Network Connectivity Probability of Linear Vehicular Ad-Hoc Networks on Two-Way Street

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1 Communcatons and Ntwok,, 4, ublshd Onln Novmb ( Ntwok Connctvty obablty of Lna Vhcula Ad-Hoc Ntwoks on Two-Way Stt. C. Nlakantan, A. V. Babu Dpatmnt of Elctoncs and Communcaton Engnng, Natonal Insttut of Tchnology, Calcut, Inda Emal: Rcvd August 8, ; vsd Sptmb 7, ; accptd Octob, ABSTRACT In ths pap, w psnt an analytcal modl to dtmn th ntwok connctvty pobablty of a lna vhcula adhoc ntwok (VANET) fomd by communcaton quppd vhcls on a two-way stt scnao. W consd th hghway to b consstng of two lans wth vhcls movng n both dctons on ths lans and focus on th pobablty of bng abl to convy mssags fom a souc vhcl to a dstnaton vhcl, whch may b multpl hops away. Closd fom analytcal xpsson s obtand fo th ntwok connctvty pobablty n th psnc of Nakagam fadng channl. In ou modl, th tansmsson ang of ach vhcl s modld as a andom vaabl du to channl fadng. Th analytcal sults a valdatd by xtnsv smulatons. Kywods: Two-Way Connctvty; Nakagam Fadng; Vhcula Ad-Hoc Ntwok. Intoducton Vhcula Ad-Hoc Ntwoks (VANETs), whch allow vhcls quppd wth wlss communcatons dvcs to fom a slf-oganzd ntwok wthout th qumnt of pmannt nfastuctus, a hghly mobl wlss ad-hoc ntwoks nvsond to povd suppot fo passng safty, taffc managmnt and nttanmnt applcatons by nablng both vhcl-to-vhcl (VV) as wll as vhcl-to-nfastuctu (VI) communcatons []. Th Ddcatd Shot Rang Communcatons (DSRC) has bn poposd as th mgng tchnology that suppots vhcula communcatons. Th Fdal Communcaton Commsson (FCC) n USA has appovd 75 MHz of spctum btwn 585 and 595 MHz fo DSRC to nhanc safty and poductvty of th tanspotaton systms. Th Task Goup known as IEEE 8. p has cntly poposd an amndmnt to th 8. standad to suppot communcatons n vhcula nvonmnts []. Th IEEE wokng goup 69 has bn fomd to spcfy addtonal lays of th potocol stack. Th combnaton of IEEE 8. p and th IEEE 69 potocol sut s dsgnatd as WAVE (Wlss Accss n Vhcula Envonmnts). Th ovall WAVE achtctu ncluds IEEE standads 69. to 69.4 (fo souc managmnt, scuty achtctu, ntwokng svcs, and multchannl opaton, spctvly), and IEEE 8. p (fo MAC and HY) [-3]. Ntwok connctvty s a fundamntal qumnt n VANETs,.., all vhcls on a hghway sgmnt should b abl to communcat wth ach oth dctly, o va multpl hops btwn ntmdat vhcls. To nsu that a tm ctcal mssag fom a souc vhcl s convyd to anoth (dstnaton) vhcl whch may b multpl hops away, th hghway sgmnt should hav a ctan numb of vhcls quppd wth wlss communcaton dvcs. It s th task of a ntwok dsgn to dtmn th mnmum numb of vhcls (o mnmum vhcl dnsty) ncssay to fom a fully connctd ntwok. Moov, chaactzng th connctvty of VANETs whn th vhcl dnsty s low and th spd of th vhcls and th flow a ndpndnt,.. n f-flow phas, s a cucal sach challng fo alzng commcal VANET applcatons. In th ltatu, sval attmpts hav bn mad to analyz th connctvty popts of VANETs (.g. [4-5]). Th connctvty analyss of VANETs n [4] advocats a dynamc tansmsson ang fo ach vhcl to adapt to th fqunt topology changs. In [5], ntwok connctvty of on-dmnsonal VANET has bn analyzd usng a quung thotc appoach. In [6], authos psnt a tchnqu to mpov th connctvty n VANET by addng xta nods known as mobl bas statons. Th connctvty popts of a mobl lna ntwok wth hgh spd mobl nods and stct dlay constants a nvstgatd n [7]. In [8], VANET connctvty has bn analyzd basd on a comphnsv moblty modl. A nw analytcal modl fo VANET connctvty basd on poduct-fom quung ntwoks has bn poposd n [9]. Authos of [] psntd con- Copyght ScRs.

