A Network Traffic Flow Model for Motorway and Urban Highways

Transcription

1 A Newor Tr Flow Moel or Moorwy n Urn Hghwys Cho Yng Rs Remenye-Preso John Anrews * Nonghm Trnsporon Engneerng Cenre Unversy o Nonghm NG7 RD Nonghm UK Asr The reserh repore n hs pper evelops newor level r low moel (NTFM) whh s pplle or oh moorwy n urn ros. I oress he r low res ueue propgon he unons n rvel elys hrough he newor. NTFM uses su-moels ssoe wh ll ro n unon ypes whh omprse he hghwy. The low ny one pr o he newor s ovously very epenen upon he lows ll oher prs o he newor. To pre he wo-wy r low n NTFM n erve smulon meho s exeue o genere he evoluon o epenen r lows n ueues. To emonsre he ply o he moel s pple o smll se suy newor n lol Loughorough-Nonghm hghwy newor. The resuls ne h NTFM s ple o enyng he relonshp eween r lows n purng r phenomen suh s ueue ynms. By nroung reue low re on lns o he newor hen he ees o sreges employe o rry ou rowors n e mme. Keywors: Pvemen mnenne; Tr low moels; Invul unon moels; Ierve smulon meho 1

2 Noons p sr ( ) low py on he ln eween noes n (pssenger r un (pu)/hour) ln pne.e. he mxmum numer o rs whh n ueue on he ln rom noe (pu) whh s one se on he ull lengh rom unon o unon soure low enerng he ln n me or exmple umulve r onng he mn ro rom n ese.e. housng eses or wor ples (pu/hour) s ( ) sn low levng he ln n me or exmple umulve r levng he mn ro or n ese.e. housng eses or wor ples (pu/hour) proporon o low on he ln hoosng he oulow reon l l s expresse eher n reon le rgh he or n he ID o he esne noe.e. +1 ( l ) low on he ln n me (pu/hour) verge numer o vehles ueung on he ln n me (pu) 1 Inrouon (pu) verge numer o vehles propgng o he upsrem lns o noe n me In reen yers hghwys genes hve urne her enon rom onsruon o new pvemens o he mnenne n rehlon o exsng ones. Aorng o he Annul Lol Auhory Ro Mnenne Survey ((AIA) 011) n Engln he governmen hs spen hevly on ro mnenne n reen yers. 40m ws spen n m n 007 n noher 861m n 008 n ggrege ol o 6867m rom 00 o 008 n orer o mnn he servely level o pvemens. The survey lso repors h urher s urrenly reure o rng he UK s ros o he reure snr. In on o he expenure on rryng ou he wor he rvel ely os o ro users use y mnenne s sgnn n expee o susnlly exee he orresponng os o mnenne. Conseuenly wh he purpose o exmnng n unersnng he rvel elys whh our when mnenne s perorme he NTFM newor r low moel hs een evelope. I pres he r lows n ueues ul up n ro newor. When rowor s perorme wll use resron n he low re py o prs o he newor. By omprng he low n ely hrerss resulng rom eren mnenne sreges he es wy o eepng he hghwys n goo se o repr n e eslshe. Typlly r low moels re egorse no wo mn groups: mrosop moels n mrosop moels. Mrosop r moels re use o eny he ggrege ehvour o ses o vehles re generlly esy o vle n ensure goo rel-me uly suh s he

3 lu-ynm r moels (Lghhll n Whhm 1955; Rhrs 1956). Mrosop moels re pple o moel he rvel ehvour o n nvul vehle whh s reognse s unon o he r onons n s envronmen (Cremer n Luwg 1986; Ngel n Shreenerg 199). As rvers ehvour n rel r s ul o oserve n mesure mrosop moels re ul o vle urely (Dgnzo 1994). In on he ompuonl eor reure y mrosop moels s sgnnly hgher hn h or mrosop moels n he reure y mrosop moels re more ul o reor. Due o he resons esre ove n he suly o mrosop moels or newor-level nlyss mrosop moel hs een evelope n hs pper. Mny mrosop r moels hve een onsrue o eny r ehvour on moorwys n urn ros. Lghhll n Whhm (1955) n Rhrs (1956) prove poneerng lowynm moel (LWR moel) o esre unreonl r low on hghwy newors. Bse on he r-ollowng moel (Rohery 1997) h onserng he rver s reon me Pyne (1971) evelope seon-orer moel (Wgner Homnn e l. 1996) n whh he ynm low phenomen re moelle. Dgnzo (1994) propose ell rnsmsson moel (CTM) h ope onvergen pproxmon o he LWR moel o evlue he r on hghwy newor wh sngle enrne n ex. Aerwrs more ell ypes re pple n CTM o roen s pplly (Dgnzo 1995; Lo 1999; Lo 001; Lo Chng e l. 001). METANET (Messmer n Ppgeorgou 1990) onsere he suon o moorwy newor se on he seonorer moel. Exensve reserh hs een perorme o mprove METANET nlung he opon o vrle spee lms (Breon Hegy e l. 00; Hegy Br De e l. 005) n he pplon o roue gune (Deloro 003; Krm Hegy e l. 004). Suseuenly Vn en Berg Hegy e l. (007) evelope n negre r onrol ply or mxe urn n moorwy newors. However prory unons.e. T-unon n rounou re no onsere n CTM n METANET so he onlng reuremens o he r lows rom ompeng reons nno e pure. In Vn en Berg Hegy e l. (007) he urn r moel ssgns su-ueues or 3

