Utlty-based Routng Je Wu Dept. of Computer and Informaton Scences Temple Unversty
Roadmap Introducton Why Another Routng Scheme Utlty-Based Routng Implementatons Extensons Some Fnal Thoughts 2
. Introducton Z. Mao (Serve the People) Knowledge begns wth practce. Theoretcal knowledge acqured through practce, must then return to practce. G. H. Hardy (A Mathematcan's Apology) The real mathematcs of the real mathematcans s almost wholly useless. It s not possble to justfy the lfe of any genune mathematcan on the ground of the utlty of hs work. 3
Implcatons Poltcans (when they become poltcally weak) Start new revolutons (and young people become followers) Mathematcans (when they become old) Start wrtng books (and young people prove theorems) Professors (when they become senors) Gve presentatons (and students wrte papers) 4
2. Why Another Routng Scheme Why routng agan? Because t s nterestng (a non-serous answer) A new routng algorthm: composte utlty Beneft (of packet delvery) Cost (of forwardng) Relablty (of lnks) Tmelness (of reachng a destnaton) 5
A Postage Example Best route: mportance of the package Valuable package: Fedex (more relable, costs more) Regular package: Regular mal (less relable, costs less) route package sender route 2 route k recever cost/relablty 6
A Sample Network Tradtonal metrcs: cost/relablty The mnmum cost path: s d Cost 2 + 3 = 5 Relablty 0.8 0.9 = 0.72 The most relable path: s 2 d Cost 4 + 3 = 7 Relablty 0.9 0.9 = 0.8 7
3. Utlty-Based Routng (Lu&Wu 06) Each packet s assgned a beneft value, v s transmts a packet wth beneft v to d Transmsson cost/relablty: c/p Utlty: v c f success, 0 c otherwse Expected utlty: u = p(v-c) + (-p)(0-c) = pv - c The best route maxmzes u Success: Falure: -p p s c d 8
A General Expresson General form of u for path R: s (= 0),,, +,, d (= n) where P R : route stablty, and C R : route cost + p,+ c, + s d R R n j j j n C P v p c v p u = = = = + + = + 0 0,, 0, ) ( ) ( 9
How to calculate u? Drect calculaton 0.8 *0.9*20 2 3*0.8=0 Backward calculaton s 2/0.8 3/0.9 d V=20 u = p,+ u + - c,+ (vrtual s/d) 0.9*20 3 = 5 (at ) 0.8*5 2 = 0 (at s) 0
Beneft-Dependent Best Paths R : s d R 2 : s 2 d R 3 : s 2 d R 4 : s 2 d R P C R 0.72 4.4 R 2 0.8 6.7 R 3 0.5 5.3 R 4 0.57 7.7 v=20 R U R 0 R 2 R 3 9.5 4.7 R 4 3.7 v=30 7.2 R U R R 2 7.6 R 3 9.7 R 4 9.4 Dfferent beneft values may have dfferent best paths!
