STA p i 8

9 Infrastructured Networks Node Payoff with Bidirectional Traffic Assumption: AP is a legacy station τ AP =f(p AP ) equally sharing the downlink throughput among the stations. For the i-station: Uplink throughput: S i u (, p i i i(1 ) pi )(1 E[ slot] AP ) P τ i Downlink throughput: S i d (, i p i ) x i AP (1 pap ) P E[ slot] τ i The utility function with ki in (0, ) J i (, p ) min( S i u, k S i d ) i i i 9

10 Infrastructured Networks Main Results Determination of Nash Equilibria and Pareto Optimality Mechanism design -> using of the AP to force desired equilibria Implementation of new DCF operations with best response strategy Implementation of Channel Monitoring functionalities (estimation of number of nodes and load conditions) Analysis of NE convergence and stability 10

11 Infrastructured Networks References - I.Tinnirello, L. Giarré, G. Neglia. MAC design for WiFi infrastructure networks: a game theoretic approach. IEEE Transaction on Wireless Communication, 8(19), pp , L. Giarré, G. Neglia, I. Tinnirello. Medium Access in WiFi Networks: Strategies of Selfish Nodes", IEEE Signal Processing Magazine (SPM), Vol. 26, Issue 5, pp , I. Tinnirello, L. Giarré, G. Neglia, The role of the Access Point in Wi-Fi networks with selfish nodes, IEEE GAMENETS, L. Giarré, G. Neglia, I. Tinnirello, Performance Analysis of Selfish Access Strategies on WiFi Infrastructure Networks, IEEE Globecom L. Giarré, G. Neglia, I. Tinnirello, Resource Sharing Optimality in WiFi infrastructure networks, IEEE CDC, I. Tinnirello, L. Giarré, G. Neglia. A Game Theoretic Approach to MAC Design for Infrastructure Networks, IEEE CDC,

12 Ad-hoc Networks Ad-hoc networks Suitable for a large number of applications: - from low-range sensor networks targeted to distributed monitoring - to high-range mesh networks targeted to build infrastructure-less transport networks. 12

13 Ad-hoc Networks Ad-hoc Networks Most ad-hoc networks rely on contention-based medium access protocols, regardless to the specific physical layer technology ( IEEE PHY or a/b/g/n PHY, defining available bandwidth, transmission power, modulation coding scheme..) The use of carrier sense and random backoff mechanisms is a simple and well-established solution to manage multiple access over a shared channel bandwidth. CSMA/CA protocols exhibit very poor performance for multihop transmissions (inter-link interference due to imperfect carrier sensing). 13

14 Ad-hoc Networks Ad-hoc Networks Reason for preallocating slots: to mitigate hidden nodes 14

15 Ad-hoc Networks Ad-Hoc networks Aim: Distributed resource allocation problems for multi-hop wireless networks. Approach: Combining the TDMA approach for grouping the contending nodes in non-interfering sets with the CSMA/CA approach (for managing the final access to the shared channel). Our Solution: determining the best number of slots in a frame and the best assignment of slots to different nodes via a map coloring problem. 15

16 Ad-hoc Networks Main Results Problem: Determine via a distributed protocol setting the number x of slots in a frame and the slots allocations, in order to maximize the per-node throughput in saturation conditions (greedy sources) Network transport capacity is critically affected by the number of slots x! Incompatibility constraints: all neighbors and hidden nodes on different colors only hidden nodes on different colors 16

17 Ad-hoc Networks References (Ad hoc networks) I. Tinnirello, L.Giarrè and R. Pesenti. Decentralized Synchronization for Zigbee Sensor Networks in Multihop topology. Necsys, L.Giarrè, F.G. La Rosa, R. Pesenti and I. Tinnirello. Coloring-based Resource Allocations in Ad-hoc Wireless Networks. Medhoc, I. Tinnirello, L. Giarrè, R. Badalamenti, F.G. La Rosa Utility-Based Resource Allocations in Multi-Hop Wireless Networks, NetGCoop,

18 Infrastructured Networks 18

19 Infrastructured Networks Infrastructure Networks with heterogeneous applications AP - All applications are bidirectional - Ki is modelling heterogeneous applications (k1!= k2) chat File download J i (τ i,p)=min(s u i,k i S di ) 1. Does a best response policy lead to a NE? 2. How should the AP share the downlink throughput? (choice of xi) 19