4 eh urnng reon on ro ln; hus shre lnes re no en no oun where r heng o eren reons mgh e mxe ogeher. To moel prory nerseons gp epne heory n ueung heory hve een wely presene n nvesge. Gp epne moels hve een pple o esme he rl gps n pes prory nerseons (Segloh 1973; Cown 1975; Pln n Chpole 1984; Troue n Brlon 1997; Brlon Koeng e l. 1999; Nng 001; Wu 006; Guo n Ln 011). Queung heory s generlly use o evlue suons whh nvolve verge elys verge ueue lenghs sruons o elys n ueue lenghs (Kremser 196; Tnner 196; Kremser 1964; Yeo n Weesul 1964; Dgnzo 1977; Poeshl 1983; Nng 001). One svnge or he gp epne moels s h hey hve le o pure onls mong he mor srems (Rusn n Wng 00). Also he en sgnlze nerseons n hve sgnn mp on py n perormne o prory nerseons whh le o he vron o hewys (Ronson Tn e l. 1999; Trz n Gone 000). Hene gp epne heory no longer pples. Sne ueung heory s lso onsrue se on hewy sruon moels suers he sme rws o he gp epne heory. As gp epne heory n ueung heory mnly ous on nvesgng he r on sngle nerseon n re no ure or moellng reonl low (Tn Troue e l. 000) hey re no ple o enyng he r hrerss newor level. Conserng he r neron oh sgnlze n prory unons hs pper esres mrosop r low moel he purpose o whh s o prove meho or preng he r low n rvel ely or eh unon n he newor. One novel eure o he moel s h oh moorwy n urn newors re evlue se on he sme prnple o onserng mxmum py low re he unons where lows ompee lnng ou he r low n he newor n moellng r overlow hrough o he rele unons. Anoher novel eure s h wo-wy r low long newor lns s nvesge when n erve smulon meho s ulse o genere he evoluon o epenen r lows n ueues. Moels or lrge vrey 4

5 o unons suh s prory unons moorwy rounous e. re nroue n shre lnes or r heng o eren reons re moelle n orer o moel rel suons on hghwy newors. Ro Newor Moel The ro newor sue n NTFM s ompose o noes n lns. Lns represen ros.e. moorwy lns n urn ro lns n noes emonsre unons nlung sgnlze nerseons n T-unons e. Also prs o he sme ro wh eren hrerss suh s low py re sepre y noe (e.g. when ul rrgewy reues o sngle r srem). Pror o he evluon o he ro newor he relonshps eween r lows n ueue ul up unons nee o e spee. Moels or unons hve lns whh enle he ex r rom one unon o ener he seon unon hs wll wor n wo reons s or hese wo unons wo-wy r low s eploye. In hs wy ll he unons n he newor re lne o eh oher. From he newor low heory newor n hve numer o soure noes n sn noes where soure noe enes he low no he newor n sn noe enes he low ou o he newor. Soure n sn noes n e use o moel he eges o he newor or nlue he res o he newor n he moel o su-newor. In on he lns hemselves n hve soure n sn noes whh re use o moel umulve r enerng/levng he ln. Ths n represen sgnn r lows o/rom he newor rom suh elemens s housng eses rpors rlwy sons or ples o employmen. In hs wy s possle o vo he nluson o ll mnor ros on he newor. NTFM s se on he prnple o he ueue moel. Frs o ll lows rom he newor soure noes re psse hrough he newor o ll he sn noes lulng he low on eh ln. Then he low on eh ln s ompre wh he low py o he ln pplyng he generl euons or he ueue on he ln n he moels or he eren ypes o unon n he ueue s lule. I he ueue exees he ln pne ees o he ueue re propge 5

6 hrough he newor. Fnlly n he ollowng me seps eren lows rom he newor soure noes re propge hrough he newor o represen suon suh s he rush hour n her ees re e o he ueues presen on he newor rom he prevous me seps. I he low hrough he newor mproves or exmple r low res rom he soure noes erese or r lghs re use o llow eer low hrough he ongese lns he ueues n erese n evenully he lns n eome ler o ueues. In hs mnner he r hrers or gven hghwy newor hroughou y n e ene y NTFM. Dele rules or lulng lows n ueues on he ln re esre n Seon.1..1 Mn prnple o NTFM Flow on he ln - n me s lule s sum o ll he lows o noe he low enerng he ln n he negve low levng he ln: sr s s s lls (1) One he low on eh ln n me s lule (or he rumsnes h here re no resrons) he low vlue n he ueue vlue on he ln - mgh nee o e upe orng o he low py on hs ln n he ln pne p. The upe low s expresse s n he upe ueue s expresse s. Two ses re onsere: (1) Flow on he ln s hgher hn he low py n me : hen I () ( ) p p n hen p ( ) () Flow on he ln s lower hn he low py n here s ueue on he ln n me : I n 0 hen n (3) (3 ) 6

7 0 hen n 0 (3 ) One he ueue s lrger hn he ln pne s esre n he Euons he ueue he en o he ln s psse o he onneng newor.e. o he lns h onrue o he ul-up o he ueue. Ths s one usng he ueue propgon lgorhm. The generl e s h proporon o he ueue s psse o eh ln h onrue o he ul-up o he ueue. The proporon o he ueue or eh ln s lule s he proporon o he low rom h ln onrung o he overll low. For exmple ueue uls up on he ln rom o +1 n exees he py o he ln y he numer o vehles s proporonlly srue o ll he lns h ener noe. Ths proess s gong o nrese he sze o he ueue n erese he low on eh ln h eners noe : 1 1 (4) (5) I er hs proess he sze o he nrese ueue exees he py o he ln p he ees o he ueue re psse urher hrough he newor unl ueue n e ommoe n oes no exee he py o he ln. For exmple p hen p n p (6) s psse o he upsrem lns h ener noe e. I he ueue s presen n me.e. 0 s lso presen he egnnng o he moellng sep 1.e. 1 whh hen epens on he low n me +1 1 n he relevn euons re pple o upe he low n he ueue on he ln s neessry. More omplexy s nroue n he unon moels when sepre lnes re moelle on he lns n he low py n he pne on eh lne re onsere. 7