2 . C. NEELAKANTAN, A. V. BABU 333 nctvty analyss of both on way and two way hghway scnaos assumng that all vhcls mantan a constant spd. In [], authos analyzd th connctvty of mssag popagaton n a two-dmnsonal VANET, fo hghway and cty scnaos. In [], authos addss th ffcts of ntsctons and two-dmnsonal oad topology on th connctvty of VANETs n uban aas. An analytcal modl to nvstgat th mpact of vhcl spd on VANET connctvty has bn psntd n [3] assumng vhcls tansmsson ang to b dtmnstc. In [4], authos psnt an analytcal modl to comput th ntwok connctvty pobablty of VANET on on-way stt n th psnc of channl fadng. In [5], authos analyz connctvty popts of on-dmnsonal VANET fom a quung thotc pspctv to fnd th avag connctvty dstanc and avag clust sz, n th psnc of fadng. In ths pap, dffntly fom th abov, ou am s to dvlop an analytcal modl to fnd th ntwok connctvty pobablty of a VANET on a two-way stt scnao shown n Fgu. In ths cas, w consd th hghway to b consstng of two lans (say, low lan and upp lan), wth vhcls movng n both dctons on ths lans. If th connctvty pobablty on a spcfc lan (say, low lan), s lss than, thn th ntwok fomd by vhcls on ths lan may conssts of mo than on clust, (wh a clust s dfnd as a unt of connctd vhcls), btwn whch no communcaton s possbl. If th connctvty pobablty s low, thn th chanc of havng multpl clusts s hgh and vc vsa. To nsu that a tm ctcal mssag fom a souc vhcl s convyd to anoth vhcl whch may b multpl hops away, all th vhcls on th lan sgmnt should b abl to communcat wth ach oth dctly, o va multpl hops btwn ntmdat vhcls, to mt ths qumnt, th ntwok must consst of only on connctd clust. To mpov th pobablty of connctvty on a typcal lan (say, low lan), and to nsu that th ntwok on ths lan conssts of only on clust, t may b possbl to tak advantag of vhcls movng n th oppost dcton on th scond lan (say, upp lan). Ths mans Fgu. Vhcls on a typcal two-lan hghway. that, f th s a lnk falu on th low lan, th lnk connctvty can b stod wth th hlp of opposng vhcls on th oth (upp) lan. Lt us consd a spcfc scnao shown n Fgu, wh th s a twoway stt (say, low lan and upp lan), and wh a packt s bng layd fom th lft nd of a oad sgmnt (vhcl A) to th ght nd of th sgmnt on th low lan (vhcl B). Assum that along th mult-hop out fom A to B, th packt fom a vhcl V cannot b fowadd to anoth vhcl on th sam lan V bcaus th nt-vhcl dstanc X, s gat than th vhcl s tansmsson ang. Thus th connctvty on th low lan wll b lost at ths pont. Howv, t s possbl to tak advantag of th vhcls on th scond lan. Not that, n ths cas, f th s a vhcl S on th upp lan, that s wthn th tansmsson ang of th vhcl V, vhcl V can fst fowad th packt to S, and whn S gts clos to V, t can thn fowad th packt futh to V. Wth ths fowadng statgy, th ntwok connctvty on th low lan can b stod. Ths fowadng statgy s usually fd to as stocay-fowad outng, and s sutabl only fo dlay tolant applcatons. In ths pap, w psnt an analytcal modl to fnd th ntwok connctvty pobablty of a VANET fo th two-way stt scnao wth sto-cay-fowad appoach. In ou modl, th ffct of fadng s also consdd and th tansmsson ang of ach vhcl s modld as a andom vaabl. Th andom tansmsson ang modl s lvant fo th connctvty analyss bcaus t can account fo vaablty n th communcaton lnks causd by fadng, and thus wll b abl to accuatly stmat th connctvty. Th hghway and th vhcl moblty modl that w mploy fo th analyss s basd on th wok psntd n [5,6,3]. W consd on-dmnsonal lna VANET fomd by vhcls on a two-way hghway opatng n th f flow stat, n whch th vhcl dnsty on th hghway s vy low and th vhcl spd and taffc flow a ndpndnt; thus dvs can dv as fast as thy want (subjct to a lmt on maxmum spd known as fway vlocty) and ovtakng s allowd [5,6]. Th f flow taffc stat has bn assumd fo th analyss snc th connctvty of th ntwok s vy low n ths stat. Futh th vhcl spd s assumd to b a Gaussan andom vaabl. Ths patcula modl fo hghway and vhcl moblty psnts a alstc VANET scnao fo unntuptd hghways and smla modl has bn usd n many paps [5-7,3-5]. Th poposd analyss dos not consd th ffcts of th undlyng MAC potocol. It s assumd that an dal MAC potocol s mployd that can solv contnton ffctvly. Futh, snc ou focus s on VANETs usd fo dssmnaton of boadcast nfomaton latd to taffc safty, w do not consd Copyght ScRs.

