Layering as Optimization Decomposition

Transcription

1 TLEN7000/ECEN7002: Analytical Foundation of Network Layering a Optimization Decompoition Lijun Chen 11/29/2012

2 The Internet Compleity i ever increaing Large in ize and cope Enormou heterogeneity Incomplete information Uncertain environment Emerging technologie New application New deign dimenion Deign (& undertanding) i increaingly dominated by Efficiency (optimality) Manageability Reliability & Security Economic viability Scalability Evolvability emerging, global propertie 2

3 Sytem requirement: functional, efficient, robut, ecure, evolvable, architecture Component Contraint that decontrain Organizational principle, including abtraction and interface Highly conerved core reource allocation and management mechanim 3

4 Sytem requirement: functional, efficient, robut, ecure, evolvable, Undertand architecture and main mechanim of eiting network architecture Component Deign architecture and main mechanim for emerging network 4

5 Internet Application Divere Highly conerved core mechanim Phyical TCP/AQM IP MAC Divere Layered architecture 5

6 Internet architecture Application TCP/AQM IP Little quantitative undertanding Why? Optimal? In what ene? Lot of problem Efficiency, ecurity, mobility, accountability, MAC Phyical fie (middle boe & overlay) 6

7 Sytem requirement: functional, efficient, robut, ecure, evolvable, architecture Component Rigorou foundation and new methodologie for undertanding & deigning architecture and variou mechanim Employ and develop technique in contrained optimization game theory ditributed control 7

8 Cro-layer deign in ad hoc wirele network Application TCP/AQM IP MAC Phyical Network performance can be improved if network layer are jointly deigned Mot work deign baed on intuition, evaluated by imulation unintended conequence 8

9 Cro-layer deign in ad hoc wirele network Application TCP/AQM IP MAC Phyical A theory-baed approach Capture global tructure of the problem deign objective contraint Derive the deign from the ditributed decompoition of certain optimization problem 9

10 10 Protocol decompoition: TCP/AQM Duality model: TCP/AQM a ditributed primal-dual algorithm over network to maimize aggregate utility (Kelly 98, Low 99, 03) c R U.t. ) ( ma 0 + l l l l l l p p c p R U ) ( ma min 0 0 Primal: Dual c c + = c c R c 2 c 1

11 Protocol decompoition: TCP/AQM Duality model: TCP/AQM a ditributed primal-dual algorithm over the network to maimize aggregate utility (Kelly 98, Low 99, 03) Primal: ma 0.t. U R c ( ) Dual min p 0 ma U 0 ( ) l R l p l + l p c l l ' 1 () t = U ( Rl pl ) l pl ( t+ 1) = [ pl ( t) + γ ( Rl( t) cl )] horizontal decompoition + 11

12 Cro-layer deign/optimization Application ma 0 U ( ).t. R c Tranport Network Link/MAC Phyical Etend to include deciion variable and contraint of other layer Derive cro-layer deign from decompoition of etended utility maimization 12

13 Cro-layer deign/optimization each ource : ending rate and utility U ) ( c f l N l N, Π ; f Π Network model d routing of ervice requirement H() allocation of ervice capacity A( f ) H ( ) A( f ) 13

14 Problem formulation Network reource allocation: ma, f. t. U ( H ( ) A( f Π ) f ) contraint for routing contraint from wirele interference 14

15 15 Protocol decompoition )} ( ma )) ( ) ( ( min{ma ), ( ) (.. ) ( ma 0, Dual: Primal: f A p H p U f f A H t U T f T p f Π + Π Rate control Scheduling Routing rate contraint chedulability contraint

16 Cro-layer implementation Dual: T T min{ma ( U ( ) p H( )) + ma p A( f)} p 0 f Π Application Rate control Routing Scheduling Tranport Network Link/MAC Phyical q q q q Rate control: T ( t) = ( p( t)) = argmau ( ) p ( t) H( ) Routing: olved with rate control or cheduling Scheduling: T f ( t) = f ( p( t)) = arg ma p ( t) A( f ) f Π Congetion update: vertical decompoition 1) = [ p( t) γ { A( f ( p( t))) H ( p( t + ( p( t)))}] t + 16

17 Etenion to time-varying channel Application Tranport Network Link/MAC Phyical q q q q channel tate h : i.i.d. finite tate proce with ditribution Rate control: T ( t) = ( p( t)) = argmau ( ) p ( t) H( ) Routing: olved with rate control or cheduling Scheduling: f ( t) = f ( p( t)) = arg Congetion update ma f Π ( h( t)) p T q(h) ( t) A( f ) random p( t + 1) = [ p( t) γ { A( f ( p( t))) H ( ( p( t)))}] t + 17

18 Etenion to time-varying channel: Stability and optimality Theorem (Chen el al 06; 10): The Markov chain i table. Moreover, the cro-layer algorithm olve the following optimization problem Applicable to any queueing network with interdependent, time- varying, parallel erver q q ma, f. t. H ( ) f U Π ( Π = { r : r = q( h) r( h), r( h) Π( h)} optimality hold even with time-varying topologie throughput-optimal when flow-level dynamic i conidered ) A( h f ) 18

19 Cro-layer deign A Wi-Fi implementation by Rhee et al how ignificantly better performance than eiting ytem Thi erie of work (tarting with Kelly-Low model) ha rekindled an interet in theory-baed network deign q e.g., DARPA CB-MANET program Layering a optimization decompoition q ee urvey article Chiang et al, IEEE Proceeding 07 19

20 Generalized utility maimization Objective function: uer application need and network cot Contraint: retriction on reource allocation (could be phyical or economic) Variable: Under the control of thi deign Contant: Beyond the control of thi deign Application utility Network cot ma, R, c, p ubj to IP: routing i U ( R c c X ( p) i i ) λ T R Phy: power Link: cheduling 20

21 Layering a optimization decompoition Network generalized NUM Layer ub-problem Interface function of primal/dual variable Layering decompoition method Application TCP/AQM IP Link/MAC Phyical Vertical decompoition: into functional module of different layer Horizontal decompoition: into ditributed computation and control over geographically diparate network element 21

22 Layering a optimization decompoition Network generalized NUM Layer ub-problem Interface function of primal/dual variable Layering decompoition method Application TCP/AQM IP Link/MAC Phyical Epoe the interaction among protocol layer a different way to modularize and ditributed a centralized computation Formalize the common practice of breaking down the deign for a comple ytem into impler module 22

23 Layering a optimization decompoition Network generalized NUM Layer ub-problem Interface function of primal/dual variable Layering decompoition method Application TCP/AQM IP Link/MAC Phyical Provide a top-down approach to deign protocol tack q eplicitly tradeoff deign objective q eplicitly model contraint and effect of, e.g., new technologie q provide guidance on how to tructure and modularize different function q make tranparent the interaction among different component and their global behavior 23

24 Utility deign, i.e., how to model the uer or application need q Inelatic traffic q Delay enitive traffic, time-baed utility Nonconve problem q Nonconcave objective function q Nonconve contraint Stability under delay Iue related to control plane q Implementation and management compleity q Evolvability q 24