20 Infrastructured Networks Node Best Response S up <kis down S up =kis down S up >kis down ki=k=1, xi=1/n (τ, p) outcome br kixi 1 (1 k x i AP i ) AP where: τ AP =f(p AP ) is function of the strategy set (τ,p) 20

21 Infrastructured Networks Nash Equilibrium (ki=k=cost,xi=1/n) Proposition: The homogeneous strategy vector (τ *, τ *, τ * ) such that * n * kf(1 (1 ) ) * n n ( n k) f (1 (1 ) ) is the only Nash equilibrium in [0,1) n of the game with non-null utility. τ AP k= k=10 τ * k=50 Proof sketch: At the NE point, two conditions simultaneously hold: * k AP g( n ( n k) AP * N AP f( 1 (1 ) ) being f() decreasing in τ * starting from 0, and g() increasing in τ AP, a single intersection exists AP ) 21

22 τ AP Infrastructred Networks Nash Equilibrium (ki, xi=1/n) Proposition: For a given vector k=(k 1,k 2,..k n ) of application requirements, by equally sharing the downlink throughput, it exists a unique NE with non-null utility. τ1 k1=1, k2=2 1 0 k=10, k2= τ Proof sketch: At the NE point, N+1 conditions simultaneously hold: k1 AP 1 n ( n k1) AP k2 AP 2 n ( n k2) AP... kn AP n n ( n kn) AP AP f (1 (1 i )) The first N conditions represent a 1-dim curve in a N+1 space; the last one a surface.. 22

23 Infrastructred Networks Nash Equilibrium (ki, xi) Proposition: For a given vector k=(k 1,k 2,..k n ) of application requirements, and a given vector of downlink throughput coefficients (x1,x2..,xn), it exists a unique NE with non-null utility. 23

24 Infrastructred Networks Mechanism design Can the AP play the role of arbitrator in order to improve the performance of its access network? 1. Using τ AP as a configuration parameter (rather than f(p AP )) Employing a downlink scheduling xi according to the application requirement k=(k1,k2,k2,..,kn) 24

25 Infrastructred Networks Tuning the AP channel access probability The best response is The NE becomes the intersection between an hyperplane T AP =c and the parametric curve identified by the best response equations 25

26 Infrastructred Networks Per-station total bandwidth 26

27 Infrastructred Networks Downlink Scheduling AP AP k=1 k=10 k=1 k=10 By equally sharing the downlink, stations with higher k get an higher total up-down capacity A fairer criterion could be an equal repartition of the perstation up+down capacity! S di =x i S AP with The unique NE still exists 27

28 Infrastructred Networks Scheduling policies AA: Application Agnostic The AP is not aware of the per station application requirements (Ki). AP equally shares the downlink throughput among the stations (S d =S AP /n). At NE each station perceives a throughput of (1+k i )S d AW: Application aware The AP is aware of Ki. AP can allocate and heterogeneous downlink throughput S i d =x i S AP with 28

29 Infrastructred Networks Game-based MAC Scheme implementation and evaluation Each station has two estimators for probing uplink and downlink load conditions The station best response depends not only on the application requirements (Ki) but also on the uplink load (n) and downlink load (Tap) Cases 1) AP as a legacy 2) AP implementing the adaptive tuning mechanism of the channel access probability Algorithms: AA (Application Agnostic scheduling) and AW (Application aware scheduling) 29

30 Infrastructred Networks Numerical Example: Resource Repartition -Custom-made simulation platform; -Interval update:0.5 seconds; b; P=1500 bytes Standard DCF 30

31 Infrastructured Networks Effects of best response strategy (Time-varying Application requirements ) k1=k2=1 k2=5, k1=1 31

32 Infrastructred Networks Final Remarks on Infrastructured Networks Contention-based access protocols can be defined in terms of non-cooperative games - Standards are somehow limited with the proliferation of open-source drivers 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 AP can be used for mechanism design, in order to force desired equilibrium conditions - by tuning its channel access probability - by employing scheduling policies for improving the network fairness 32

