Enhancing Energy Efficiency among Communication, Computation and Caching with QoI-Guarantee

Transcription

1 Enhancing Energy Efficiency among Communication, Computation and Caching with QoI-Guarantee Faheem Zafari 1, Jian Li 2, Kin K. Leung 1, Don Towsley 2, Ananthram Swami 3 1 Imperial College London 2 University of Massachusetts Amherst 3 US Army Research Laboratory Sept 25, 2017 DAIS-ITA Annual Fall Meeting 2017 Zafari et al. C3 Energy Optimization Sept 25, / 24

2 Motivation Energy is one of the fundamental limitations of sensors Zafari et al. C3 Energy Optimization Sept 25, / 24

3 Motivation Energy is one of the fundamental limitations of sensors Sensors are responsible and consume energy for Communication Computation Caching Zafari et al. C3 Energy Optimization Sept 25, / 24

4 Motivation Energy is one of the fundamental limitations of sensors Sensors are responsible and consume energy for Communication Computation Caching Tradeoffs among communication, computation and caching energy costs Computation (e.g. compression) consumes energy, but may reduce communication energy cost Caching reduces communication cost but also consumes energy Zafari et al. C3 Energy Optimization Sept 25, / 24

5 The Big Question? To achieve desirable tradeoffs How much data compression is needed? Where to cache data optimally? Zafari et al. C3 Energy Optimization Sept 25, / 24

6 Importance of C3 tradeoffs to DAIS-ITA/P1? Coalition infrastructure includes the C3 resources which we need to use efficiently Zafari et al. C3 Energy Optimization Sept 25, / 24

7 Importance of C3 tradeoffs to DAIS-ITA/P1? Coalition infrastructure includes the C3 resources which we need to use efficiently Sensor networks often have limited energy supply = important to optimize energy usage Zafari et al. C3 Energy Optimization Sept 25, / 24

8 Importance of C3 tradeoffs to DAIS-ITA/P1? Coalition infrastructure includes the C3 resources which we need to use efficiently Sensor networks often have limited energy supply = important to optimize energy usage We developed optimization solution for C3 tradeoffs that can be applied to other problems Zafari et al. C3 Energy Optimization Sept 25, / 24

9 Data movement direction System Model Tree network is modeled as a directed graph G = (V, E ) sink node s Cached data S v δ ki K Leaf nodes Data source nodes Tree-Structured Network Zafari et al. C3 Energy Optimization Sept 25, / 24

10 Data movement direction System Model Tree network is modeled as a directed graph G = (V, E ) K V : the set of leaf nodes (data source) with K = K sink node s Cached data S v δ ki K Leaf nodes Data source nodes Tree-Structured Network Zafari et al. C3 Energy Optimization Sept 25, / 24

11 Data movement direction System Model Tree network is modeled as a directed graph G = (V, E ) K V : the set of leaf nodes (data source) with K = K Only leaf nodes k K can generate data of y k bits Cached data S v sink node s δ ki K Leaf nodes Data source nodes Tree-Structured Network Zafari et al. C3 Energy Optimization Sept 25, / 24

12 Data movement direction System Model Tree network is modeled as a directed graph G = (V, E ) K V : the set of leaf nodes (data source) with K = K Only leaf nodes k K can generate data of y k bits Data is transmitted from a leaf node towards the sink node s δ ki Cached data S v sink node s K Leaf nodes Data source nodes Tree-Structured Network Zafari et al. C3 Energy Optimization Sept 25, / 24

13 Data movement direction System Model Tree network is modeled as a directed graph G = (V, E ) K V : the set of leaf nodes (data source) with K = K Only leaf nodes k K can generate data of y k bits Data is transmitted from a leaf node towards the sink node s Data of leaf node k can be compressed before further transmission with δ k,i reduction factor δ ki Cached data K S v Leaf nodes sink node s Data source nodes Tree-Structured Network Zafari et al. C3 Energy Optimization Sept 25, / 24

14 Data movement direction System Model Tree network is modeled as a directed graph G = (V, E ) K V : the set of leaf nodes (data source) with K = K Only leaf nodes k K can generate data of y k bits Data is transmitted from a leaf node towards the sink node s Data of leaf node k can be compressed before further transmission with δ k,i reduction factor Leaf node data can be cached at most in one node along the path towards sink node s δ ki Cached data K S v Leaf nodes sink node Tree-Structured Network s Data source nodes Zafari et al. C3 Energy Optimization Sept 25, / 24

