Pah Aalabl A Hoc Newok Da Yu Hu L a Igo Gube Semes AG ICM N PG SP RC FR Gusa-Heema-Rg 5 873 Müche Gema Emal: Da.Yu@c.semes.e Tel. +49 89 636 4557 Fa: +49 89 636 4559 Absac. Due o he comple a hgh aomess mos cue eseaches o a hoc ewoks ae base o smulao esuls a empcal aalss lackg heoecal uesag o he a hoc ewoks a he behao. Ths pape peses a geeal a hoc ewok moel a ees he sasc esuls o lk a pah aalabl popees a hoc ewok. Smulao esuls ae ge o e ou heo. Ths su coul see as gouwok o uhe a hoc ewok eseaches clug a hoc ewok peomace aalss a oug algohms esg. Iouco A hoc ao ewok has ma aaages oe aoal cellula weless ewok [] []. I oes o eque asucues a pomses geae lebl lowe opeag cos hghe houghpu a bee coeage. Howee he esg o a hoc ewoks s a cul ask because o couous chage o ewok opolog a ma ewok paamees ha ae hghl aom a hghl epee o each ohe. Because o he comple o a hoc ewoks cue eseaches mal ocus o usg smulaos ools. Howee ou opo s ha beses smulao s sll ecessa o o heoecal aalss oe o ge eep uesag o sasc popees o moble weless a-hoc ewok e.g. ewok coec ewok capac a lk aalabl. I hs pape we emphasze o he aalss o lk a oue aalabl popees o a hoc ewoks. Thoughou hs pape ou eo o lk aalabl s he pobabl ha a weless lk bewee wo moble oes ema es ae a ge me. Lk aalabl ma be ake o accou pah seleco a pah upae oug algohms o achee bee peomace. I a a hoc ewok lk aalabl s eee o pah aalabl whch meas he pobabl ha a mulhop pah s aalable ae a cea me. I [3] lk a pah aalabl moels o weless a hoc ewoks wh a aom walk-base mobl wee ee. Base o hs mobl moel each oe s moeme cosss o a sequece o aom legh eals calle mobl epochs ug whch a oe moes a cosa eco a a cosa spee. The spee a eco o each oe aes aoml om epoch o epoch. The epoch leghs ae epoeall sbue. The spee ug each epoch s a aom aable o Gaussa sbuo whle he eco o he moble ug each epoch s uoml sbue oe [. The pape compae aalc a smulae esuls a
Da Yu Hu L a Igo Gube coclue ha he elae eo ceases wh ceasg pah legh o small alues o epochs. I hs pape we ee lk a pah aalabl moels o a-hoc ewoks wh a aom walk mobl moel ha s ee om he oe [3]. Ou aalabl su wll poe eal sgh o he lk a pah aalable me a ohe aalabl popees a geeal a hoc ewok. The kowlege o lk aalabl ca see as gouwok o uhe aalss o ewok peomace as well as gue o a hoc ewok poocol esg. The pape s sucue as hs. Fs we ge a escpo o ou smple a hoc ewok moel. The moel s apple o ou aalabl aalss whch oules lk aalable me sbuo a lk aalabl a mulhop pah aalabl popees. Eeuall smulao esuls o aeage lk aalable me ae ge o e ou heo. The smulao esuls cleal emosae he coecess o ou aalcal appoach. Ou smulao esuls also eeale ha o ou mobl moel he epeec bewee cosecue hops a mulhop lk s que small o be eglgble. A las seeal possble applcaos o ou heo ae popose. Moel Descpo Real wol ao ewoks ae luece b ma acos. Iegula ea asmme ao asmsso ao eeece all ca hae mpac oe he opeao o he ewoks. I ou su we make some assumpos o ge a smple e easoable moel. Alhough a hoc ewoks moble oe sbuo usuall ehbs some sucue o smpl ou su we wll sck o he assumpo ha oes ae uoml sbue. We also assume ha he ea s peecl la a all he moble oes hae he same e asmsso powe a ae equppe wh om eco aea. Theeoe he all hae equal asmsso age R. Ou assumpo smples a oe s he ao coeage shape o a peec ccle whose aus s R. The saus o lk bewee wo oes s also smple. Whe he sace bewee wo oes s lage ha R he hae o a lk wheeas he hae a a lk whe he sace s smalle ha R. I hs pape we ake R as he u o ou legh mec.e. R. I ou mobl moel each oe moes a a aoml chose eloc. Hee eloc s a aom eco wh eco a spee s absolue alue elemes. The eco s a aom aable φ whch s uoml sbue bewee a. The spee s a aom aable whose sbuo ca be aba. We ee he pobabl es uco PDF o eloc as φ. Fuhe moe we pa specal aeo o a smple mobl moel whee he eloc s a uoml sbue aable wh he age om o ma. Ths mobl moel has bee poe o be able o maa he uom sbuo pope [4]. The a hoc ewok moel escbe aboe s apple o he esgao o lk aalabl popees a hoc ewoks o boh sgle-hop lk a mul-hop pah.
