Ituitive Uderstdig of Throughput-Dely Trdeoff i Ad hoc Wireless Networks Term Project: EECS 557 Witer 005 by Howrd Aderso Shrutivd Shrm
Outlie Itroductio Modelig of d hoc etworks Throughput-Dely trdeoff Fixed etworks Mobile etworks with oe rely A scheme chievig optiml trdeoff
Itroductio Ad hoc Network Ech ode c be S, D d R simulteously Chlleges Iterferece Topology chge Alysis Rdom cofigurtio Stedy stte Orders re more importt
Defiitios Dely : D Throughput : λ Mximum dely costried throughput : T whp With High Probbility : w.p. / Trsmissio rte : W Fctors ffectig throughput d dely Fixed etworks Trsmissio rge Number of hops Mobile etworks W Node velocity
Models for successful receptio Relxed Protocol model d k, j + Δ d i, j Physicl model SNIR N d + k k I i P i i, j α P d k, k j α β for α >, d P i P i P physicl model is equivlet to Protocol model
Network Topologies -Dimesiol Squre Circulr disk 3-Dimesiol Sphere Torus Avoid edge effects Need to tke ito ccout curvture of sphere For torus, the lysis c be doe by cosiderig equivlet squre
Throughput-Dely Trde-off for Fixed Networks Assumptios Uit torus Slotted time Relxed protocol model Θ T Θ D Θ D T
Throughput esures t lest oe ode i ech cell Mximum trsmissio rge Successful trsmissio requires o other trsmissio i rge # of iterferig cells # of SD lies pssig through y cell Frctio of time SD pir s pcket trsmitted through cell: 8 r / log r r Δ + Θ Θ Θ r c π c Θ Θ. c c T
Dely Averge distce of SD lie Averge legth of hop Dely per pcket Hece Θ L h Θ Θ Θ h L D Θ D T
Throughput Dely Trdeoff for Mobile Networks Assumptios Uit torus with cells, ech re / v scles dow s fuctio of v θ Slotted Time Results o throughput d dely D O v T θ
TDMA for mobile etworks Pcket trsmissio is broke up ito slot A d B Slot A Source trsmits to destitio if i sme cell OR source trsmits to rely i the cell Slot B the rely rdomly chooses ode i the sme cell d trsmits pcket tht is destied to it
Throughput # of cell time slots to void iterferece + c For / probbility of t lest two odes per cell / e 0. 6 Probbility tht ode hs pcket for other ode frctio of time for which ode hs pcket for other ode c Probbility tht trsmissio tkes plce withi cell throughput of ech cell Θ 0.6 c / + c Combied throughput of ll cells Throughput per SD pir T Θ Θ Θ
Dely + με σ σ μ, mx ] [ s D E Θ / v t If the verge dely, Time i which ode crosses cell A GI-GI--FCFS queue c be defied with time step d sttes ] [ ; ] [ ] [ ; ] [ s S Vr A Vr S E A E σ σ μ ε μ t, t X t X ij ij + με σ σ μ, mx ] [ s D E
Dely The M.C. X t, X speds equl time i ll sttes therefore, Avg. iter-meetig time of S&R From the M.C. model, hece, Actul dely Hece ij ij t Vr E[ D] Θ mx, T E [ A] [ A ] Θ Θ D Θ v / Θ t Θ Θ Θ D
Optiml Throughput-Dely Trde-off for Mobile Networks Scheme 3 For log v ο / T Ο D T Θ
Justifictio for ode velocity If iitil distce betwee S&D d I sigle hop, the distce will icrese by t lest d will decrese by t most + c v l After hops, the distce will be less th For pcket to evetully rech the destitio c v d l + log v ο ο / Sice velocity is very smll compred to the edge legth of the cell, Scheme 3 is essetilly equivlet to tht of Fixed Node Networks
Scheme 3b Throughput For evetul delivery of pcket betwee SR d RD, b log v ο ο / log v ο ο / # of sub-cells d / b # of odes i sub-cell m Θ Throughput betwee SR & RD d hece SD T Θ m d Θ log / Θ log m Θ
Scheme 3b Dely Two kids of dely, hop dely, d mobile dely Becuse of the costrit o velocity, mobile dely domites hop dely The derivtio of dely is ideticl to scheme two, except the rdom wlk is o re of size / by /, isted of by The time for ode to move out of cell is t Θ v The dely is hece D Θ v
Commets Whe torus is ufolded to mke squre, the miimum distce betwee the odes chges Torus hs bee used to void edge effects but i the derivtios, the fctor correspodig to edge effects ws icluded ij ij I the M.C. model Scheme, the sttes X, should be i t X t 0,,..., / 0,,..., / isted of 0,,..., 0,,..., I the rdom wlk model, X ij k but with rdom mobile odes, it should be X ij k ij X t + K mod, where {, } t + K + k ij X t + K mod /, where {,,0, +, } t + K + k I Scheme 3b, hop dely should be Θ isted of b Θ b
Commets The pcket size ws scled to T i the lysis, so the ctul throughput i terms of bits will be of the order T Θ T Orders do ot give cler picture,000 d 0, 000 mke huge differece!
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