15 Data movement direction System Model The caching capacity at node v V : S v sink node s Cached data S v δ ki K Leaf nodes Data source nodes Tree-Structured Network Zafari et al. C3 Energy Optimization Sept 25, / 24

16 Data movement direction System Model The caching capacity at node v V : S v Caching decision variable for leaf node data k at depth i: b k,i {0, 1} Cached data S v sink node s δ ki K Leaf nodes Data source nodes Tree-Structured Network Zafari et al. C3 Energy Optimization Sept 25, / 24

17 Data movement direction System Model The caching capacity at node v V : S v Caching decision variable for leaf node data k at depth i: b k,i {0, 1} Per-bit transmission, reception and computation energy cost: ε vt, ε vr, and ε vc, define f (δ v ) = ε vr + ε vt δ k,i + ε kc ( 1 δ k,i 1) δ ki Cached data K S v Leaf nodes sink node s Data source nodes Tree-Structured Network Zafari et al. C3 Energy Optimization Sept 25, / 24

18 Data movement direction System Model The caching capacity at node v V : S v Caching decision variable for leaf node data k at depth i: b k,i {0, 1} Per-bit transmission, reception and computation energy cost: ε vt, ε vr, and ε vc, define f (δ v ) = ε vr + ε vt δ k,i + ε kc ( 1 δ k,i 1) During a time period T, R k requests for data y k generated by leaf node k δ ki Cached data K S v Leaf nodes sink node Tree-Structured Network s Data source nodes Zafari et al. C3 Energy Optimization Sept 25, / 24

19 Energy Efficiency Optimization E C : energy for data received, transmitted, and possibly compressed k by all nodes on the path from leaf node k to sink node s E C k y k f (δ k,i ) = h(k) i=0 h(k) m=i+1 δ k,m (1) Zafari et al. C3 Energy Optimization Sept 25, / 24

20 Energy Efficiency Optimization E C : energy for data received, transmitted, and possibly compressed k by all nodes on the path from leaf node k to sink node s E C k y k f (δ k,i ) = h(k) i=0 h(k) m=i+1 δ k,m (1) E R : the total energy consumed in responding to the subsequent k (R k 1) requests E R k = h(k) i=0 { y k (R k 1) f (δ k,i ) + ( h(k) m=i h(k) m=i+1 i 1 ) δ k,m (1 b k,j j=0 } w ca T δ k,m )b k,i ( (R k 1) + ε kt ). (2) Zafari et al. C3 Energy Optimization Sept 25, / 24

21 Energy Efficiency Optimization E total (δ, b) k K ( ) E C k + E R k Non-convex Mixed Integer Nonlinear Programming (MINLP) (3) min δ,b s.t. E total (δ, b) k K δ k,i γ, y k h(k) i=0 b k,i {0, 1}, k K, i = 0,, h(k), k C v b k,h(v ) y k h(v ) j=h(k) δ k,j S v, v V, h(k) b k,i 1, k K. (4) i=0 Zafari et al. C3 Energy Optimization Sept 25, / 24

22 Part 1: Solving the Non-Convex MINLP Problem using our Variant of Spatial Branch and Bound Algorithm (V-SBB) Zafari C3 Energy Optimization September 15, / 24

23 Symbolic Reformulation Reformulated Problem Non-Convex MINLP problem min ψ(x, Y ) s.t. G (X, Y ) 0 H(X, Y ) = 0 X L X X U, X R Y [Y L,..., Y U ] min w s.t. w obj Aw = b w l w w u Y [Y L,..., Y U ] w k w i w j (i, j, k) τ bt w k w i w j (i, j, k) τ lft w k w n i (i, k, n) τ et w k fn(w i ) (i, k) τ uft Zafari C3 Energy Optimization September 15, / 24

24 Spatial Branch-and-Bound BBM example (taken from https: //optimization.mccormick.northwestern.edu/index.php/file:sbb.png) Zafari C3 Energy Optimization September 15, / 24

