Optimizing Client Association in 60 GHz Wireless Access Networks

Transcription

1 Optimizing Client Association in 60 GHz Wireless Access Networks G Athanasiou, C Weeraddana, C Fischione, and L Tassiulas KTH Royal Institute of Technology, Stockholm, Sweden University of Thessaly, Volos, Greece {chatw, georgioa,carlofi}@kthse; leandros@uthgr CWC Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

2 Outline Past, Present and Future in wireless communications 60 GHz millimeterwave wireless technology Optimizing resource allocation Distributed client association (DAA) Numerical analysis of DAA Conclusions and open research topics Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

3 Outline Past, Present and Future in wireless communications 60 GHz millimeterwave wireless technology Optimizing resource allocation Distributed client association (DAA) Numerical analysis of DAA Conclusions and open research topics Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

4 Growth of Mobile Traffic Source: Cisco VNI Mobile Forecast, 2013 Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

5 Growth of Mobile Traffic Source: Cisco VNI Mobile Forecast, : 70% mobile traffic growth compared to 2011 Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

6 Growth of Mobile Traffic Source: Cisco VNI Mobile Forecast, : 12 times the entire global internet traffic in 2000 Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

7 Growth of Mobile Traffic Source: Cisco VNI Mobile Forecast, : 13 times higher compared to 2012 Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

8 LTE Deployment Source: Cisco, 2013 Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

9 LTE Deployment Source: Cisco, 2013 End of 2013: # of mobile connected devices > earth population Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

10 LTE Deployment Source: Cisco, : 4G will represent 45% of mobile traffic Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

11 LTE Deployment Source: Cisco, : 2,7 GB mobile traffic per smartphone per month Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

12 Mobile Traffic Offloading Source: Cisco VNI Mobile Forecast, 2013 The amount of traffic offloaded from smartphones will be 46%, and the amount of traffic offloaded from tablets will be 71% in 2017 (Cisco, 2013) 90% of all cellular base stations will be small cells by 2016 (IEEE Spectrum Magazine, Informa Telecoms & Media, 2013) Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

13 Priorities High bandwidth High coverage Green Cheap Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

14 Mobile Data Offloading Cost reduction Data rate improvement Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

15 Mobile Data Offloading Cost reduction Data rate improvement Are there better solutions for mobile data offloading? Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

16 Outline Past, Present and Future in wireless communications 60 GHz millimeterwave wireless technology Optimizing resource allocation Distributed client association (DAA) Numerical analysis of DAA Conclusions and open research topics Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

17 60 GHz Wireless Access Networks Unlicensed short range transmissions in the 60 GHz millimeter wave (mmw) band Achieve Gbps communication Reduced interference Low-cost mmw transceivers Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

18 MillimeterWave Band History (JC Bose, 1897) High path loss High oxygen absorption Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

19 60 GHz Wireless Standards IEEE 80211ad WiGig IEEE c WirelessHD ECMA-387 Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

20 Applications Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

21 60 GHz to the Mobile 60 GHz small base stations (eg on lamp posts) Downlink offload traffic in 60 GHz band with uplink LTE feedback 60 GHz radio on mobile device in receive-only mode Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

22 Outline Past, Present and Future in wireless communications 60 GHz millimeterwave wireless technology Optimizing resource allocation Distributed client association (DAA) Numerical analysis of DAA Conclusions open research topics Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

23 Optimizing Client Association in 60 GHz Wireless Access Networks Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

24 Optimizing Client Association in 60 GHz Wireless Access Networks Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

25 Optimizing Client Association in 60 GHz Wireless Access Networks Goal: - Distributed client association and fair load distribution - find the client association that minimizes the maximum AP utilization Solution method: Based on Lagrangian duality theory Results: Theoretical and numerical analysis G Athanasiou, P C Weeraddana, C Fischione and L Tassiulas, Optimizing Client Association in 60 GHz Wireless Access Networks, arxiv: , Cornell University Library, 2013 [Online] Available: Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