3 334. C. NEELAKANTAN, A. V. BABU th ffcts of spcfc uncast outng schm [5-5]. W mploy Nakagam fadng fo ou connctvty analyss snc cnt studs hav shown that Nakagam fadng can b usd to dscb statstcal chaactstcs of small scal fadng n a VV channl [6-8]. A dstanc dpndnt pow law modl s usd fo th path loss snc cnt mpcal and analytcal modlng studs hav shown that, fo hghway, uban, and sububan scnaos, a classcal pow law modl s sutabl to dscb th VV path loss [9,]. Th valdty of ou thotcal analyss s vfd by xtnsv smulaton studs. To th bst of ths authos knowldg, analytcal modls to dtmn th mpact of physcal lay dpndnt paamts on VANET connctvty on a two-way stt hav not appad n th ltatu so fa. Rst of ths pap s oganzd as follows: Scton dscbs th systm modl. In Scton 3, analytcal modls a psntd fo th connctvty. In Scton 4, w psnt th analytcal and smulaton sults. Th pap s concludd n Scton 5.. Systm Modl Th systm modl usd fo th connctvty analyss, whch ncluds modls fo hghway and vhcl moblty, s smla to that of [5] and s bfly dscbd as follows: Assum that an obsv stands at an abtay pont of an unntuptd hghway (.., wthout taffc lghts, tc.). Empcal studs hav shown that osson dstbuton povds an xcllnt modl fo vhcl aval pocss n f flow stat []. Accodngly, assum that th numb of vhcls passng th obsv p unt tm s a osson pocss wth at vh/h. Thus th nt-aval tms a xponntally dstbutd wth paamt. Futh, assum that th a M dsct lvls of constant spd v, =,,,M wh th spds a..d., and ndpndnt of th nt-aval tms. Lt th aval pocss of vhcls wth spd v b osson wth at, =,,, M, and lt M. Ths aval pocsss a ndpndnt and th pobablty of occunc of ach spd s p. Lt X n b th andom vaabl psntng th dstanc th btwn n closst vhcl V n to th obsv and n th closst vhcl, V n to th obsv. It has bn povd n [5] that th nt-vhcl dstancs (IVD s) a..d., and xponntally dstbutd wth paamt M M p. v v Empcal studs hav shown that th vhcl spd V n f flow stat follows a Gaussan pobablty dstbuton []. To avod dalng wth ngatv spds o spds clos to zo, two lmts a dfnd fo th spd,.., v and max vmn fo th maxmum and mnmum lvls of vhcl spd, spctvly. Fo ths, a tuncatd Gaussan DF s usd gvn by [5]. fv v gv v () vmax fv udu wh f V v vmn v xp π s th Gaussan DF, μ = avag spd, σ-standad dvaton of th vhcl spd, vmax = 3 s th maxmum spd, v = 3 mn s th mnmum spd. Substtutng fo fv v n (), th tuncatd Gaussan DF g v s gvn by [5]: v v fv gv v, vmn vvmax vmax vmn f f () wh f s th o functon. Wth ths modl, th cumulatv dstbuton functon (CDF) of nt-vhcl x dstanc X s gvn by FX x, x, wh M p E V. v H E s th xpctaton opato and psnts th avag vhcl dnsty (vh/km). Whn th vhcl spd follows tuncatd Gaussan DF, th avag vhcl dnsty s computd as follows [5]: vmax vmn π vmax vmn f f v xp d v v It may b notd that th avag vhcl dnsty gvn n (3) dos not hav a closd fom soluton, but has to b valuatd by numcal ntgaton. Snc ach vhcl nts th hghway wth andom spd, th numb of vhcls on th hghway sgmnt of lngth L s a andom vaabl. Th avag numb of vhcls on th hghway sgmnt, n th stady stat s thn gvn by N = L. 3. Analyss of Ntwok Connctvty Consd th two-way stt (consstng of low and upp lans) shown n Fgu. Assum that vhcls a movng fom ght to lft on th low lan (fd to as man lan); and fom lft to ght on th upp lan. (3) Copyght ScRs.