4. Implementatons Centralzed greedy approach Apples the Djkstra s shortest path from d Each node mantans the maxmum u (nt. to 0) relaxes j: u j = p j, u - c j, untl reachng s Wreless and moble: reactve approach Route dscovery (from s) followed by route reply (from d) Tme out: each node set an approprate order of relaxatons s j relax d 2
5. Extensons All optmal routes Dfferent beneft values Wreless networks Opportunstc routng Incentve compatble routng Handlng selfsh nodes Real-tme responses Duty cycles n WSNs Probablstc contacts n DTNs (Others: data gatherng and network codng) 3
All Optmal Routes Requrement Fnd all optmal routes for dfferent benefts Challenges Enumeratng all benefts s nfeasble For a gven range of benefts Checkng all paths s too expensve Exponental to the number of nodes One mportant property The benefts range can be parttoned nto subranges, each of whch has one dstnct optmal path 4
Intersecton Pont R: s -> -> d R2: s -> 2 -> d U R = 0.72v 4.4 U R2 = 0.9v-7 Complexty: O(R 2 ) (R: number of paths) 5
Bnary Partton Iteratve and parallel partton the beneft range nto sub-ranges Stoppage condton: r tan θ tan θ 2 < Δ (r: sub-range, θ and θ 2 : angle of R and R 2 ) 6
Wreless Networks (Wu, Lu, & L 08) Opportunstc routng (OR) wth adjustable transmsson range Relay set: more than one node can relay Prorty: ETX or cost to destnaton 7
OR Example Best expected utlty u s = 0 for v = 20 Prorty s < 2 < < d Best expected opportunstc utlty opus = 4.6 for v = 20 Optmal soluton NP-hard: the dffculty les n the global prorty 8
Incentve Compatble Routng Nodes are selfsh and gve false cost nformaton Wthout reward, they wll not help relay packets Maxmze utlty = payment cost Mechansm desgn Te self-nterest to socetal nterest VCG scheme: enforcng the reportng of correct costs Nodes on optmal path: utlty remans the same when lyng Nodes not on optmal path: utlty reduces when lyng 9
Second Prce Path Aucton: VCG Why doesn t the frst prce work? Socetal objectve s nconsstent wth ndvdual nodes objectves The soluton: second prce Loser s payment s 0 Wnner s payment: (lowest cost wthout - lowest cost wth ) + cost of node 20
A VCG Example s 2 3 2 4 3 2 Case : nodes on an optmal path le If (s, ) s changed to 3 d S stll gets 7 6 + 3 = 4 (same as 7 5 + 2 = 4) Case 2: nodes on a non-optmal path le If (2, d) s changed to 2 gets 5 5 + = < 3 (utlty s negatve) Who s payng the prce dfference: socety Even an deal socety charges tax 2
Real-Tme Responses (Xao, Wu, & Wang 2) Energy savng: on/off mode n WSNs Duty cycle = 4: up every 4 unts Asynchronous send Wth a delay, 2, 3, or 4 s, 2, 3, 4 d Extendng utlty functon: delay-senstve 22
Duty Cycles n WSNs Utlty for a delvery path R: s (=0),, 2,, n-, d (=n) Drect computaton Iteratve computaton forward backward = = + + = = + + = 0 0,, 0 0,, ) ( n j j j n n p c t v p u δ,, + + + = c u p u + + =, t v v δ ) nt, ( 0 u u v u n n = = 23 forward backward d s
Probablstc Contacts n DTNs DTNs Probablstc contacts (uncertanty) Mnmzng the expected decreased utlty Opportunstc forwardng Relay s extended from a sngle node to a tme-varyng forwardng set (FS) A message copy s forwarded from to the frst contact j at tme t f j s n FS(, t) md cost, md uncertanty low cost, hgh uncertanty large cost, low uncertanty 24
6. Some Fnal Thoughts Is research on routng over? Probably yes: MANETs and sensor nets No: Other networks (e.g. DTNs and socal networks) Moblty n Wreless Networks: Frend or Foe? Moblty as a Foe: toleratng and maskng Moblty as a Frend: moblty-asssted routng 25
Some Challenges Future world beng more wreless and moble Complexty and dversty New challenges for routng protocol desgn From top: more demand from the end user (e.g., moblty support) From bottom: emergng technologes (e.g., new abstracton for wreless lnks) 26
Graphs for Dynamc Networks E.g. Moblty affects network model/protocol Tme-space vew vs. space vew Vew wndow Tme Space Vew(-) Vew() Vew(+k) Vew consstency n statc graphs Wu & Da (IEEE Network 05): functon of multple vews Connectvty & routng n evolvng graphs Lu & Wu (MobHoc 07, 08, 09) Wu (Graph and Computng 0) 27
Collaborators Former students Prof. Mngmng Lu (CSU) Prof. Feng L (IUPUI) Vstng scholar Prof. Mngjun Xao (USTC) 28
Questons 29