Pah Aalabl A Hoc Newok 3 3 Theoecal aalss The aalss s ogaze o hee pas. All he oes ae couousl moeme Theeoe elae eloc bewee wo oes shoul be measue oe o ge he sace bewee wo oes. Ths s aalze he s pa. I he seco pa lk aalable me sbuo o a oe-hop lk s ge whch sees as he bass o ou uhe esgao o mulhop case he h pa ogehe wh some eesg obseao. 3. Relae eloc bewee wo oes A a ge me po we ake a close look a wo eghbo moble oes MN a MN. Assume he eloc ecos ae V a V especel. We hae he elae eloc eco V V V V V V Fgue Relae eloc Because ou moel oe moeme pae s ceosmmec.e. moble oes ae equall possble o moe o a eco. Whou lose o geeal we ca assume eco V s paallel o X-as. Le a be he Caesa oms o eco V V a V whle a beg he pola oms. Also we eoe as he Caesa om o he eloc PDF as he Caesa a he pola om o he elae eloc PDF. These wo oms hae he elaoshp cos s Smlal
4 Da Yu Hu L a Igo Gube s cos 3 The pobabl ha we oba a elae eloc eco V s he summao oe all he possble combao o V a V ha oms a agle wh V as sae. Ths PDF ca be omulae as V V V 4 Because o he elaoshp bewee hee ecos ol wo o hem ae epee. The h oe s eemsc we kow he ohe wo. Theeoe we ol ee o egae oe all possble a eeme om a. Pocees wh he calculao he pola om we hae 5 Accog o he law o cose ca be epesse as a uco o a cos + 6 The cumulae es uco CDF o elae eloc s F 7 Fo he specc sceao whee spee uoml sbues oe [ ma ] PDF a CDF o he elae eloc alog aus ae llusae Fgue. I hs case he elae eloc ca be as lage as ma whee wo oes moe opposel.
Pah Aalabl A Hoc Newok 5.8 PDF CDF P DF CD F.6.4..5.5 ma Fgue PDF a CDF o elae eloc As we ca see om Fgue abou 8% o he elae spee sbues wh he age.3 ~.3 ma. Ths suggess us ha e ew oes ema elae sac a geeal s a lle hghe ha oe oe s. Alhough ou aalss hee s ol specc o a cea mobl moel he mehoolog coul sll be apple o ohe moels. 3. Lk aalable me Cose he oe-hop lk bewee wo moble oes MN a MN. Because o he ceosmec aue o ou moel whou loss o geeal we ca assume ha he al sace bewee hem s a he le coecg wo pos s paallel o X-as. I we ake MN as he eeece po he om he ewpo o MN MN moes a a elae eloc whose sbuo s escbe beoe a MN emas sac. Ae me MN moes ou o he ao asmsso age o MN. The sace aele ug hs peo s ρ. Accog o he law o cose ρ R s cos 8 The CDF o he lk aalable me.e. he pobabl ha he lk aalable me s less ha s F F m 9 whee m s he mmum eque eloc o each he boe o he coeage aea eacl ae me. ρ m The PDF o he lk aalable me ca be obae om s CDF
6 Da Yu Hu L a Igo Gube R ρ MN MN MN Fgue 3 Lk aalable me F Now we coul calculae he epecao o he aalable me o hs weless lk ] [ E Ee moe we ca coclue he mea lk aalable me sbuo bewee wo abal chose oes whch s he mea alue o lk aalable me oe all he possble poso o MN.e. R 3 R R R F F 4 Theeoe he aeage aalable me bewee wo oes s