4 . C. NEELAKANTAN, A. V. BABU 335 Lt and spctvly psnt th avag vhcl dnsts on th low and th upp lans; and lt N and N spctvly psnt th avag numb of vhcls on ths lans. Futh, assum V and V to b th andom vaabls psntng vhcl spd and and spctvly psnt th vhcl aval ats on ths lans. Assum that and, spctvly b th man and th standad dvaton of vhcl spd on ths lans. Thn, w hav N L and N L, wh L s th hghway lngth; and a computd accodng to (3). It s assumd that packts a layd fom th lft to th ght of th oad sgmnt on th low lan, whch mans that packts a layd n th oppost dcton of vhcl movmnt. Ths s a asonabl assumpton bcaus taffc nfomaton such as safty wanng, s usually layd fom th souc vhcl to th vhcls followng t. W now pocd to dv an analytcal xpsson fo th ntwok connctvty on on-way stt (low lan), and us ths xpsson to fnd ntwok connctvty on two-way stt. 3.. Ntwok Connctvty on On-Way Stt Consd th ntwok fomd by vhcls on th man (low) lan, wh th avag numb of vhcls s qual to N, that cosponds to N lnks on th stt. Two conscutv vhcls n th ntwok wll b connctd f th nt-vhcl dstanc btwn thm s small than vhcl s tansmsson ang R. Accodngly, th pobablty that two conscutv vhcls V and V a connctd s gvn by X R, wh X s th nt-vhcl dstanc. Th ntwok wll b connctd f th s a path connctng any pa of vhcls. Mo pcsly, t s qud that th nt-vhcl dstancs X R fo =,,3,, N. Lt th vhcl tansmsson ang b a andom vaabl wth CDF FR. Lt b th pobablty that a pa of conscutv vhcls n th ntwok a connctd (lnk connctvty pobablty). As mntond bfo, ths pobablty s computd as = X R. It may b notd that both X and R a ndpndnt andom vaabls. Accodngly, w fnd ths pobablty as follows: R < x Xn x fx xdx (4) wh f X x s th DF of th nt-vhcl dstanc (IVD), X. Lt NC b th pobablty that th ntwok s connctd. It follows that X R, X R, R. NC, XN Not that Xn ; n,, N a..d. andom vaabls [5]. Hnc th ntwok connctvty pobablty of on-way stt ( ) s computd as follows: NC, way N NC, way R < x Xn x fx xdx n (5) To comput th connctvty pobablts, th CDF of th tansmsson ang, F R must b known. Nxt, w fnd FR, assumng that VV channls xhbt Nakagam fadng chaactstcs, and thn dv xpsson fo ntwok connctvty pobablty. Consd th Nakagam fadng channl wth th assumpton that th fadng s constant ov th tansmsson of a fam and subsqunt fadng stats a..d. Th cvd sgnal to nos pow at a dstanc d away fom tansmtt n a fadng channl s wttn as d Z d T nos wh Z s th fadng coffcnt, s a constant assocatd wth path loss modl, T s th tansmt pow, s th path loss xponnt, and nos s th total addtv nos pow. H GGc 4πf T R o, wh G and T G R spctvly psnt th tansmt and cv antnna gans, c s th spd of lght and f o s th ca fquncy []. Now s dtmnd by assumng G T G R and f o = 5.9 GHz []. Th thmal nos pow s gvn by nos = FKTo B wh F s th cv Nos Fgu, K s th Boltzmann constant, T o s th oom tmpatu and B s th bandwdth. Now nos s dtmnd by assumng that F 6 db, K =.38 3 J/Klvn, T o = 3 Klvn and B MHz fo 8. p []. Assum- ng that E Z, th avag SNR can b wttn as T d nos. Th DF of th cvd SNR und Nakagam-m fadng s gvn by []: f a m a m m m m ma wh s th avag SNR, m s th Nakagam fadng paamt.5 m, and. s th Gamma functon. Th pobablty that a tansmttd mssag s coctly cvd at a dstanc d s gvn by, (6) mm, d d f ada (7) m d s, a wh d T nos and s th upp ncomplt Gamma functon [3]. Th CDF of th tansmsson ang can b computd as follows: R x mm, F x R x m x wh x T x nos. As mntond n Scton, th IVDs a..d., and xponntal wth DF x f x, th lnk connctvty pobablty, X (8) Copyght ScRs.