8 . Su-Moels In on o he s ln moel he su-moels or eh unon ype re onsrue o express he r neron unons. The nvolve unon ypes re lse n Tle 1. Tle 1: Junon ypes n NTFM Junon groups Junon ypes Sgnlze Junons Sgnlze T-unon Sgnlze Inerseon Sgnlze Rounou Prory Junons T-unon Urn Rounou Moorwy Rounou One-wy Junons On-rmp n O-rmp Merge n Dverge Rowor noe The r low sgnlze unon s nluene y oh he low py o he enry rm n he green spl me o he r sgnls (proporon o mes he sgnls gves prory o low n s reon) where he onlons mong ompeng r lows re elmne owng o he pplon o r lghs. For he group o one-wy unons where (exep or he on-rmp o moorwys) he enerng r or he one-wy unon s only hrerze y he orresponng low py. The on-rmp s lso evlue s prory unon. For prory unons he r low s se on rgh-o-wy rules where he enerng r low or eh rm o he unon s resre y he low py n lso y he r lows rom ompeng rms. The unerlyng mehoologes or he T-unon urn rounou n moorwy rounou re esre n el o explly emonsre hese oneps...1 T-unon moel Fgure 1: T-unon Ths unon shown n Fgure 1 s onrolle ssumng h rvers oey he rgh-o-wy rules. On he T-unon vehle rvellng on he mor ros hs rgh-o-wy n vehle pprohng he mor ro mus llow o pss eore onng he low o r. Some ros o he nerseon 8

9 hve sngle lne some hve wo lnes. Two lnes re use on he le pr o mor ro where lne 1 s use or gong srgh on n lne s use or urnng rgh n rossng he onomng r on he mor ro. Also wo lnes re use on he mnor ro lne 1 s use or urnng le n lne s use or urnng rgh. The res o he ros hve sngle lne. The unon spe pple n hs moel s: 1 l ( 1 l ) low noe h omng rom reon -1 n gong n lne l.e. 1 represens he le lne n me (pu/hour) noe low py or he r omng rom reon -1 n gong n lne l epenng on gps eween vehles n vehle spee (pu/hour) ln pne n lne l.e. he mxmum numer o rs whh n ueue n lne l o he ln (pu) 1 l ( ) verge numer o vehles ueung on lne l o rm -1 or noe he egnnng o (pu) p 1 l The T-unon s onrolle y rgh-o-wy rules n prory s se or ern reons. Thereore n orer o lule he ueue or eh reon on he unon.e. he mor ros -1 n +1 n he mnor ro -1 hs o e onsere seprely The mor ro -1 For he low rom reon -1 o reon +1.e. n lne 1 no onlng r resron on he low exss. Thereore ueue n only ul up ue o he low py on he ln er he unon ollowng he generl rule esre n Seon.1. For he low rom reon -1 o reon -1.e. n lne he onlng low s he low rom reon +1 o. A ueue uls up he low n lne or he onlng low s hgher hn he low py n lne hrough he nerseon. The upe low s expresse s ( 1 l ) n he upe ueue s expresse s 1 l ( ). Fve ses re onsere: (1) Flow on he ln n lne s hgher hn he low py n lne hrough he nerseon he onlng low rom reon +1 s lower hn he low py n lne hrough he nerseon n here s no ueue n he lne n me : I 1 1 n 1 1 n 1 0 hen (7) 9

10 1 1 n (7 ) p 1 1 hen p 1 1 n (7 ) 1 1 p 1 1 () The onlng low rom reon +1 s hgher hn he low py n lne hrough he nerseon n here s no ueue n he lne n me : I 1 1 n 1 0 hen 0 1 n (8) 1 1 (8 ) p 1 1 hen p 1 1 n (8 ) 1 p 1 1 (3) Flow on he ln n lne s hgher hn he low py n lne hrough he nerseon he onlng low rom reon +1 s lower hn he low py n lne hrough he nerseon n here s ueue n he lne n me : I 1 1 n 1 1 n 1 0 hen (9) 1 1 n (9 ) p 1 1 hen p 1 1 n (9 ) 1 1 p (4) The onlng low rom reon +1 s hgher hn he low py n lne hrough he nerseon n here s ueue n he lne n me : n I hen 0 n (10) (10 ) p 1 1 hen 1 1 p n (10 ) 10

11 1 1 p 1 1 (5) Flow on he ln n lne s lower hn he low py n lne hrough he nerseon he onlng low rom reon +1 s lower hn he low py n lne hrough he nerseon n here s ueue n he lne n me : I 1 1 n 1 1 n 0 1 l hen (11) 1 1 n (11 ) 0 1 hen n 0 1 (11 )..1. The mor ro +1 For he low rom reon +1 o reon -1 or reon -1 no onlng r reuremen s presen. Thereore ueue n only ul up ue o he low py on he ln er he unon ollowng generl rule esre n Seon The mnor ro -1 For he low rom reon -1 o reon -1.e. n lne 1 he onlng low s he low rom reon +1 o -1. Whle or he low rom reon -1 o reon +1.e. n lne he onlng low s he sum o he low rom reon +1 o -1 n he low rom reon -1 o +1. Boh lows on mnor ro -1 re evlue s he low n lne rom reon