26 System Model W System bandwidth 7 8 P ij Transmission power of AP i to client j 6 j = 1 5 i = R13 R33 3 (Q3) i = 2 9 i = 3 10 G ij N 0 I j M i N j Power gain from AP i to client j Power spectral density of the noise Interference spectral density at client j Set of clients that can be associated to AP i Set of APs that client j could be associated with N = {1,, N} APs and M = {1,, M} clients Achievable rate from AP i to client j M i is ( R ij = W log P ) ijg ij (N 0 + I j )W Q j is the demanded data rate of client j Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

27 System Model Channel utilization between AP i and client j is Utilization of AP i is β ij = Q j R ij j M i β ij x ij (x ij ) j Mi are binary decision variables, which indicate the client association { 1 if client j is associated to AP i x ij = 0 otherwise Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

28 Client Association Problem Formulation 7 8 i = j = minimize max i N j M i β ij x ij subject to i N j x ij = 1, j M i = 1 2 R13 R33 3 (Q3) i = 3 10 x ij {0, 1}, j M, i N j Variable: (x ij ) i N, j Mi Main problem parameters: (β ij ) i N,j Mi, (Q j ) j M, (R ij ) i N,j Mi Constraints: a) Client j can only be assigned to one AP, b) The decision variables are binary Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

29 Equivalent Epigraph Form 7 8 i = j = minimize t subject to j M i β ij x ij t, i N i N j x ij = 1, j M x ij {0, 1}, j M, i N j i = 1 2 R13 R33 3 (Q3) i = 3 10 Variable: (x ij ) i N, j Mi and t Main problem parameters: (β ij ) i N,j Mi Mixed integer linear program (MILP) Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

30 Solution Method Challenges Existing MILP solvers are centralized Typically based on global branch and bound algorithms the worst-case complexity grows exponentially with the problem size Even small problems, with a few tens of variables, can take a very long time Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

31 Solution Method Challenges Existing MILP solvers are centralized Typically based on global branch and bound algorithms the worst-case complexity grows exponentially with the problem size Even small problems, with a few tens of variables, can take a very long time Our approach: efficient, optimality? Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

32 Lagrangian Duality 7 8 Partial Lagrangian L ( t, x, λ ) = t + ( λ i i N ) β ij x ij t j M i ( = t 1 ) λ i + i N j M i N j β ij λ i x ij λ = (λ i ) i N : multipliers for the first set of inequality constraints j = 1 6 i = i = R13 R33 i = 3 3 (Q3) 10 Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

33 Lagrangian Duality 7 8 Partial Lagrangian L ( t, x, λ ) = t + ( λ i i N ) β ij x ij t j M i ( = t 1 ) λ i + i N j M i N j β ij λ i x ij λ = (λ i ) i N : multipliers for the first set of inequality constraints j = 1 6 i = i = R13 R33 i = 3 3 (Q3) 10 Dual function X = { x=(x ij ) j M,i Nj g ( λ ) = inf L ( t, x, λ ) t IR x X i N j x ij =1, x ij {0, 1}, j M i N j } Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

34 Dual problem Lagrangian Duality anchor maximize g(λ) = j M g j(λ) subject to i N λ i = 1 λ i 0, i N λ 3 λ 2 λ 1 λ = (λ 1, λ 2, λ 3 ) variables: λ = (λ i ) i N g j (λ) is the optimal value of the subproblem minimize i N j β ij λ i x ij subject to x j X j, with the variable x j Solved client j Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

35 Dual problem Lagrangian Duality anchor maximize g(λ) = j M g j(λ) subject to i N λ i = 1 λ i 0, i N λ 3 λ 2 λ 1 λ = (λ 1, λ 2, λ 3 ) variables: λ = (λ i ) i N anchor g j (λ) is the optimal value of the subproblem minimize i N j β ij λ i x ij subject to x j X j, x j3 X j with the variable x j Solved client j x j2 x j1 x j = (x j1, x j2, x j3 ) Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

36 Dual problem Lagrangian Duality anchor maximize g(λ) = j M g j(λ) subject to i N λ i = 1 λ i 0, i N λ 3 λ 2 λ 1 λ = (λ 1, λ 2, λ 3 ) variables: λ = (λ i ) i N anchor g j (λ) is the optimal value of the subproblem minimize i N j β ij λ i x ij subject to x j X j, x j3 X j with the variable x j Solved client j x j2 x j1 x j = (x j1, x j2, x j3 ) Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