5 336. C. NEELAKANTAN, A. V. BABU s dtmnd by combnng (4) and (8) and s gvn by x mm, m x dx (9) Th ntwok connctvty pobablty s computd by combnng (5) and (9) as: x NC, way Fo ntg valus of s, s s mm, m x dx N s, a can b wttn as k a s a sa, s! k, k! () and! [3]. Accodngly, fo ntg valus of m, (9) bcoms: k m x nos m x m T nos k k! T k x dx () To valuat th ntgal n (), w us th followng sult potd n [4]: p x π, z, p > zx x dx p p, z G, z p p ;,, () Not that () s vald fo postv ntg valus of mn, and G p, q s th Mj s G functon [4]. Accodngly, whn s a postv ntg, th ntgal n () can b wttn n tms of Mj s G functon basd on (). Thus s computd as follows: m m k nos π k k! T, T G, k k m,, nos k k (3) Fo ntg valus of and m, th ntwok connctvty pobablty on on-way stt can b wttn as, k m m nos NC, way π k k! T G, T, mnos k k N k k,, (4) Fo non-ntg valus of, () has no closd-fom soluton and hnc both and NC, way hav to b valuatd by numcal tchnqus usng (9) and () spctvly. 3.. Ntwok Connctvty fo th Two-Way Stt In ths scton, w psnt th connctvty analyss fo th two-way stt scnao. Consd th two-way stt scnao shown n Fgu, wh vhcls on th low lan lay packts oppost to th dcton of moton and sto-cay-fowad outng s usd whn th s a bokn lnk on th low lan. Wth ths appoach, ntwok connctvty on th low lan can b stod wth th hlp of vhcls that mov n th oppost dcton on th upp lan. Lt LB b th pobablty that connctvty on a spcfc lnk s lost (.., th lnk s bokn) on th low lan. Ths happns whn th IVD btwn a pa of vhcls bcoms gat than th tansmsson ang. Accodngly, LB s qual to th complmnt of th lnk connctvty pobablty, th analyss of whch was conductd n Scton 3.. Thus w hav,. X R (5) LB wh s computd usng (9). Out of a total of (N ) lnks on th low lan, th pobablty that J of ths lnks wll b bokn, s gvn by: N j N j J j LB LB j C ; j,,, N. (6) If all of th bokn lnks on th low lan a fxabl wth th hlp of vhcls on th upp lan, th ntwok connctvty on th low lan can b stod. Consd th bokn lnk btwn vhcls V and V shown n Fgu. In ths cas V has a packt to b snt to V. Ths bokn lnk s fxabl f th s at last on vhcl on th upp lan n th ntval of lngth R cntd aound V. Lt U b a andom vaabl dnotng th numb of vhcls that a psnt n th ntval of R on th upp lan. Accodng to th systm modl dscbd n Scton, th IVDs on th low as wll as th upp lans a..d. xponntal wth paamts ρ and ρ spctvly. Hnc th numb of vhcls on th low and upp lans s osson wth paamts ρ and ρ spctvly. Accodngly U s also osson wth pobablty mass functon gvn as follows: UuR u U R u u! (7) A bokn lnk on th low lan s not fxabl f th a no vhcls n th ntval of R on th upp lan. Copyght ScRs.

6 . C. NEELAKANTAN, A. V. BABU 337 Thus th condtonal pobablty that bokn lnk s not fxabl s computd as U R=. Uncondtonng, th pobablty that a bokn lnk s not fxabl ) s calculatd as follows: ( L, nf Lnf, frd (8) wh f R s th DF of R. Fo Nakagam fadng, fr s gvn by th followng xpsson (oof gvn n Appndx A). m k k fr k k wh m nos T (9). Substtutng (9) n (8), th followng xpsson can b obtand fo L, nf : (oof gvn n Appndx B) (s fomula () blow). Lt NC J b th condtonal ntwok connctvty pobablty gvn that th a J bokn lnks. Snc th pobablty that ach bokn lnk s fxabl s qual to L, nf, CJ s computd as follows: NC J j Lnf j, ; j,,,, N () Th ntwok connctvty pobablty on th two-way stt s thn computd as follows: NC,way N j () j CJj J It may b notd that, to comput NC, way accodng to (), Equatons (9), (5), (6), () and () must b usd. 4. Analytcal and Smulaton Rsults In ths scton, w psnt sults fo th ntwok connctvty. Both th analytcal as wll as smulaton sults a obtand usng MATLAB. As mntond bfo, n th f flow stat, th vhcl spd and th taffc flow a ndpndnt and hnc th a no sgnfcant ntactons btwn ndvdual vhcls. Thfo, gnatng vhcl taffc aval pocss s possbl wthout usng commcal taffc o ntwok smulatos [5]. Hnc MATLAB s usd to smulat an unntuptd hghway. Th vhcl aval modl and th moblty modl of Scton a mplmntd usng an vnt dvn smulaton usng MATLAB. Th ffct of fadng s ntoducd nto th smulaton usng Mont-Calo tchnqus. W consd a hghway of lngth L = km and th vhcls a gnatd fom a osson pocss wth at λ vh/sc. Each vhcl s assgnd a andom spd chosn fom a tuncatd Gaussan dstbuton. Tabl shows typcal valus fo th man (μ km/h) and standad dvaton (σ km/h) of th vhcl spd on th hghway [5]. To fnd th ntwok connctvty, w fx λ =. vh/sc. Th vhcl spd follows a tuncatd gaussan andom vaabl wth man μ = 7 km/h and standad dvaton σ = km/h. Ths valus of λ, μ and σ cospond to avag vhcl dnsty 5.8 vh/km on th low lan. Futh, th tansmt pow s fxd as T = 33.3 dbm accodng to DSRC and IEEE 8. p spcfcatons [] and cv SNR thshold s slctd as db. Th snap shot of th hghway at th aval nstant of ach vhcl s obsvd and th nt-vhcl dstanc valus a dtmnd. Fo ach lnk, th avag SNR d s dtmnd cospondng to th masud valu of nt-vhcl dstanc, d of that lnk. Assumng Nakagam fadng nvonmnt, w thn gnat a andom vaabl psntng th cvd SNR ov that lnk wth avag valu d. If th cvd SNR s gat than th thshold valu, th lnk s consdd to b connctd. Th pocdu s patd fo all th N lnks wth th cospondng nt-vhcl dstanc valus. If all th lnks n a snap shot a connctd, th ntwok s consdd to b connctd. Th connctvty valuaton pocss s thn patd, tms. Th ntwok connctvty pobablty s calculatd fom ths, sampl valus. Fgu shows th ntwok connctvty pobablty of on-way stt and two-way stt ( NC, way and ) plottd aganst path loss xponnt ( ), fo a NC, way Tabl. Nomal-vhcl spd statstcs [5]. v (km/h) (km/h) v m k k k, Lnf, π G, k k k,, m k k, k k π G, k k k,, () Copyght ScRs.