25 V-SBB Algorithm 1 Variant of Spatial Branch-and-Bound (V-SBB) Step 1: Initialize φ u := and L to a single domain Step 2: Choose a subregion R L using least lower bound rule if L = or R L, φ R,l is infeasible then Go to Step 6 if φ R,l φ u ɛ then Go to Step 5 Step 3: Obtain the upper bound φ R,u if upper bound cannot be obtained or if φ R,u > φ u then Go to Step 4 else φ u :=φ R,u and, from the list L, delete all subregions S L such that φ S,l φ u ɛ if φ R,u φ R,l ɛ then Go to Step 5 Step 4: Partition R into new subregions R right and R left Step 5: Delete R from L and go to Step 2 Step 6: Terminate Search if φ u = then Problem is infeasible else φ u is ɛ-global optimal Decomposes non-linear functions of the original problem symbolically and recursively with simple operators into simple functions Zafari C3 Energy Optimization September 15, / 24

26 Evaluation Parameters used in simulations Parameter Value y k 1000 R k 100 w ca T 10s ε vr ε vt ε cr γ [1, k K y k ] Candidate network topologies used in the experiments Zafari C3 Energy Optimization September 15, / 24

27 Evaluations The Best Solution to the Objective Function (Obj.) and Convergence time for Seven-node network (γ is the required QoI threshold) Method γ = 1 γ = 1000 γ = 2000 γ = 3000 γ = 4000 Obj. Time (s) Obj. Time (s) Obj. Time (s) Obj. Time (s) Obj. Time (s) Bonmin NOMAD GA V-SBB Summary of Results V-SBB outperforms all other algorithms in terms of obtaining better objective value Bonmin is faster but it has infeasibility issue and poor performance for some cases Zafari C3 Energy Optimization September 15, / 24

28 Evaluations Infeasibility: Not being able to find a solution when it exists Infeasibility of Bonmin for different networks Networks (a) (b) (c) (d) Number of testing γ values Number of infeasible solutions Infeasibility (%) Comparison between V-SBB and Bonmin for small γ values in seven-node network Method γ =1 γ =5 γ =50 Obj. Time (s) Obj. Time Obj. Time Bonmin V-SBB Imp. (%) Zafari C3 Energy Optimization September 15, / 24

29 Importance of C3 over C2 tradeoffs Total Energy Cost C3 ( =1000) C3 ( =3000) C2a C2o ( =1000) C20 ( =3000) Comparison of C3 with C Number of Requests Comparison of C3 and C2 optimization for the seven nodes network. Zafari C3 Energy Optimization September 15, / 24

30 Conclusions Formulated energy tradeoffs among communication, computation and caching with QoI guarantee as non-convex MINLP optimization problem Zafari C3 Energy Optimization September 15, / 24

31 Conclusions Formulated energy tradeoffs among communication, computation and caching with QoI guarantee as non-convex MINLP optimization problem Proposed a variant of spatial branch-and-bound (V-SBB) algorithm, which can solve the MINLP with ɛ-optimality guarantee Zafari C3 Energy Optimization September 15, / 24

32 Conclusions Formulated energy tradeoffs among communication, computation and caching with QoI guarantee as non-convex MINLP optimization problem Proposed a variant of spatial branch-and-bound (V-SBB) algorithm, which can solve the MINLP with ɛ-optimality guarantee Observed that C3 optimization improves energy efficiency by as much as 88% compared with either of the C2 optimizations Zafari C3 Energy Optimization September 15, / 24

33 Ongoing Work 1 New formulation: minimize latency with energy constraints Zafari C3 Energy Optimization September 15, / 24

34 Ongoing Work 1 New formulation: minimize latency with energy constraints 2 Design approximate algorithms to these non-convex MINLP problems to achieve a constant approximation ratio in polynomial time Zafari C3 Energy Optimization September 15, / 24

35 Ongoing Work 1 New formulation: minimize latency with energy constraints 2 Design approximate algorithms to these non-convex MINLP problems to achieve a constant approximation ratio in polynomial time 3 Formulate Multi-Objective Optimization (MOO) for Software Defined Coalitions (SDC) Zafari C3 Energy Optimization September 15, / 24

36 Ongoing Work 1 New formulation: minimize latency with energy constraints 2 Design approximate algorithms to these non-convex MINLP problems to achieve a constant approximation ratio in polynomial time 3 Formulate Multi-Objective Optimization (MOO) for Software Defined Coalitions (SDC) Apply Cooperative Game Theory to coalition environment Zafari C3 Energy Optimization September 15, / 24

