Optimal Utility-Lifetime Trade-off in Self-regulating Wireless Sensor Networks: A Distributed Approach Hithesh Nama, WINLAB, Rutgers University Dr. Narayan Mandayam, WINLAB, Rutgers University Joint work with Dr. Mung Chiang, Princeton University WINLAB RESEARCH REVIEW May 15, 2006 IAB Meeting: May 15, 2006 p. 1
Overview IAB Meeting: May 15, 2006 p. 2
Motivation: Sensors over Information Fields Energy-limited sensors collect data and deliver to a sink IAB Meeting: May 15, 2006 p. 3
Motivation: Routing and Power control Route with many short hops Low transmit power per hop IAB Meeting: May 15, 2006 p. 4
Motivation: Routing and Power control Route with fewer but longer hops Higher transmit power per hop IAB Meeting: May 15, 2006 p. 5
Motivation: Application Performance Less data from sensors Coarse resolution IAB Meeting: May 15, 2006 p. 6
Motivation: Application Performance More data from sensors Fine resolution But more data more energy dissipation in sensors IAB Meeting: May 15, 2006 p. 7
In short... Energy-efficient designs should address all layers of protocol stack Application performance or Network Utility increases with amount of gathered data Network Lifetime decreases with amount of gathered data Network Utility vs. Network Lifetime: An inherent trade-off IAB Meeting: May 15, 2006 p. 8
Objective #1: Characterize optimal Utility vs Lifetime trade-off through efficient cross-layer design 19 18 Network Utility in bps (log 10 scale) 17 16 15 14 13 12 11 10 0 50 100 150 200 Network Lifetime (in s) IAB Meeting: May 15, 2006 p. 9
Objective #2: Design distributed algorithms to achieve any desired trade-off IAB Meeting: May 15, 2006 p. 10
System Model: The Network - I Network modeled as a directed graph G(V, L) V = N D; N - Set of sources; D - Set of sinks/destinations L - Set of arcs/links O(n) - Set of outgoing links of node n O(n2) = l2, l3 I(n) - Set of incoming links of node n I(n2) = l1, l4 N n - Set of one-hop neighbors of node n IAB Meeting: May 15, 2006 p. 11
System Model: The Network - II Self-regulating network source rates are adaptive Sources route data to sinks possibly over multiple hops Any two links with a common node cannot be simultaneously scheduled E.g., {l1, l4} - NO but {l1, l6} - YES Link-transmissions are orthogonal i.e., no interference E.g., DSSS/FHSS systems with orthogonal sequences IAB Meeting: May 15, 2006 p. 12
System Model: Routing and Source Rate Control Multi-commodity flow model Non-negative source rates {rn} d and flows {fl d} Flow conservation constraint: fl d fl d = rn, d d D, n N l O(n) l I(n) Total flow through link l f l = d D f d l IAB Meeting: May 15, 2006 p. 13
System Model: Radio Resource Allocation - I Feasible mode of operation consists of independent set of links E.g., {}, {l1},..., {l6}, {l1, l5}, {l1, l6}, {l2, l5}, {l2, l6} A feasible schedule corresponds to time-fractions τ m of each feasible mode m m τ m = 1 Average Tx power of link l in mode m - P m l Link Tx power constraint: P m l P max l IAB Meeting: May 15, 2006 p. 14
System Model: Radio Resource Allocation - II We assume schedule is fixed {τ m } are constants τ l - Total fraction of time link l is in operation Capacity of link l with power P l Link capacity constraint: C l (P l ) = W log 2 (1 + P lkd α l N 0 W ) f l τ l C l (P l, W), l L IAB Meeting: May 15, 2006 p. 15
Network Utility Maximization - I Application performance depends on the amount of data gathered U d n(r d n) - Increasing and strictly concave function of r d n, e.g., log(r d n) Network utility is sum of node utilities Network utility maximization: max {r d n,f d l,p l} 0 n N d D U d n(r d n) subject to Flow conservation constraint, Link capacity constraint, & Link Tx power constraint. IAB Meeting: May 15, 2006 p. 16
Network Utility Maximization - II Convex optimization problem with a unique set of source rates Useful formulation in broadband ad hoc wireless networks But sensors are energy-constrained Network utility maximization does not factor in power dissipation at nodes Can lead to widely varying power dissipation levels Potentially results in a disconnected network IAB Meeting: May 15, 2006 p. 17