7 338. C. NEELAKANTAN, A. V. BABU fxd avag vhcl dnsty. To dtmn th two-way stt connctvty, th avag vhcl dnsty on th upp and th low lans a assumd to b qual (.., = ). In Fgus 3 and 4, ntwok connctvty pobablts on both on-way as wll as two-way stts a plottd aganst avag vhcl dnsty ( ) fo =.8 and 3.5 spctvly. In ths cas, to fnd two-way stt connctvty pobablty, s st qual to 5 vh/km. Th sults show that th connctvty on two-way stt s always gat than that of th on-way stt cas. Futh, both Nakagam facto (m) and path loss xponnt ( ) hav stong nflunc on th connctvty. As ncass both NC, way and NC, way dcays vy apdly. Dpndng on th valu of m, th ntwok gts almost dsconnctd whn bcoms mo than 3. Futh, th ntwok connctvty pobablty gts dgadd whn th Nakagam paamt m gos blow.5 (low most plot n Fgu 3), and gts mpovd whn m >.5. As xpctd, th connctvty pobablty ncass as avag vhcl dnsty ncass. Moov, t can b obsvd that, th avag vhcl dnsty ( ), cospondng to th low lan, qud to Fgu. Ntwok connctvty pobablty (on-way and two-way) vsus athloss xponnt ( T = 33 dbm, L = km, λ = λ =.3 vh/sc, μ = μ = 7 km/h, σ = σ = km/h). Fgu 3. Ntwok connctvty pobablty (on-way and two-way) vsus avag vhcl dnsty ( T = 33 dbm, α =.8, L = km, ρ =.5 vh/m). Copyght ScRs.

8 . C. NEELAKANTAN, A. V. BABU 339 satsfy a tagt valu fo th ntwok connctvty pobablty, dcass whn th pathloss xponnt dcass. Fgu 5 shows th two-way ntwok connctvty pobablty plottd aganst avag vhcl dnsty fo two dffnt valus of, avag vhcl dnsty on th upp lan, and fo a fxd path loss xponnt.8. Rsults show that as ncass, th two-way connctvty pobablty ncass, whch mans that dployng mo vhcls on th upp lan can mpov th connctvty of th low lan. Th analytcal modl and th sults of ths pap would b usful fo dvlopng a slf oganzng VANET fo ntllgnt tanspot applcatons. Th psntd modl gvs a unqu famwok fo analyzng th mpact of taffc latd and channl dpndnt paamts on ntwok connctvty on two-way stt. Th sgnfcanc of th modl s that t can b usd as a tool to fnd th mnmum avag vhcl dnsty qud to satsfy a ctan connctvty pobablty. Gvn a ctan knd of taffc flow, th modl may b of hlp to dtmn whth a fully connctd ntwok can b fomd. Mssag outng s a challngng poblm n VANETs du to th nhnt hgh dg of moblty of th vhcls n th ntwok. Du to th dynamc natu of th taffc and th nvonmnt, ndvdual communcaton lnks a shotlvd and th outng paths that ly on such lnks a hghly vulnabl to conncton dsuptons. A mult-hop out stablshd btwn two vhcls may gt dsuptd du to moblty of th souc, th dstnaton, o th ntmdat vhcls, causng out falus to occu. Futh, whn vhcl dnsty vas consdably, th tadtonal mult-hop fowadng appoach fo uncast outng fals snc locatng a vhcl fo fowadng a mssag bcoms dffcult. Instad, a cay-and-fowad tchnqu Fgu 4. Ntwok connctvty pobablty (on-way and two-way) vsus avag vhcl dnsty ( T = 33 dbm, α = 3.5, L = km, ρ =.5 vh/m). Fgu 5. Two-way ntwok connctvty pobablty vsus avag vhcl dnsty on th low lan, ρ ( T = 33 dbm, α =.8, L = km, m = ). Copyght ScRs.