Pah Aalabl A Hoc Newok 7 E[ X ] E[ X ] 5 Fo he specc sceao whee eloc uoml sbues oe [ ] he aalable me wh ee lk legh s llusae Fgue 4. Seeal eesg hgs ae oce he gue. Fs he begg hee ae some la egos equal o zeo o. o.7. Ths meas ha lks ae alwas aalable ug hs me whch ca be eplae b ou spee lm. Because we hae a mamum spee o ma. I MN s se he coeage o MN cao escape MN s coeage beoe a cea me. We call heshol me whch s he mmum eque me o MN o each he coeage boe o MN.e. h R 6 ma Aohe hg o be oce s he zeo heshol me whe MN sas a he boe o ao coeage o MN. A hs po aalabl mmeael gows o 5% whe MN sa o moe. Fom he mcoscope ew he boe ca be egae as a le. Theeoe MN has equal pobables o moe boh o a ou o MN s coeage. ma.8 CDF.6.4...7..5.5.5 3 Fgue 4 Lk aalable me CDF Lk aalabl a a ge me s he pobabl ha a coece lk a me s sll aalable a me. Ths s he same as o sa ha s he pobabl ha a lk s aalable ae moe ha secos whch s P a F 7 a I s ploe Fgue 5.
8 Da Yu Hu L a Igo Gube.5 ma.5.8.6.4..8.6.4. Aalabl Fgue 5 Lk aalabl as a uco o lk sace a me 3.3 Aalable me o mulhop lks pah Now we cose a e-o-e pah wh > hops whch ees om moble oe MN alog MN ul eaches MN + a he legh o each hop ae. Obousl hese hops ae o oall epee o each ohe. Fo sace he moeme o emeae oe MN wll aec boh o s lks o MN a MN 3 Theeoe hee s epeeces bewee lks om MN o MN a om MN o MN 3 o ae o eel epee. Howee o smpl ou su we ma s eglec he eec o epeec bewee wo cosecue lks. Assume aalable me o each hop ae aom aables whose sbuo cooms o Fgue 4. The he lk aalable me o hs -hop lk s a aom aable ha s he mmum alue o he lk aalable me o each o s hops whose CDF s m{ 8 F... P X P X k k k > P X > [ P X ] [ F ] k k k 9
Pah Aalabl A Hoc Newok 9 To ge eepe sgh o he aalable me o hs -hop pah we wll coceae ou su o aeage pah aalable me sbuo. Follow he same eao as 9 he CDF ca be obae wh F [ F ] [ F ] k a he PDF s F [ F ] Now we ca coclue aeage aalable me o he -hop pah as E[ X ] [ F ] lm [ F ] [ F ] + [ F ].8 CDF.6.4. 4 8.5.5.5 3 Fgue 6 Mea aalable me sbuos -hop lk Fo he specc sceao ha eloc s uoml sbue bewee [ ] u/seco lk aalable me sbuo s llusae Fgue 6. The aeage aalable me o he mulhop pah wh ee umbe o hops s eeale Fgue 7. The aalable me ops quckl om o oe-hop lk o a lle moe ha.5 o 3-hop lk. Howee he cue sas elae la whe we uhe
Da Yu Hu L a Igo Gube cease he umbe o hops he pah whch ol ops om.45 o a 4-hop pah o.4 o a 8-hop lk. Aalable m e.75.5.5.75.5.5 3 4 5 6 7 8 Numbe o hops Fgue 7 Aeage aalable me mulhop pah Fo he aeage pah aalabl mulhop cases we hae a P F [ F ] 3 I Fgue 8 he lk aalables o he mulhop lk wh ee umbe o hops ae ge. The aeage aalable me ca be obae as E[ P a ] R a P 4 Aalabl.8.6.4 4 8..5.5.5 3 Fgue 8 Mea lk aalabl esus me I s obous ha he peomace eeoaes e as whe umbe o hops cease. Fo sace a me.3 o aeage hal o he lks wll be al o sgle-hop lk wheeas.7 o -hop lks.4 o 3 hop lks a. o 8 hop lks. Ths as ecease o he aalabl sogl ssuaes he usage o lks wh oo ma hops a hoc mulhop oug algohm.