12 .. Rounou moel Fgure : Rounou A rounou s moele n ee s seres o prory unons wh prory o r on he rounou. As sgnlze rounou s opere y sgnl onrol whou onseron o onlng lows urn rounou n moorwy rounou re nvesge n hs seon. Assume rounou wh our enry rms n or rounou llusre n Fgure use o represen o upsrem lns respevely. The orer n whh he r low s lule he rounou progresses lowse roun he rounou srng rm : ---. The low rom rm wll e epenen on he low rom rms n hs s euse only prs o lows rom rms n hve o pss hrough he enrne o rm.e. lne 1 n lne o leve he rounou whle he low rom rm exs he o he enrne.e. lne 3 n lne 4 o rm. The sme or oher rms he nlow epens on preeng rulng nlows. Eh ro o he rounou s onsere o hve wo lnes; lne 1 s use or urnng le n gong srgh n lne or urnng rgh. I ssumes h he vehles nenng o me u-urn n reurn n oppose reon long he ro n whh hey pproh he rounou re suenly smll h hey n e gnore. Anoher ssumpon s h he r on lne 1 o eh 1

13 enry rm only es he ouer lne rulng he rounou whle he nner lne s oupe y he r on lne....1 Urn Rounou moel The urn rounou moel ssumes h vehles re no llowe o ueue on he rounou. Beuse rounou s usully symmerlly onsrue only he low on rm s nlyse. For he low rom rm o rm n.e. n lne 1 he onlng low nlues he merge low rom rm h s gong srgh on n he low rom rm h s urnng rgh: n ( l n m n l n m ) ( ) mn( 1 ) mn( ) 1 onlng low or he low on enry rm n.e. n n lne l.e. 1 n (pu/hour) low rom rm n o rm m (pu/hour) low py or lne l o rm n (pu/hour) (pu/hour) proporon o he r h gong o rm m rom rm n (1) The mn ormul s use o resr he nlow rom eh rm. The rs mn ormul n Euon 1 es he mnmum o: he rs prmeer whh represens he r low nenng o move rom rm o rm n he seon prmeer whh orrespons o he low py or hs r low n lne 1 o rm. The seon mn ormul emonsres he r low rom rm o rm h shoul e less hn or eul o he orresponng low py. For he low rom rm o rm he onlng low s he sum o he lows rom rm o rm n n he low rom rm o rm esre s: ( ) mn( 1 ) mn( ) mn( ) (13) The rs erm n he hr erm n Euon 13 re enl o Euon 1 s he onlng low or lne 1 o rm lso resrs he low on lne o rm. The low on lne o rm s urher lme y he r rom rm o rm h esre s he seon erm. The evluon o he wo r low on rm ollows he sme rule n Seon

14 ... Moorwy Rounou moel The exenson or hs rounou s h vehles re llowe o ueue on he rounou. In on o he resron o nlows oulows re lso resre orng o he low py o he ou-gong lnes or eh rm. The resuls rom urn rounou re employe s npus or he lulon o oulows o he moorwy rounou. I ssumes h rs n he ueue on he rounou wll leve gps or enerng n exng he rounou. Anoher ssumpon s h he ou-gong low on he ouer lne wll only e he le lne s ex whle he r low on he nner lne n e eher s ex s llusre n Fgure. As he rounou nvesge s ssume o e ul symmerlly he ree spes or eh pr o he rounou re he sme. The onl unon s employe n moorwy rounou: p o p n l o o op p pne or ouer lne o rounou (pu) pne or nner lne o rounou (pu) oulow or lne l o rm l nlues 3 n 4 (pu/hour) oulow o rounou rom rm o rm (pu/hour) lengh o he ueue orme n seon o he ouer lne o rounou (pu) s llusre n Fgure 3 lengh o he ueue orme n seon o he nner lne o rounou (pu) s llusre n Fgure 3 ueue propgon o ueue or seon o ouer lne o oher lns (pu) ueue propgon o ueue or seon o nner lne o oher lns (pu) Fgure 3: The ormon o ueue he rounou The r lows rom eh rm wll oupy her ene ph hrough he rounou; he mxe r low eh omponen o he rounou s represene n Tle. 14

15 15 Tle : Composon o r lows Componens o rounou Ouer lne Inner lne The urn rounou moel s nlly eploye s he rs pr o he moorwy rounou moel. The resuls o urn rounou moel re hen employe s npus or he nex lulon n he moorwy rounou moel. Lne 3 n lne 4 or rm (s n Fgure ) re nlyse seprely. The evluon o he exng r n lne 3 or rm s esre s ollows: (1) A ueue uls up low on he ln n lne 3 s hgher hn he low py o lne 3 o rm. I For seon o ouer lne he rounou he sure r or exng r rm.e. n n me s lule s ) ( 3 urher le o he loge o low erve s 3 ) ( se on he low proporons on seon o ouer lne. Ths s euse hese hree reonl r lows re mxe ogeher on seon o ouer lne. As resul he ueue orme on seon o ouer lne s upe s: o o 3 ) ( (14) In on he vron o ueue n s represene s: o o p o o ) 4 mn( (15) Euon 15 s use o resr he ueue nremen n seon. The rs erm represens he upe ueue lengh n when s greer hn he pne s resre s 4 p o. Due o he r surne he r lows h pssng hrough seon o ouer lne re erese y:

16 16 o o o (16) I ueue s less hn he ueue pne 4 o p o he ueue s resre n. I 4 o p o pr o he ueue propges o upsrem lns esre s: 4 o p o op n 4 o p o (17) As hs ueue propgon s onrue y r lows rom rms n splls o lne 1 o rm n seon o ouer lne. The rs pr h nue y n s e o he ueue n lne 1 o rm esre s: op 1 1 (18) n he nlow rom lne 1 rm s erese s: op 1 1 (19) I 1 1 p ueue propges o he soure lns o rm p p n 1 1 p (0) The res pr splls o seon o ouer lne n he ueue n seon s upe s: op o o (1) The sure r o urher resule n he loge o n s hey re mxe n seon o ouer lne. Conseuenly he r h oul ex he rounou rm rom rm s ompue s:

17 17 o 1 () () Flow on he ln n lne 3 s less hn he low py o lne 3 hrough he rounou I 3 (-) I 0 3 no ueue. 3 (3) (-) I o p ueue loe n pr. 3 3 (4) 3 0 o o o o (5) o o 3 ) ( (6) Euon 6 s evlue s Euon 14 whh s se on he low ros on seon o ouer lne. Inremen o lows ue o lerne o ueue s evlue s: ) mx( o o o o (7) Ths mx ormul s use o resr he lerne o ueue; he mxmum vlue o ueue reuon woul e he prevous ueue lengh. As resul o ueue lerne he r lows h pssng hrough pr o ouer lne re nrese y: o o o (8) I 0 o ueue sll exss n. I 0 o

18 3 3 o n o 0 (9) Conseuenly he r lows h pssng hrough re upe s: o o o (30) (-) I p o 3 ueue loe n pr n some oher prs. Queue lers rom s en o 4. The mehoology use ove wll e pple. As or he lne 4 o rm he exng r low s ompue s: mx( 30) (31) Euon 31 eermnes he oulow py or lne 4 rm. As low n ex he rounou y eher lne 3 or 4 he oulow py or s lule s he sum o py o lne 4 n resul low py o lne 3. The mehoology use o evlue he r onon n lne 3 or rm s lso pple o he oulow hrough he lne 4 or rm. 3 Newor Soluon Roune In perormng he newor level nlyss he nlows eh unon resul rom he oulows o s upsrem unons n enres o he newor; wheres s oulows re unons o he nlows or he unon. Thus he whole sysem o r lows s neronnee n epenen. I s o vl mporne o eermne he seuene o noe evluons or r low. These wll sr rom he orgnl noe progress roun he newor n en he sme noe. The smulon o hese noes s proesse ervely unl onvergene hs een rehe when ll ou proles re eevely unhnge y urher erons. As or he rs eron he unnown npus or eh unon n he moel re suppose o e zero whh wll e upe y he ouomes o s upsrem lns n he sme eron n pple o he nex eron. Exep or he r lows rom soure noes r lows or eh smulon eron re upe s he npus or he nex eron. I s worh nong h he egnnng o eh eron ueues orme n he newor re 18

19 rese o he onon he en o prevous me pero so s o onserve he moun o r n he newor. For nsne ueues re nlze o zero or he smulon erons he rs me sep sne here ws no r n he newor prevously. The evluon o r onons or hghwy newor lls no wo mn seps. The rs sep s o lule he enerng lows exng lows n ueues or eh unon ervely unl hose prmeers reh sle se. The nex sep s o eny he ee o vehles h propgng o her upsrem lns whh mes he r onon even more severe. Conseuenly he r onon or he hghwy newor he urren me sep s one n hen hs n urn s ulse s he nl r onon nex me sep. By hs mens he r onon se or hghwy newor over me pero s evlue. The NTFM sowre s progrmme n Vsul C++ n whh lss s onsrue or eh unon sue n he NTFM n s use o esre he ype n he low py o he unon n o sore s nlows oulows n ueues. The sowre s use o moel he r on he newor hroughou y. 4 D Soures NTFM reures omprehensve ls o npus whh spey he geogrphl hrerss o he ro newor long wh he r lows hrough eren prs o he y. Inlue n he geogrphl newor eures re: he lengh or eh ln n he low py or eh rm o he unons. In on he r enerng eh ln o he newor ll pons o he y re reure long wh he proporon o vehles levng eh unon on eh o he ex rms n he sgnl onrol npus eh me nervl. In he NTFM r lows n urnng movemens re onsn over eh me nervl. The vlle r npus on he hghwy newor use n hs suy were he numer o rs per hour whh h een ollee vrous loons on run ros n vrous unons over he ls ouple o yers. Suh r were one rom he Hghwys Ageny n 19

20 Nonghm Couny Counl or he mory o he ros n were rely pple n he NTFM o moel wo-wy r low urng y. However he r some pons urng y were unvlle hey were erve usng he lner exrpolon eween wo pons. For he ro seons on he lol newor where he were no reore n he se olleon ws rre ou y he uhors o on some r normon urng ypl y o e use n he NTFM. 5 Moel Applon 5.1 Cse Suy 1 Fgure 4: The se suy newor For ese o exposon smple newor n Fgure 4 s prove o llusre he properes o NTFM. Ths ro newor s ompose o 4 sgnlze nerseon n 1 ul -lne lns. The low py or eh nerseon s ene s 1500 pu/hour; he pne or eh nner ln s 1000 pu; he urnng ros or eh rm o eh unon re ene s n 0.3 (urnng le gong srgh urnng rgh); he green me spl or r h urnng le n gong srgh s se o 0.5 n 0.3 or rgh urnng r. As EA FA GB HB IC JC KD n LD re exernl lns her pes re ssgne s nny o vo ueue propgon. In orer o llusre he ormon o ueue n he newor relvely hgh r lows re employe. The nlows or 1 o 8 re pu/hour respevely. The moellng 0