Power Dissipation Model E tx - Energy dissipated per bit in transmitter electronics E rx - Energy dissipated per bit in receiver electronics E s - Energy dissipated per bit in sensing Average power dissipated in a node n P avg n = {τ l P l + f l E tx } + l O(n) l I(n)f l E rx + d D r d ne s f l - Total flow through link l P l - Average Tx power of link l r d n - Source rate of node n towards destination d IAB Meeting: May 15, 2006 p. 18
Network Lifetime Maximization E n - Initial energy of node n Lifetime of node n, t n = E n /P avg n Network lifetime, t nwk = min n N t n, i.e., time until death of first node Node power dissipation constraint: = E n /t n E n /t nwk = E n s, n N P avg n Network lifetime maximization: min {s,r d n,f d l,p l} 0 s subject to Flow conservation constraint, Link capacity constraint, Link Tx power constraint, & Node power dissipation constraint. IAB Meeting: May 15, 2006 p. 19
Utility-Lifetime Trade-off - I Vector objective function in 2D - [utility, inverse-lifetime] 20 18 Network Utility in bps (log 10 scale) 16 14 12 10 8 6 4 2 0 0 0.5 1 1.5 2 Inverse Network Lifetime (in s 1 ) IAB Meeting: May 15, 2006 p. 20
Utility-Lifetime Trade-off - II Choose γ (0, 1) and scalarize to obtain Pareto-optimal points max γ Un(r d n) d (1 γ)s {s,rn,f d l d,p l} 0 n N subject to l O(n) l O(n) τ l P l + l O(n) f d l d D l I(n) d D f d l = r d n, d D, n N f d l τ l C l (P l, W), l L P l Pl max, l L f l E tx + l I(n) f l E rx + d D r d ne s E n s, n N IAB Meeting: May 15, 2006 p. 21
Numerical Illustration - Utility vs. Lifetime 19 18 Network Utility in bps (log 10 scale) 17 16 15 14 13 12 11 10 0 50 100 150 200 Network Lifetime (in s) IAB Meeting: May 15, 2006 p. 22
Numerical Illustration - Source rate vs. Lifetime 6.5 6 node n1 node n2 node n3 Node source rate in bps (log 10 scale) 5.5 5 4.5 4 3.5 3 0 50 100 150 200 Network Lifetime (in s) IAB Meeting: May 15, 2006 p. 23
Towards a distributed implementation Layering as optimization decomposition approach: Network protocols as distributed solutions to some global optimization problems Each protocol layer corresponds to a separate sub-problem Distributed implementation of each sub-problem Alternate formulation of the joint optimization problem Enables recovery of primal solutions Alternate formulation of the lifetime maximization problem Add a regularization term involving flows in the objective function IAB Meeting: May 15, 2006 p. 24
Joint Utility-Lifetime Maximization: Primal Problem max γ {s n,rn,f d l d,p l} 0 n N d D U d n(r d n) (1 γ) n N F n (s n ) ǫ l L d D (f d l )2 subject to l O(n) f d l d D l I(n) f d l = r d n, d D, n N f d l τ l C l (P l ), l L P l P max l P avg n, l L E n s n, n N s n s m, m N n, n N IAB Meeting: May 15, 2006 p. 25
Lagrange Dual Function and Dual Problem D(λ, µ, ν, δ) = max γ Un(r d n) d (1 γ) F n (s n ) {s n,rn d,f l d,p l m } 0 n N d D n N ǫ l l L d D(f d )2 { } λ l fl d τ l C l (P l ) { } µ n Pn avg E n s n l L d D n N δn d rd n fl d + fl d } νn {s m n s m n N n N m N n d D l O(n) subject to P l Pl max, l L l I(n) Dual problem: min D(λ, µ, ν, δ) λ 0,µ 0,ν 0,δ IAB Meeting: May 15, 2006 p. 26
Dual-based Solution of Primal Problem IAB Meeting: May 15, 2006 p. 27
Dual Decomposition Application/Transport Layer: { } D 1 (λ, µ, ν, δ) = max γ Un(r d n) d µ n rne d s δnr d n d {rn} 0 d n N d D Network Layer: D 2 (λ, µ, ν, δ) = min {fl d} 0 n N { } ǫ(fl d )2 +fl d {λ l + µ n E tx + µ p E rx δn d + δp} d l O(n) d D Physical Layer: D 3 (λ, µ, ν, δ) = max {0 P l P max l } n N l O(n) {λ l τ l C l (P l, W) µ n τ l P l } Energy-Management { Layer: } D 4 (λ, µ, ν, δ) = min (1 γ)f n (s n ) µ n E n s n + s n (νn m νm) n {s n } 0 m N n n N IAB Meeting: May 15, 2006 p. 28
Vertical and Horizontal Decomposition IAB Meeting: May 15, 2006 p. 29
Conclusions and Future Work Characterized the optimal utility-lifetime trade-off in sensor networks Proposed distributed solutions that result in near-optimal performance Future Work Asynchronous implementations Variable scheduling but with fixed powers Joint scheduling and power control Extensions to networks with interference IAB Meeting: May 15, 2006 p. 30