33 Ad-Hoc Networks 33

34 Ad-hoc Networks Ad hoc Networks Reason to preallocating time slots: to mitigate hidden nodes 34

35 Ad-hoc Networks Ad-hoc Networks Minimum Graph Coloring Minimum Graph Coloring (MGC) problem on an incompatibility graph, built on the basis of network topology G = (V,E) V: nodes i of the network, E: pairs of nodes He is the Incompatibility graph type I (V, Fe), where for each e 2 E : F e ={(j,k): i V s.t. (j,i),(i,k) E} (j,k) frame may collide if transmitted simultaneously H e =G 2 : all nodes have non-interfering allocations and we can guarantee a collision-free throughput proportional to r/x H0 is the Incompatibility graph type II (V, F0), where for each e 2 E : F 0 ={(j,k): i V s.t. (j,i),(i,k) E, but (j.k) ɇ E} (j,k) collide and reciprocally hidden H =G 2 -G: visible nodes share the same allocations 35

36 Ad-hoc Networks Coloring Algorithms Select and Compare (SC): 1. First coloring Randomly pick a color from a list of available colors. 2. Conflict Resolution If none of your (1-hop or 2-hop) neighboring nodes has chosen the same color, keep it as definitive color, otherwise remove it form the list and try again the next step. 3. List update If the color list is empty, add new colors. The list is updated starting from min( c+1, xmax) color, where c=max(neighboring node colors) Choose the First Available color (CFA) : Instead of randomly picking a color from the available ones, each node first updates the list of available colors and then selects the color with the lowest index 36

37 Ad-hoc Networks Example of colored network A network topology colored with different CFA maps for the incompatibility graphs G,G 2, G 2 -G 37

38 Ad-hoc Networks Coloring-based + Contention-based allocations Neighbour nodes on the same color contend for channel access e.g.yellow nodes on the purple cluster have to share the same frame slot Nodes with a number of neighbour colors lower than the frame size, might content for extra slots e.g. the cyan node pointed out by the arrow might try to transmit on the green slot (with success, if destination is not the red node connected to the green one) 38

39 Ad-hoc Networks Contention strategies within a clique Nodes could be motivated in using heterogeneous access probabilities (using protocols such as the IEEE EDCA) for delivering more traffic. We consider then a game-theoretical analysis of intra-clique contention. The impact of heterogeneous access probabilities have been considered for 1-hop wireless networks, but this problem has not been explicitly addressed for multi-hop networks. 39

40 Ad-hoc Networks Contention-based allocations as a non-cooperative game Consider the channel sub-set of resources available for a cluster of visible nodes (i.e. the assigned color + the available extra colors) -Contending stations in visibility = players 1,2 3,4 1,2 3,4 1,2 3, 4 -Channel access probability τ = player strategy Game definition: M players, [0,1] M set of strategies, node payoff (J1, J2,, JM) -Payoff perceived by each station depends on the whole set of probability ( 1, 2, M ) chosen by all the stations ( 1, 2, M )->( i, p i ) with pi = 1(1 ji j ) Station 1 and 2 may transmit with homogeneous probability equal to ½ or with heterogeneous probability (not a traditional backoff) Station 1, 2 may contend for the extra slot (with a potential interference due to nodes 3 and 4) 40

41 Ad-hoc Networks Node Payoff - Which performance metric has to be optimized?? - Throughput i (1-p i )/slot: for a given pi, station i best response leads to i = 1 If exists j =1 (p i =1)->resource waste and equilibrium with 0 payoff! - Throughput + energy cost/penalty: [ i (1-p i )-c i i ]/slot Non-zero payoff at equilibrium states, but arbitrary cost definitions or penalty functions - Our idea: consider not only the transmission process of a given node, but also the transmission process of the neighbors, i.e. the whole transport capacity of the cluster!! Nodes belonging to a multi-hop network need neighbor nodes for forwarding their traffic. Therefore, they are interested not only in their transmissions, but also in the neighbor transmissions 41

42 Station Utility (How to express the transport capacity of a cluster)? i the per-slot packet generation probability = i (1-p i ) is the transmission troughput (per-slot packet delivery probability of node i) each node i has average queue (where K is the buffer size) The higher is the transport capacity of the cluster, the lower are the cluster queues, then J= J1=J2= JM= - maxi{qi} (Nodes are prevented from using i=1 to leave channel resources to the other nodes) Utility -> the same for all the nodes in the cluster -> expressed as the opposite of the residual traffic cost 42