21 horzon n hs se suy s se o me seps one me sep s ene s one hour. Aonlly AB s use o enoe he low rom noe A o noe B n AB represens he ueue h orme noe B n exene o noe A whh s reognse s prou o AB Newor Smulon The seuene or he evluon o he noes n hs newor s ene s A-B-C-D-A. For eh eron he r lows n he newor re evolve wh respe o he ollowng rule unl onvergene s one: Junon A 1 DA n BA re use o lule he oulows AB AD AE n AF Junon B 3 4 AB n CB re use o lule he oulows BC BA BG n BH Junon C 5 6 BC n DC re use o lule he oulows CD CB CJ n CI Junon D 7 8 CD n AD re use o lule he oulows DA DC DK n DL I shoul e noe h DA BA CB n DC re nlse s 0 on he rs eron. Aer he vlues o hese vrles remn sey ueue propgon hrough he newor s evlue. As resul o hs he r onon urren me sep s one. Queues orme hs me sep re reore s he nl r onon nex me sep. In hs pproh he r onon or hs newor over he plnnng spn s evlue. I es roun 1 seon or NTFM o moel he r hrerss on hs newor urng wo me seps Evluon o Tr Conon A rs he moel s e wh he nl r ses.e. nlows urnng ros or unons n sgnl onrol npus. The nl r onon or he newor s epe n Tle 3: Tle 3: Inl r onon n me 1 Junons Inl r onon n me 1 A B C AB BA AE AD BC BH AF BG CD CJ CI CB

22 D DL DK DC DA As or eh eron or me 1 he nl r onon ses or eh unon shoul e rese orng o Tle 3 so s o eep he lne eween r npus n oupus. In orer o on sle r onon se he evluon o he newor s run ervely unl onvergene s rehe he evoluon o r or eh unon re represene n Tle 4: Tle 4: Evoluon o he r onon or he se suy newor n me 1 Junon Tr onon ses n me 1 Enerng low (pu/hour) Exng low (pu/hour) Queue lengh (pu) A Ieron 1 DA BA AE B Ieron AB CB 4 3 BA C Ieron DC 6 5 AD BC AB BH AF BG AE BA AD BC AB BH AF BG BC CD CJ CI CB CD CJ CI CB D Ieron 8 7 CD AD DL Exmnng Tle 4 he r onon or hs newor rehe sey se er 5 erons s s ue smll newor h only reures lle ompuonl eor. Also we oun h ueues orme ll he our unons hs s euse enerng r low exees he orresponng low DK DC DA DL DK DC DA py. For nsne n erms o he urnng ros or rm BA o unon BA s ve no wo su-lows or eh lne.e. 777 pu/hour urnng le n gong srgh n lne 1 n 333 pu/hour urnng rgh n lne. Conserng he green spls he enerng low pes or hese wo lnes re 750 pu/hour n 450 pu/hour respevely. As he enerng r n lne 1 s

23 hgher hn s enerng low py he poron o he vehles h exees he low py.e. 7 pu s sure n lne 1. For oher unons euse hey experene more r hn unon A more serous r ongesons suere. As or he nex me sep he enerng lows or he newor remns he only erene s h here re ew ueues presene. The nl r onon or he newor n me sep s esre n Tle 5 whh s reeve rom he r onon he en o me 1. Tle 5: Inl r onon n me Junons Inl r onon n me A B C D AE AD AB AF BA BC BH BG CD CJ CI CB DL DK DC DA The nl r onon on eh eron n me shoul e rese orng o Tle 5. The sme proess s onue s me 1 n he r onon or he newor he en o me s shown n Tle 6: Tle 6: Tr onon or he se suy newor n me Junon Tr onon ses n me Enerng low (pu/hour) Exng low (pu/hour) Queue lengh (pu) A Ieron 1 DA BA AE B Ieron AB CB 4 3 BA C Ieron DC 6 5 BC CD D Ieron 8 7 AD DL DC DA DL DC CD AD BC CJ DK AB BH CI AF BG CB AE BA CD AD BC CJ DK AB BH CI AF BG CB DA In omprson o r onon n me 1 he enerng r lows n exng r lows re he sme whle he lengh o ll ueues n he newor re oule. Ths s euse he r npus or he newor remne whh resule n he we lns suerng more severe ongeson. 3

24 5. Cse Suy To llusre he perormne o he NTFM on rel hghwy newor se suy se on he Loughorough-Nonghm hghwy newor hs een presene whh nlues oh urn ro lns n moorwy lns. The opology o hs hghwy newor s llusre n Fgure 5. There re hree mn roues rom Loughorough o Nonghm whh re A60-A5 (A-B-C-D) A6-A453-A5 (A-J-G-K-C-D) n A51-M1-A5 (A-H-G-F-D). Fgure 5: Loughorough-Nonghm hghwy newor Only run ros n ros eween mor unons re rene n he newor s shown n Fgure 6. Some symols e.g. M1 n A5 enoe he ro lss n ro numer o he ro lns where M represens moorwy n A - run ro. Oher symols represen he ype n ID o unon or nsne verge unon n Loughorough s nme D. There re 47 unons moelle n he newor nlung 8 rounous (R) 3 sgnlse rounous (SR) 5 verge unons (D) 3 merge unons (MG) 1 o-rmps n 1 on-rmps (oh enoe y S) sgnlse T-unons (ST) n sgnlse nerseons (SI). (Inser he numer o lns!)the seuene o he evluon o hese unons s eermne s: SR1-SR-SR3-R6-R7-R8-R-R5- MG1-D5-MG3-D6-MG-R4-R1-SI-R3-SI1-ST-D-ST1. The on-rmps n o-rmps re 4