37 Dual problem Lagrangian Duality anchor maximize g(λ) = j M g j(λ) subject to i N λ i = 1 λ i 0, i N λ 3 λ 2 λ 1 λ = (λ 1, λ 2, λ 3 ) variables: λ = (λ i ) i N anchor g j (λ) is the optimal value of the subproblem minimize i N j β ij λ i x ij subject to x j X j, with the variable x j Solved client j x j3 X j x j2 x j1 x j = (x j1, x j2, x j3 ) Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

38 Dual problem Lagrangian Duality anchor maximize g(λ) = j M g j(λ) subject to i N λ i = 1 λ i 0, i N λ 3 λ 2 λ 1 λ = (λ 1, λ 2, λ 3 ) variables: λ = (λ i ) i N anchor g j (λ) is the optimal value of the subproblem minimize i N j β ij λ i x ij subject to x j X j, x j3 X j with the variable x j Solved client j x j2 x j1 x j = (x j1, x j2, x j3 ) Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

39 Dual problem Lagrangian Duality anchor maximize g(λ) = j M g j(λ) subject to i N λ i = 1 λ i 0, i N λ 3 λ 2 λ 1 λ = (λ 1, λ 2, λ 3 ) variables: λ = (λ i ) i N anchor g j (λ) is the optimal value of the subproblem minimize i N j β ij λ i x ij subject to x j X j, x j3 X j with the variable x j Solved client j x j2 x j1 x j = (x j1, x j2, x j3 ) Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

40 Subgradient Method Proj subgradient method to the dual problem λ (k+1) = P ( λ (k) α k u (k)) anchor P : Euclidean projection onto the unit simplex Π = {λ i N λ i = 1, λ i 0} α k > 0 is the kth step size ( ) u (k) = u (k) i : a subgradient of g at λ (k), where i N λ 3 λ (k) α k u (k) λ 1 λ 2 λ (k+1) u (k) i = j M i β ij x ij, and (x ij ) j M i is the solution of the ith subproblems with λ = λ (k) Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

41 Subgradient Method Proj subgradient method to the dual problem λ (k+1) = P ( λ (k) α k u (k)) price update anchor P : Euclidean projection onto the unit simplex Π = {λ i N λ i = 1, λ i 0} α k > 0 is the kth step size ( ) u (k) = u (k) i : a subgradient of g at λ (k), where i N λ 3 λ (k) α k u (k) λ 1 λ 2 λ (k+1) u (k) i = j M i β ij x ij, and (x ij ) j M i is the solution of the ith subproblems with λ = λ (k) Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

42 Outline Past, Present and Future in wireless communications 60 GHz millimeterwave wireless technology Optimizing resource allocation Distributed client association (DAA) Numerical analysis of DAA Conclusions and open research topics Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

43 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

44 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

45 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

46 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

47 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

48 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

49 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

50 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

51 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

52 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

53 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

54 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

55 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

56 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

57 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

58 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

59 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

60 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

61 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

62 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

63 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

64 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

65 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

66 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

67 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

68 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

69 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

70 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

71 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

72 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

73 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

74 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

75 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

76 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

77 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

78 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

79 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

80 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

81 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

82 a DAA Illustration init price broadcast AP 3 determine local association clients signals its best AP AP i computes u i construct u / compute prices stopping criterion? YES AP 1 AP 2 NO Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

83 DAA Properties Proposition (Convergence) Let g (k) best denote the best dual objective value found after k subgradient iterations, ie, g (k) best = max{g(λ(1) ),, g(λ (k) )} Then, ɛ > 0 n 1 such that k k n ( d g best) (k) < ɛ Proof Standard convergence proof for the projected subgradient method [Boy07, 32][Ber99] Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