43 Ad-hoc Networks Utility as common function The utility function is common to all the stations (clique transport capacity) Each node has to relay on others for delivering and receiving its own traffic, then there is no point in implementing greedy behaviors Such common utility prevents other malicious behaviors such as the signaling of wrong traffic generation rates Each node is induced to collaborate by the need of maximizing the common utility, so we assume that in each notification message about neighbor nodes and traffic rates nodes, they also communicate their current strategy i (even if an estimation can be also implemented) 43

44 Ad-hoc Networks Best response queue length For a given node i, let x the station different from i with the longest queue Q x (x=argmax j i Q j ) br = i x /[ i x + x (1- x )] e.g. 4 nodes, [1, 2, 3, 4]=[0.01, 0.02, 0.03, 0.04] [ 1, 2, 3, 4]=[0.1, 0.1, 0.1, 0.1] Let station 1 be the station in blue 44

45 Ad-hoc Networks Heterogeneous case A best response strategy for the heterogeneous case (being x the index of the node experiencing the worst congestion, the longest queue): We noted, by repeating such a best response strategy for all the nodes, that in a finite number of steps the system converges towards a Nash Equilibrium (NE) point, in which all the clique queues are equalized. The equilibrium point is not unique and depends on the initial strategies of the nodes. 45

46 Nash Equilibrium 46 For a given vector of traffic generation rate =[ 1, 2.. N ], let Q=[Q 1, Q 2, Q N ] be the vector of queues corresponding to a specific vector of strategies =[ 1, 2, N ]. Proposition 1: If there exist at least two stations with saturated buffers, i.e. i, j {1, 2, N} with ij : Q i = Q J =K, then is a NE. Proposition 2: Let m be the index of the station experiencing the maxium traffic m. If it exists m* (0,1) verifying the condition then the vector of strategies with is a NE in which all the stations have non saturated buffers. Ad-hoc Networks 1 ) ( 1 ) ( N m i i m i m m N m m N m m i m i m i m m m i m i * * * ) (

47 Ad-hoc Networks Performance Evaluation Given a graph He, the maximum number of needed colors is upper bounded by e +1, where e is the maximum node degree of the graph. Let x e the number of colors required in H e and c e the number of cliques. After coloring, the throughput sum perceived by all the nodes belonging to each clique is obviously r/x e, thus resulting in a total throughput equal to: Average per-node throughput as tot /n = r / x e E[d e ] (E[d e ] = n/c e represents the average after coloring clique size). 47

48 Ad-hoc Networks Performance Evaluation Comparison of the saturation (collision free) theoretical bounds with the best throughput values measured after 10 different CFA coloring runs 48

49 Ad-hoc Networks Performance Evaluation (coloring + contention allocations G2+ and G2-G+) Average throughput under the SC coloring scheme Average throughput under the CFA coloring scheme 49

50 Ad-hoc Networks Some Observations on the coloring 1. Coloring G can be useless, because the carrier sense functionality is already able to avoid interference among adjacent nodes. For the CFA case, the performance obtained under the G coloring are even worse than the ones obtained with the CSMA/CA protocol, because the slot allocations may synchronize hidden nodes for lower packet generation rates. 2. Coloring G2 can be more efficient (CFA case) or less efficient (SC case) than coloring G2-G, according to the network topology and to the effectiveness of the coloring scheme in selecting a limited number of colors and/or leaving a limited number of bottlenecks. 3. If we allow node i to transmit during the slots associated to its color and to colors different form the ones of its adjacent nodes (schemes G2+ and G2-G+), we improve the network performance with a game theoretic conflict resolution 50

51 Ad-hoc Networks Final Remarks on the GT analysis Actual implementation of best response requires to estimate i (prob. of generating a packet) and i (prob. of accessing channel) of neighbors nodes We are currently investigating: Best response implementation based on simple channel measurements and minimal signaling overhead To extend the game theoretical analysis not only to one single cluster, but also to the entire network To analyze property of NE and to force convergence to a desired optimum via a mechanism design algorithm 51

52 From PALERMO THANKS! 52