25 evlue he sme me s he unons h hey re onnee o. The r or hs newor re one rom he Hghwys Ageny n Nonghm Couny Counl (HA 011) n pple o he r low moel n he orm o wo-wy hourly r low. Where suh were unvlle he numer o rs per hour were esme s susse n Seon 4. The ous o hs suy s o pre he oulow n ueue lengh or eh unon/ln n hs rel hghwy newor n o eny he we lns/unons h experene severe r ongeson. There re 16 one hour me seps use o moel he hghwy newor whh represens he moellng uron rom 7:00 m o 11:00 pm per y. The ompuonl me or NTFM o smule hs newor urng he ene plnnng pero s 10 seons. On he ss o he resuls one ws onlue h rounous R1 R6 n R7 suere he wors r ongeson urng he mornng n evenng pe peros s hey re onnee o he ples wh lrge r lows.e. he moorwy he y enre n some resenl res; whle oher unons n ommoe her npu lows whou usng ny ueues. 5

26 Fgure 6: Loughorough-Nonghm moelle hghwy newor The numerl soluon o hs hghwy newor hrough ypl y s emonsre n Fgure 7. On he le hn se o Fgure7 he ol low no he newor n ou o he newor hs een presene wh he expee nrese pe mes. On he rgh hn se he sum o ll he ueues orme n he newor hroughou he y s presene. I n e seen h he hghwy newor experene hevy r ongeson urng he pe mes.e. eween 8:00 n 11:00 n eween 17:00 n 0:00. When he low py on he lns wh ueues s hgher hn he enerng r low he ueues reue n evenully he newor eomes ler o ueues s llusre eween 11:00 n 16:00. 6

27 Fgure 7: Tr onon o he exmple newor uner norml onon 5.3 Dsusson Bse on he resuls ove he nlow n oulow or eh unon n he ueue sore on eh ln n he smple exmple newor re one. In he lgh o hese prmeers he ol exng r low n ggrege ueue lengh n he newor n e erve y summng up he oulows o ll he exs o he newor n y summng up he lengh o ueues orme n he newor respevely. The ol exng r low n ggrege ueue lengh re use o mesure he rnsporly o he newor he hgher he exng r low he eer he newor rnsporly whle ggrege ueue lengh s n nre proporon o he newor rnsporly. In on he ly perormne o lol rel newor n he Loughorough- Nonghm re whh s ompose o oh urn n moorwy ro seons s presene. Usng hs moel n on o he norml ro onons mnenne ons n e mplemene n he newor. NTFM n e eploye o lule he resulng low res n he newor when mnenne s perorme n o ompre hem wh he low res whou mnenne. When ro mnenne s rre ou onl ely ueue lengh n e evlue n orer o on he os o ro users. Aerwrs y omprng he ees o vrous mnenne ons on he ro newor n ro users he es opon h resule n he les mnenne n ro user oss n e oun. 7

28 5 Conlusons In hs suy we hve propose mrosop newor level r low moel n s ssoe unon moels whh re n onssen wh he ueue moel n rgh o wy rules. The moel lules he lows hrough he newor unons n he ueues whh ul up n sperse eren pons urng he y. The moellng ply evelope proves vnes on he prevously evelope lernves n he ollowng eures:. I ouns or oh moorwy n urn ros n he sme ro newor releng he nerve nure o he wo sysems.. I opes wh wo-wy r low y employng erve smulon meho o eermne he vlue o he epenen r lows n he newor.. The moels eure enles enry n ex pons or r low long eh urn newor seon ln (ro). Ths smules r exng/onng he newor housng eses or wor ple loons. v. I eploys shr lne.e. lne h s oupe y r h s urnng le n gong srgh o llusre he r neron mong mxe reonl r lows. The resuls showe h hs moel hs he ply o esre he evoluon o epenen r lows n ores he r movemen n ueue ynms hrough rel mxe hghwy newor h onsss o oh urn n moorwy lns. Also s expee h er he nl suy o he proessng me he NTFM s sule o moel rel hghwy newors n he ees o mnenne wors newor level. ACKNOWLEDGMENT John Anrews s he Royl Aemy o Engneerng n Newor Rl Proessor o Inrsruure Asse Mngemen. He s lso Dreor o The Lloy s Regser Founon* Cenre or Rs n Relly Engneerng he Unversy o Nonghm. Rs Remenye-Preso s he Lloy s Regser Founon Leurer n Rs n Relly Engneerng. They woul oh le o express her grue o ll o hese orgnsons or her suppor. * The Lloys Regser Founon (The LRF) suppors he vnemen o engneerng-rele euon n uns reserh n evelopmen h enhnes sey o le se on ln n n he r. 8