84 DAA Properties Theorem (Constant Duality Gap and Relative Duality Gap) The optimal duality gap of the mixed integer linear program is bounded as follows: p d (N + 1)(ϱ + max j M ϱ j), where ϱ = max i N,j Mi β ij and ϱ j = min i Nj β ij Moreover, the relative duality gap (p d )/p diminishes to 0 as M Proof Here we capitalized on - the equivalent problem reformulations - the separability of the problem - problem s geometry The essential guide lines are provided in [Ber98, 561] Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

85 DAA Properties minimize j M f j(y j ) subject to y j Y j, j M j M h j(y j ) b 0, variables: y j Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

86 DAA Properties anchor j M f j(y j ) minimize j M f j(y j ) subject to y j Y j, j M j M h j(y j ) b 0, variables: y j eg 1: Y j = {0, 1}, M = {1, 2} anchor j M h j(y j ) b Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

87 DAA Properties anchor j M f j(y j ) minimize j M f j(y j ) subject to y j Y j, j M j M h j(y j ) b 0, variables: y j eg 1: Y j = {0, 1}, M = {1, 2} anchor j M h j(y j ) b Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

88 DAA Properties anchor j M f j(y j ) minimize j M f j(y j ) subject to y j Y j, j M j M h j(y j ) b 0, variables: y j eg 1: Y j = {0, 1}, M = {1, 2} p d anchor j M h j(y j ) b Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

89 DAA Properties anchor j M f j(y j ) minimize j M f j(y j ) subject to y j Y j, j M j M h j(y j ) b 0, variables: y j eg 1: Y j = {0, 1}, M = {1, 2} p d anchor j M h j(y j ) b Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

90 DAA Properties anchor j M f j(y j ) minimize j M f j(y j ) subject to y j Y j, j M j M h j(y j ) b 0, variables: y j p d eg 1: Y j = {0, 1}, M = {1, 2} eg 2: Y j = {0, 1}, M = {1, 2, 3, 4} anchor p d j M h j(y j ) b Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

91 DAA Properties anchor j M f j(y j ) minimize j M f j(y j ) subject to y j Y j, j M j M h j(y j ) b 0, variables: y j p d eg 1: Y j = {0, 1}, M = {1, 2} eg 2: Y j = {0, 1}, M = {1, 2, 3, 4} anchor p d j M h j(y j ) b Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

92 Implementation Over Existing Standards Initially the clients follow the RSSI-based association policy that IEEE 80211ad and IEEE c define DAA is periodically executed to correct possible suboptimal client associations by reallocating the available resources Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

93 Implementation Over Existing Standards APs trigger the initialization of DAA by setting a special bit into the beacon frame Information exchange is performed through the control frames or piggy-backing the data frames Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

94 Outline Past, Present and Future in wireless communications 60 GHz millimeterwave wireless technology Optimizing resource allocation Distributed client association (DAA) Numerical analysis of DAA Conclusions and open research topics Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

95 Numerical Analysis Consider a multi-user multi-cell environment Compare DAA to Random association RSSI-based association (IEEE 80211) Optimal association (IBM CPLEX) Measure Convergence Scalability Efficiency (time) Fairness Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

96 Topologies i = 2 i = 2 i = 4 λ Wavelength d 0 Far field reference distance i = 1 i = 3 i = 1 i = 3 i = 5 η Path loss exponent SNR operating point at a distance d from any AP { P0 λ 2 /(16π 2 N SNR(d) = 0 W ) d d 0 P 0 λ 2 /(16π 2 N 0 W ) (d/d 0 ) η otherwise Radius of each cell r is chosen such that SNR(r) = 10 db Clients are uniformly distributed at random, among the circular cells Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

97 Convergence of DAA 22 5 APs, 100 clients random policy, P rand 4 5 APs, 200 clients random policy, P rand average objective value RSSI, P RSSI DAA, P (k) optimal primal value, P* optimal dual value, D* average objective value RSSI, P RSSI DAA, P (k) optimal primal value, P* optimal dual value, D* subgradient iterations, k subgradient iterations, k Average primal objective value from DAA after k subgradient iterations: P (k) = (1/ T ) T T =1 p(k) best (T ) Average dual optimal value by DAA: D = (1/ T ) T T =1 d (T ) Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