9 34. C. NEELAKANTAN, A. V. BABU can b usd wh a vhcl cas th data packt untl a nw vhcl movs nto ts vcnty and thn fowads th packt. As fa as outng of mssags s concnd, t s ctcal to slct outs that hav maxmum connctvty pobablty. Th psntd analytcal modl would b an mpotant stp towads th dsgn of such connctvty awa outng potocols fo VANETs. 5. Concluson In ths pap, w dvd closd fom xpsson fo th ntwok connctvty pobablty of a lna VANET on a two-way stt, n th psnc of Nakagam fadng. Intally, w psntd a modl to fnd th ntwok connctvty on on-way stt. W thn xtndd th modl to fnd ntwok connctvty on a two-way stt scnao. Though xtnsv analytcal and smulaton studs, w stablshd that, th ntwok connctvty on a spcfc lan can b sgnfcantly mpovd wth th hlp of opposng vhcls on th oth lan. Ou analytcal modl s unqu n th sns that t can b usd to fnd th dpndnc of vaous paamts such as avag vhcl dnsty, vhcl spd, hghway lngth and sgnfcant physcal lay paamts such as path loss xponnt, Nakagam fadng facto tc., on ntwok connctvty on a two-way stt. REFERENCES [] S. Yousf, M. Mousav and M. Fathy, Vhcula Ad- Hoc Ntwoks (VANETs): Challngs and spctvs, ocdngs of Intnatonal Confnc on Intllgnt Tanspotaton Systm Tlcommuncaton, Chngdu, Jun 6, pp [] IEEE 8.p Daft Amndmnt, Wlss LAN Mdum Accss Contol (MAC) and hyscal Lay (HY) Spcfcatons, Wlss Accss n Vhcula Envonmnts (WAVE), July. [3] G. Kaaganns, O. Altntas, E. Ekc, G. Hjnk, B. Jaupan, K. Ln and T. Wl, Vhcula Ntwokng: A Suvy and Tutoal on Rqumnts, Achtctus, Challngs, Standads and Solutons, IEEE Communcatons Suvys & Tutoals, Vol. 3, No. 4,, pp do:.9/surv [4] M. Atmy, W. hllps and W. Robtson, Connctvty wth Statc Tansmsson Rang n Vhcula Ad-Hoc Ntwoks, ocdngs of th 3d Annual IEEE Communcaton Ntwoks and Svcs Rsach Confnc, Nova Scota, 6-8 May 5, pp do:.9/sr.5.9 [5] S. Yousf, E. Altman, R. El-Azouz and M. Fathy, Analytcal Modl fo Connctvty n Vhcula Ad-Hoc Ntwoks, IEEE Tansactons on Vhcula Tchnology, Vol. 57, No. 6, 8, pp do:.9/tvt [6] S. Yousf, E. Altman, R. El Azouz and M. Fathy, Impovng Connctvty n Vhcula Ad-Hoc Ntwoks: An Analytcal Study, Elsv Comput Communcatons, Vol. 3, No. 9, 8, pp [7] J. Wu, Connctvty of Mobl Lna Ntwoks wth Dynamc Nod opulaton and Dlay Constant, IEEE Jounal on Slctd Aas n Communcatons, Vol. 7, No. 7, 9, pp do:.9/jsac [8] M. Khabazan and M. Al, A fomanc Modlng of Connctvty n Vhcula Ad-Hoc Ntwoks, IEEE Tansactons on Vhcula Tchnology, Vol. 57, No. 4, 8, pp do:.9/tvt.7.96 [9] G. Mohman, F. Ashtan, A. Javanmad and M. Hamd, Moblty Modlng, Spatal Taffc Dstbuton, and obablty of Connctvty fo Spas and Dns Vhcula Ad-Hoc Ntwoks, IEEE Tansactons on Vhcula Tchnology, Vol. 58, No. 4, 9, pp do:.9/tvt [] S. anchpapboon and W. attaa-atkom, Connctvty Rqumnts fo Slf-Oganzng Taffc Infomaton Systms, IEEE Tansactons on Vhcula Tchnology, Vol. 57, No. 6, 8, pp do:.9/tvt [] Y. Zhuang, J. an and L. Ca, A obablstc Modl fo Mssag opagaton n Two-Dmnsonal Vhcula Ad- Hoc Ntwoks, ocdngs of th 7th