37 Ongoing Work 1 New formulation: minimize latency with energy constraints 2 Design approximate algorithms to these non-convex MINLP problems to achieve a constant approximation ratio in polynomial time 3 Formulate Multi-Objective Optimization (MOO) for Software Defined Coalitions (SDC) Apply Cooperative Game Theory to coalition environment Explore Trust based regions Zafari C3 Energy Optimization September 15, / 24

38 Thank you! Zafari C3 Energy Optimization September 15, / 24

39 Backup Slides Zafari C3 Energy Optimization September 15, / 24

40 System Model E v : the total energy consumption at node v E v = E vr + E vt + E vc + E vs, (5) E vr = y v ε vr is the reception cost E vt = y v ε vt δ v is the transmission cost E vc = y v ε vc l v (δ v ) is the computation cost E vs = w ca y v T is the storage cost l v (δ v ) :a decreasing differentiable function of the reduction rate, e.g., l v (δ v ) = 1 δ v 1 1 During a time period of T, R k requests for the data y k generated by leaf node k 1 Eswaran, Sharanya, et al. Adaptive in-network processing for bandwidth and energy constrained mission-oriented multihop wireless networks. IEEE Transactions on Mobile Computing 11.9 (2012): Zafari C3 Energy Optimization September 15, / 24

41 Symbolic Reformulation Example We consider k = 1 and h(k) = 1 in (4), i.e., one leaf node and one sink node. Then (1) and (2) reduce to E C 1 = y 1f (δ 1,0 )δ 1,1 + y 1 f (δ 1,1 ), [ ] E R 1 = y w ca T 1(R 1 1) f (δ 1,0 )δ 1,1 + δ 1,0 δ 1,1 b 1,0 ( (R 1 1) + ε 1T ) [ ] w ca T + y 1 (R 1 1) f (δ 1,1 )(1 b 1,0 ) + δ 1,1 b 1,1 ( (R 1 1) + ε 1T ), (6) min δ,b E total (δ, b) = E C 1 + E R 1 s.t. y 1 δ 1,0 δ 1,1 γ, b 1,0, b 1,1 {0, 1}, b 1,0 y 1 δ 1,0 δ 1,1 S 0, b 1,1 y 1 δ 1,1 S 1, b 1,0 + b 1,1 1. (7) Zafari C3 Energy Optimization September 15, / 24

42 Symbolic Reformulation min δ,b s.t. w obj y 1 w bt 1,0 γ, b 1,0, b 1,1 {0, 1}, y 1 w bt 1,0 S 0, y 1 w bt 1,1 S 1, b 1,0 + b 1,1 1, w bt 1,0 = δ 1,1 δ 1,0, w lft 1,0 = δ 1,1/δ 1,0, w bt 1,0 = b 1,0 w b 1,0, w bt 1,1 = b 1,1 δ 1,1, w bt 1,0 = δ 1,1 b 1,0, w lft 1,0 = b 1,0/δ 1,1, w obj = y 1 ε 1R δ 1,1 + ε 1T y 1 w bt 1,0 + y 1ε 1C w lft 1,0 y 1ε 1C δ 1,1 + y 1 ε 1R + ε 1T y 1 δ 1,1 + y 1 ε 1C /δ 1,1 y 1 ε 1C + y 1 (R 1 1) [ ε 1R δ 1,1 + ε 1T w1,0 bt + ε 1C w1,0 lft ε 1C δ 1,1 ] + w ca T w bt 1,0/(R 1 1) + ε 1T w bt 1,0 + y 1 (R 1 1) [ ε 1R + δ 1,1 ε 1T + ε 1C /δ 1,1 ε 1C ε 1R b 1,0 ε 1T w bt 1,0 )] ε 1C w lft 1,0 + ε 1C b 1,0 + w bt 1,1 (w ca T /(R 1 1) + ε 1T (8) Zafari C3 Energy Optimization September 15, / 24

43 Evaluations Objective Function Value Increase in Total Energy Cost with Number of Requests 2 Node Network ( =250) 2 Node Network ( =750) 7 Node Network ( =1000) 7 Node Network ( =3000) Number of Requests Total Energy Costs vs. Number of Requests. Zafari C3 Energy Optimization September 15, / 24