29 REFERENCES (AIA) A. I. A. (011). Annul Lol Auhory Ro Mnenne Survey Breon P. A. Hegy e l. (00). "Sho wve elmnon/reuon y opml oornon o vrle spee lms." Inellgen Trnsporon Sysems 00. Proeengs. The IEEE 5h Inernonl Conerene. Brlon W. R. Koeng e l. (1999). "Useul esmon proeures or rl gps." Trnsporon Reserh Pr A: Poly n Pre 33(3 4): Cown R. J. (1975). "Useul hewy moels." Trnsporon Reserh 9(6): Cremer M. n J. Luwg (1986). "A s smulon moel or r low on he ss o oolen operons." Mhems n Compuers n Smulon 8(4): Dgnzo C. F. (1977). "Tr Dely Unsgnlze Inerseons: Clron o Some Issues." TRANSPORTATION SCIENCE 11(): 180. Dgnzo C. F. (1994). "The Cell Trnsmsson Moel - Dynm Represenon o Hghwy Tr Conssen wh he Hyroynm Theory." Trnsporon Reserh Pr B- Mehoologl 8(4): Dgnzo C. F. (1995). "The Cell Trnsmsson Moel.. Newor Tr." Trnsporon Reserh Pr B-Mehoologl 9(): Deloro F. P. (003). "Evluon o reve ynm roue gune sregy." Trnsporon Reserh Pr C: Emergng Tehnologes 11(5): Guo R. J. n B. L. Ln (011). "Gp Aepne Prory-Conrolle Inerseons." Journl o Trnsporon Engneerng-Ase 137(4): HA (011). Tr Inormon Dse Hghwys Ageny. Hegy A. S. Br De e l. (005). "Opml oornon o vrle spee lms o suppress sho wves." Inellgen Trnsporon Sysems IEEE Trnsons on 6(1): Krm A. A. Hegy e l. (004). "Inegron o ynm roue gune n reewy rmp meerng usng moel preve onrol." Amern Conrol Conerene 004. Proeengs o he 004. Kremser H. (196). "En Zusmmengesezes Wrezeprolem Be Possonshen Verehrssrömen (A Complex Prolem o Dely wh Posson-Dsrue Tr Flows)." Oserrehshes Ingeneur-Arhv 16. Kremser H. (1964). "Wrezeen Un Wreshlngen Be Enelung Enes Possonprozesses n Enen Aneren Solhen Prozess (Delys n Queues wh One Posson Proess Mergng no Anoher One)." Öserrehshes Ingeneur-Arhv 18. Lghhll M. J. n G. B. Whhm (1955). "On Knem Wves. II. A Theory o Tr Flow on Long Crowe Ros." Proeengs o he Royl Soey o Lonon. Seres A. Mheml n Physl Senes 9(1178): Lo H. K. (1999). "A novel r sgnl onrol ormulon." Trnsporon Reserh Pr A: Poly n Pre 33(6):

30 Lo H. K. (001). "A Cell-Bse Tr Conrol Formulon: Sreges n Benes o Dynm Tmng Plns." Trnsporon sene 35(): Lo H. K. E. Chng e l. (001). "Dynm newor r onrol." Trnsporon Reserh Pr A: Poly n Pre 35(8): Messmer A. n M. Ppgeorgou (1990). "METANET: A mrosop smulon progrm or moorwy newors." Tr Engneerng n Conrol 31(9): Ngel K. n M. Shreenerg (199). "A ellulr uomon moel or reewy r." Journl e Physue I (1): 1-9. Nng W. (001). "A unversl proeure or py eermnon unsgnlze (proryonrolle) nerseons." Trnsporon Reserh Pr B: Mehoologl 35(6): Pyne H. J. (1971). "Moels o reewy r n onrol." Smulon Counl Proeeng 1: h6: Pln A. W. n E. A. Chpole (1984). "A generl py ormul or unonrolle nerseon." Tr Eng. Conrol 5: Poeshl F. J. (1983). "De Nh Sgnlgeseuere Neensrssenzuhr Als Verllgemeneres M/G/ 1- Wreshlngensysem (The Unsgnlze Mnor Sree Enry s Generlze M/G/1 Queueng Sysem)." Zeshr ür Operons Reserh 7B. Rhrs P. I. (1956). "Sho Wves on he Hghwy." Operons Reserh 4(1): Ronson B. W. Z. Tn e l. (1999). "Exensons o heorel py moels o oun or spel onons." Trnsporon Reserh Pr A: Poly n Pre 33(3 4): Rohery R. W. (1997). "Cr-ollowng moels." In Tr low heory: A se o he r repor - revse monogrph on r low heory N. H. Grner C. Messer n A. K. Rh Es. O Rge Tennessee O Rge Nonl Lorory. Rusn H. J. n R. Wng (00). Moelng Tr Flow n Urn Unsgnlze Inerseon. Proeengs o he Inernonl Conerene on Compuonl Sene-Pr I Sprnger-Verlg: Segloh W. (1973). "De Lesungsermlung n Knoenpunen ohne Lhsgnlseuerung g (Cpy eermnon nerseons whou r sgnls)." Shrenrehe Srenu un srenverehrsehn 154. Tnner J. C. (196). "A Theorel Anlyss o Delys n Unonrolle Inerseon." Bomer 49(1/): Tn Z. Z. R. Troue e l. (000). "A urher nvesgon on rl gp n ollow-up me " TRnsporon Reserh Crulr E-C108: 4h Inernonl Symposum on Hghwy Cpy Trz M. n S. Gone (000). "Use o smulon o nlyss o mpene mp unsgnlze nerseons." Trnsporon Reserh Crulr(E-C018): Troue R. J. n W. Brlon (1997). "Unsgnlze nerseon heory." 30

31 Vn en Berg M. A. Hegy e l. (007). "Inegre r onrol or mxe urn n reewy newors: A moel preve onrol pproh." Europen Journl o Trnsporon n Inrsruure Reserh 3(3): Wgner C. C. Homnn e l. (1996). "Seon-orer onnuum r low moel." Physl Revew E 54(5): Wu N. (006). "A new moel or esmng rl gp n s sruon unsgnlze nerseons se on he eulrum o proles." Proeeng o he 5h Inernonl Symposum on Hghwy Cpy n Quly o Serve Yoohm Jpn. Yeo G. F. n B. Weesul (1964). "Delys o Ro Tr n Inerseon." Journl o Apple Proly 1():