ACM Intnatonal Wokshop on Vhcula Intntwokng, Chcago (USA), July, pp do:.45/ [] W. Vyastavat, O. Tonguz and F. Ba, Ntwok Connctvty of VANETs n Uban Aas, ocdngs of th 6th Annual IEEE Communcatons Socty Confnc on Snso Msh and Ad-Hoc Communcatons and Ntwoks (SECON), Boston (USA), -6 Jun 9, pp. -9. [3] V. K. M. Aj,. C. Nlakantan and A. V. Babu, Ntwok Connctvty of On-Dmnsonal Vhcula Ad-Hoc Ntwok, ocdngs of IEEE Intnatonal Confnc on Communcatons and Sgnal ocssng (ICCS), Calcut (Inda), - Fbuay, pp [4] A. V. Babu and V. K. M. Aj, Analytcal Modl fo Connctvty of Vhcula Ad-Hoc Ntwoks n th snc of Channl Randomnss, Wly Intnatonal Jounal of Communcaton Systms,. do:./dac.379 [5]. C. Nlakantan and A. V. Babu, Connctvty Analyss of On-Dmnsonal Vhcula Ad-Hoc Ntwoks n Fadng Channls, EURASI Jounal on Wlss Communcatons and Ntwokng,. do:.86/ [6] J. Mau, T. Fugn and W. Wsbck, Naow-Band Masumnt and Analyss of th Int-Vhcl Tansmsson Channlat 5. GHz, IEEE 55th Vhcula Tchnology Confnc (VTC Spng), Alabama (USA), Vol. 3, May, pp [7] L. Chng, B. Hnty, D. Stancl, F. Ba and. Mudalg, Mobl Vhcl-to-Vhcl Naow-Band Channl Masumnt and Chaactzaton of th 5.9 GHz Ddcatd Shot Rang Communcaton (DSRC) Fquncy Band, Copyght ScRs.

10 . C. NEELAKANTAN, A. V. BABU 34 IEEE Jounal on Slctd Aas n Communcatons, Vol. 5, No. 8, 7, pp do:.9/jsac.7.7 [8] I. Sn and D. Matolak, Vhcl-Vhcl Channl Modls fo th 5-GHz Band, IEEE Tansactons on Intllgnt Tanspotaton Systms, Vol. 9, No., 8, pp do:.9/tits [9] J. Kadal, N. Cznk, A. a, F. Tufvsson and A. Molsch, athloss Modlng fo Vhcl-to-Vhcl Communcatons, IEEE Tansactons on Vhcula Tchnology, Vol. 6, No.,, pp [] J. Kunsch and J. amp, Wdband Ca-to-Ca Rado Channl Masumnts and Modl at 5.9 GHz, IEEE 68th Vhcula Tchnology Confnc (VTC Fall), Calgay (Canada), Sptmb 8, pp. -5. [] W. McShan and R. Ross, Taffc Engnng, 3d Edton, ason ntc Hall, Upp Saddl Rv, 4. [] A. Goldsmth, Wlss Communcatons, Cambdg Unvsty ss, Cambdg, 5. [3] I. Gadshtn, I. Ryzhk and A. Jffy, Tabl of Intgals, Ss, and oducts, Acadmc ss, Waltham,. [4] J. Chng, C. Tllambua and N. Baulu, fomanc of Dgtal Lna Modulatons on Wbull Slow-Fadng Channls, IEEE Tansactons on Communcatons, Vol. 5, No. 8, 4, pp do:.9/tcomm Appndx A Dvaton of (9): To fnd th DF of R fr, w us th CDF xpsson gvn by (8). Whn m s an ntg, mm d m m, [3], wh d T x nos m m d d k. Accodngly, th CDF gvn by (8) can b smplfd to gt th followng xpsson: m k k k! F (A.) R k wh m nos T. Now f R s obtand by dffntatng (A.) and s gvn by (9). Appndx B Dvaton of (): To pov (), w substtut (9) n (8) and wt th ntgal as follows: To valuat th fst ntgal xpsson n (B.), w us (). Whn s a postv ntg, th fst ntgal n (B.) can b wttn n tms of Mj s G functon k basd on () to gt th followng xpsson: π k k d k, G, k k,, (B.) Usng a smla appoach, th scond ntgal n (B.) can b valuatd to gt th followng xpsson: k k d k π k k,, k, G, k Substtutng (B.) and (B.3) n (B.) w gt (). (B.3) Lnf, m k k k k d d (B.) k Copyght ScRs.