Pah Aalabl A Hoc Newok 4 Smulao I oe o e ou aalss a esgae he luece o ou eglec o epeec bewee cosecue hops a mulhop lk we couce smulaos o measue he aeage aalable me. Fo each sceao we geeae + oes. Noe k+ k s eploe uoml se oe k s ao coeage. Each oe aoml chooses s eco a eloc om uom sbuo. The aalable me s measue whe a oe k+ moes ou o oe k s ao coeage. We aoml geeae such sceao a aeage oe hem. The paamees ae summaze Table. Table Smulao paamees Paamee Value Rao asmsso age R Spee sbuo Uom [ ] Deco sbuo Uom [ ] Poso sbuo Uom We smulae he aeage pah aalable me a ee umbe o hops. The ae ploe alog wh heoecal cue a elae eo Fgue 9. As we ca see he smulao esul s e ea o he cue wh ou heo slghl ueesmaes. The close-up obseao uels a eesg pheomeo. The elae eo s almos sble o sgle-hop lks. Howee he elae eo each s mamum alue o -hop pahs a goes smalle wh ceasg umbe o hops. Ths ca be eplae b he epeec bewee cosecue hops o he mulhop pahs. Because he e-hop epeec euces he aomess bewee cosecue hops we ake o accou hs epeec he acual lk aalable me peomace shoul be a lle bee ha ou aalss. As hee s o e-hop epeec ess a sgle-hop lk ou smulao esul shoul be e close o he heo ~.5%. Fo a wo-hop lk each hop has some epeec oe he ohe. Fo a lk wh moe hops because each hop s ol epee o s mmeae cosecue hops bu o he uhe hops he eec o epeec he whole lk s aeage ou. Ths eplas he elae lage eo ~4.7% o wo-hop lks ou peco a s eec o geg smalle wh ceasg umbe o hops. Fom he gue we ca easl coe o eal-wol paamees. Fo eample he ao asmsso age s mees a mamum eloc s ma m/s whch smulaes a peesa sceao. We ca ee he aeage aalable me o a 3-hop lk as.6 / 6 sec. Ths s a om eough o a omal huma coesao. Theeoe we ehe use moe powe o euce he umbe o hops o swch o ohe possbl such as a backup lk wh less umbe o hops.
Da Yu Hu L a Igo Gube Aeage aalable me.8.6.4..8.6.4. Aalss Smulao Relae Eo.5.45.4.35.3.5..5..5 Relae Eo 3 4 5 6 7 8 Numbe o hops he lk Fgue 9 Aeage aalable me mulhop lk 5 Coclusos I hs pape we esablshe a smple a hoc ewok moel. Base o he moel lk a pah aalabl popees a hoc ewoks ae sue. Speccall he aalable me a aalable pobabl sgle-hop lk a mulhop pah ae caeull esgae. I a mulhop pah mpac o epeec bewee cosecue hops s also sue whch u ou o be eglgble o geeal-pupose eseach. Ou eseach o lk aalabl ca be egae as gouwok o uhe aalss o a hoc ewok peomace as well as a gue o a hoc ewok oug poocol esg e.g. opmzao o oue seleco a oue scoe algohms. Reeeces [] MANET Wokg Goup o IETF. hp://www.e.og/hml.chaes/maechae.hml [] C. E. Peks eo A hoc ewokg Aso - Wesle [3] A Buce McDoal a T. F. Zab A pah aalabl moel o weless a hoc ewoks Poc. IEEE WCNC New Olea USA Sep. 999 [4] Elzabeh M. Roe "Roug A hoc Moble Newoks: O-Dema a Heachcal Saeges" hp://www.cs.ucsb.eu/~eoe/publcaos.hml