98 Convergence of DAA 3 APs, 30 clients 10 APs, 100 clients random policy, P rand RSSI, P RSSI DAA, P (k) optimal primal value, P* optimal dual value, D* random policy, P rand RSSI, P RSSI DAA, P (k) optimal primal value, P* optimal dual value, D* average objective value subgradient iterations, k average objective value subgradient iterations, k Convergence time is affected by the number of APs and clients: The smaller the network, the faster DAA converges Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

99 Scalability of DAA 2 APs 10 APs 4 35 random policy, P rand RSSI, P RSSI DAA, P (1000) optimal primal, P* optimal dual, D* random policy, P rand RSSI, P RSSI DAA, P (1000) optimal primal, P* optimal dual, D* average objective average objective total number of clients, M total number of clients, M DAA performs close to optimal Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

100 Scalability of DAA average objective value 40 clients 2 random policy, P rand RSSI, P RSSI 18 DAA, P (1000) optimal primal, P* 16 optimal dual, D* total number of APs, N average objective value clients random policy, P rand RSSI, P RSSI DAA, P (1000) optimal primal, P* optimal dual, D* total number of APs, N Considering constant load, the average objective value decreases while the number of APs increases DAA performs close to optimal Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

101 Optimality of DAA relative duality gap % APs 3 APs 4 APs 5 APs 10 APs number of clients, M relative duality gap wrt the best primal value % APs 3 APs 4 APs 5 APs 10 APs number of clients, M Average relative duality gap: Ave-RDG = (1/ T ) T T =1 (p (T ) d (T ))/p (T ) Average relative duality gap taking into account the best primal feasible objective value from DAA after K iterations at time slot T : Ave-RDG-best-achieved = (1/ T ) T T =1 (p(k) best (T ) d (T ))/p (K) best (T ) Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

102 Fairness Achieved by DAA fairness index Jain s fairness index: Optimal (CPLEX) DAA RSSI random policy J (k) (T ) = ( subgradient iterations, k i N Y (k) i (T ) ) 2 /(N i N Y (k) i (T ) 2 ), Y (k) i (T ) = j M i β ij x (k) ij (T ) and x(k) ij (T ) is the solution (best feasible) resulted from DAA at time slot T after k iterations Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

103 Speed and Resources Used by DAA CDF(t) Empirical CDF DAA, M= optimal (CPLEX), M=100 DAA, M=200 optimal (CPLEX), M= DAA, M=300 optimal (CPLEX), M= time, t (sec) average time to find the optimal/suboptimal solution (sec) optimal (CPLEX) DAA total number of clients, M Empirical CDF plots of the number of iterations for M = 100, 200, 300 clients, with N = 10 APs Trade-off between optimality and complexity Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

104 Outline Past, Present and Future in wireless communications 60 GHz millimeterwave wireless technology Optimizing resource allocation Distributed client association (DAA) Numerical analysis of DAA Conclusions and open research topics Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

105 Conclusions 60 GHz wireless technology: characteristics, benefits, challenges, applications Distributed association algorithm (DAA) for optimizing resource allocation in 60 GHz wireless access networks Performance evaluation of DAA: Asymptotically optimal, convergence, time efficiency and fairness Integration of DAA into current standards Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

106 Open Research Topics 60 GHz channel modeling Medium Access Control (MAC) Connectivity maintenance, blockage and directivity Coexistence and cooperation with existing wireless technologies Multi-hop communications Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

107 Thank you Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

108 Optimizing Client Association in 60 GHz Wireless Access Networks G Athanasiou, C Weeraddana, C Fischione, and L Tassiulas KTH Royal Institute of Technology, Stockholm, Sweden University of Thessaly, Volos, Greece {chatw, georgioa,carlofi}@kthse; leandros@uthgr CWC Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50

109 [Ber98] D P Bertsekas Constrained optimization and Lagrange Multiplier Method Athena Scientific, Belmont, MA, 1998 [Ber99] D P Bertsekas Nonlinear Programming Athena Scientific, Belmont, MA, 2nd edition, 1999 [Boy07] S Boyd Subgradient methods [Online] Available: subgrad_method_slidespdf, 2007 Weeraddana, et al (KTH, Univ of MD) Client Association CWC / 50