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 ( n 2) = l 2 , l 3 • I ( n ) - Set of incoming links of node n I ( n 2) = l 1 , l 4 • 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., { l 1 , l 4 } - NO but { l 1 , l 6 } - 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 { r d n } and flows { f d l } • Flow conservation constraint: � � f d f d l = r d l − n , d ∈ D , n ∈ N l ∈O ( n ) l ∈I ( n ) • Total flow through link l � f d f l = l d ∈D 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., {} , { l 1 } , ..., { l 6 } , { l 1 , l 5 } , { l 1 , l 6 } , { l 2 , l 5 } , { l 2 , l 6 } • 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 ≤ P max l 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 C l ( P l ) = W log 2 (1 + P l Kd − α l ) N 0 W • Link capacity constraint: 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: � � U d n ( r d max n ) { r d n ,f d l ,P l }≥ 0 n ∈N d ∈D 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 r d = { τ l P l + f l E tx } + f l E rx + n E s n d ∈D l ∈O ( n ) l ∈I ( n ) • 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: P avg = E n /t n ≤ E n /t nwk = E n s, n ∈ N n • Network lifetime maximization: min l ,P l }≥ 0 s { s,r d n ,f d 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 16 Network Utility in bps (log 10 scale) 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 � � U d n ( r d max l ,P l }≥ 0 γ n ) − (1 − γ ) s { s,r d n ,f d n ∈N d ∈D subject to � � f d f d l = r d l − n , d ∈ D , n ∈ N l ∈O ( n ) l ∈I ( n ) � f d l ≤ τ l C l ( P l , W ) , l ∈ L d ∈D P l ≤ P max , l ∈ L l � � � � r d f l E tx + f l E rx + n E s ≤ E n s, n ∈ N τ l P l + l ∈O ( n ) l ∈O ( n ) l ∈I ( n ) d ∈D 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 node n1 node n2 node n3 6 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 � � � � � l ) 2 U d n ( r d ( f d n ) − (1 − γ ) F n ( s n ) − ǫ max l ,P l }≥ 0 γ { s n ,r d n ,f d n ∈N d ∈D n ∈N l ∈L d ∈D subject to � � f d f d l = r d l − n , d ∈ D , n ∈ N l ∈O ( n ) l ∈I ( n ) � f d l ≤ τ l C l ( P l ) , l ∈ L d ∈D P l ≤ P max , l ∈ L l P avg ≤ E n s n , 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 � � � U d n ( r d n ) − (1 − γ ) D ( λ, µ, ν, δ ) = max l }≥ 0 γ F n ( s n ) { s n ,r d n ,f d l ,P m n ∈N d ∈D n ∈N �� � l ) 2 − � � � � � � ( f d f d P avg − ǫ λ l l − τ l C l ( P l ) − µ n − E n s n n l ∈L d ∈D l ∈L d ∈D n ∈N � � � � � � � � δ d r d f d f d ν m − n − − s n − s m l + n l n n ∈N d ∈D n ∈N m ∈N n l ∈O ( n ) l ∈I ( n ) subject to P l ≤ P max , l ∈ L l λ � 0 , µ � 0 , ν � 0 , δ D ( λ, µ, ν, δ ) min Dual problem: 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: � � � � γ U d n ( r d n ) − µ n r d n E s − δ d n r d D 1 ( λ, µ, ν, δ ) = max n { r d n }≥ 0 n ∈N d ∈D Network Layer: � � � � � l ) 2 + f d ǫ ( f d l { λ l + µ n E tx + µ p E rx − δ d n + δ d p } D 2 ( λ, µ, ν, δ ) = min { f d l }≥ 0 n ∈N d ∈D l ∈O ( n ) Physical Layer: � � � � λ l τ l C l ( P l , W ) − µ n τ l P l D 3 ( λ, µ, ν, δ ) = max { 0 ≤ P l ≤ P max } l n ∈N l ∈O ( n ) Energy-Management Layer: � � � � ( ν m n − ν n (1 − γ ) F n ( s n ) − µ n E n s n + s n D 4 ( λ, µ, ν, δ ) = min m ) { s n }≥ 0 n ∈N m ∈N n IAB Meeting: May 15, 2006 – p. 28
Vertical and Horizontal Decomposition IAB Meeting: May 15, 2006 – p. 29
Recommend
More recommend
