coride: Carpool Service with a Win-Win Fare Model for Large-Scale Taxicab Networks

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1 1 ori: Crpool Srvi with Win-Win Fr Mol or Lrg-Sl Txi Ntworks Dshng Zhng Mingming Lu Y Li Yunhui Liu Fn Zhng Tin H tinh@s.umn.u Dprtmnt o Computr Sin n Enginring, Univrsity o Minnsot, USA Shnzhn Institut o Avn Thnology, Chins Amy o Sins, Chin Thir Rsrh Institut o Ministry o Puli Surity, Chin Astrt Crpooling hs long hl th promis o ruing gs onsumption y rsing milg to livr o-rirs. Although ho rpools lry xist in th rl worl through privt rrngmnts, littl rsrh on th topi hs n on. In this ppr, w prsnt th irst systmti work to sign, implmnt, n vlut rpool srvi, ll ori, in lrg-sl txi ntwork intn to ru totl milg or lss gs onsumption. Our ori systm onsists o thr omponnts, ispthing lou srvr, pssngr lints, n n onor ustomiz vi, ll TxiBox. In th ori sign, in rspons to th livry rqusts o pssngrs, ispthing lou srvrs lult ost-iint rpool routs or txi rivrs n thus lowr rs or th iniviul pssngrs. To improv ori s iiny in milg rution, w ormult NP-hr rout lultion prolm unr irnt prtil onstrints. W thn provi (i) n optiml lgorithm using Linr Progrmming, (ii) 2 pproximtion lgorithm with polynomil omplxity, n (iii) its orrsponing onlin vrsion. To nourg ori s option, w prsnt win-win r mol s th inntiv mhnism or pssngrs n rivrs to prtiipt. W vlut ori with rl worl tst o mor thn 14, txis, n th rsults show tht ompr with th groun truth, our srvi n ru 33% o totl milg; with our win-win r mol, w n lowr pssngr rs y 49% n simultnously inrs rivr proit y 76%. Ctgoris n Sut Dsriptors H.4 [Inormtion Systm Applition]: Misllnous Gnrl Trms Algorithms, Dsign, Exprimnttion, Prormn Pro. Tin H is th orrsponing uthor o this ppr. Prmission to mk igitl or hr opis o ll or prt o this work or prsonl or lssroom us is grnt without provi tht opis r not m or istriut or proit or ommril vntg n tht opis r this noti n th ull ittion on th irst pg. Copyrights or omponnts o this work own y othrs thn th uthor(s) must honor. Astrting with rit is prmitt. To opy othrwis, or rpulish, to post on srvrs or to ristriut to lists, rquirs prior spii prmission n/or. Rqust prmissions rom Prmissions@m.org. SnSys 13, Novmr 11-15, 213, Rom, Itly Copyright is hl y th ownr/uthor(s). Pulition rights lins to ACM. ACM /13/11...$ Introution Among ll trnsporttion mos, txis ply prtiulrly prominnt rol in rsints ily ommuts in mny mtropolitn rs [2] [6]. Bs on rnt survy in Nw York City [15], ovr 1 txi ompnis oprt mor thn 13, txis, with stl mn o 66, pssngrs pr y, n trnsport mor thn 25% o ll trnsit pssngrs, ounting or 45% o ll trnsit rs pi. To ulill suh livry rqusts, ths txis trvl totl o roughly 8 million mils pr yr [6]. Unortuntly, with 25 MPG, ths txis onsum out 32 million gllons o gs vry yr, mor thn th totl nnul gs onsumption in som mil-siz ountris (.g., Cntrl Arin Rpuli [13]), thror ling to svrly hrmul tilpip missions n nrgy onsumption. On th othr hn, in ron missions tring unr th Kyoto Protool [18], govrnmnts will provi onomi inntivs or hiving rutions in th missions o ron pollutnts. Thus, or oth nvironmntl n onomi purposs, it is imprtiv to in prtil inititiv to support th sm livry rqusts or txi trnsporttion rom pssngrs with lowr totl milg n lss ron missions. In this ppr, w rgu tht txi rpool srvi is promising solution. Th ky vntg o rpool srvi is tht it n pool groups o svrl pssngrs hing in th similr irtion into on rthr thn svrl txis. In othr wors, rpool srvi provis vli solution or livring th sm numr o pssngrs with lowr totl milg n thus lss gs. Th onomi inntiv or rivrs is tht groups o pssngrs n py highr ggrgt r, whrs th inntiv or pssngrs is tht vry pssngr will py lss thn in non-rpool sitution. With n tiv r mol, w n hiv win-win sitution. Furthrmor, rpools n lso improv th vilility o txi srvi uring rush hours n tr mor vnts. Amittly, txi rpooling is not nw onpt n hs n roun or yrs. But xisting txi rpool rrngmnts r ngotit y iniviul rivrs n pssngrs in n ho mnnr without ilitting inrstrutur. Until now, w hv lk systmi stuy o rpooling in lrg sl txi ntworks. W not tht mny stuis hv ous on txi shuling [4] [9] [1] [11] [19] [23] [24] or novl systms tking vntg o txi moil trs [3] [5] [12] [17] [2] [21]

2 2 [22] [25] [26], ut littl rsrh, i ny, hs n on on txi rpool srvis with sotwr n hrwr o-sign. In this ppr, w prsnt th irst systmti s- tuy o how to sign, vlut, n implmnt txi rpool srvis in rl worl snrios. Spiilly, th ky ontriutions o this ppr r s ollows: To th st o our knowlg, w onut th irst rpool srvi tht onsirs th mutul nits or pssngrs n rivrs in lrg-sl txi ntworks n provi omprhnsiv stuy o how to ill th sm pssngr livry rqusts with lss totl milg n thus lss gs onsumption. To hiv our gol, w vlop ustomiz hrwr, TxiBox, with multipl snsors n onor vis (suh s CDMA ommunition moul, MIC, mr, n rpool r mtrs). Using TxiBox, w sign txi rpool systm, ori, to gthr rqusts rom pssngrs, to inorm rivrs o rpool rqusts, to lult rpool routs or rivrs, n to stimt rpool rs or pssngrs. In ori, w introu mthmtil onpt livry grph to rprsnt rpool rout shul or livring pssngrs. Givn rqusts provi y pssngrs, w sk n optiml livry grph to hiv th minimum totl milg. W show tht this optimiztion is NP-hr y linking it to th lssi trvling slsmn prolm, n provi (i) n optiml solution with intgr progrmming, (ii) 2-tor pproximtion solution with polynomil omplxity, n (iii) n onlin lgorithm to ommot onlin strming rqusts. In ition, w onsir irnt rl worl onstrints,.g., pssngr trvl prios, numr o vill txis, n txi pitis. Bs on th rpool rout, w propos win-win rpool r mol to nourg oth rivrs n pssngrs to prtiipt in rpooling. In this mol, givn rpool nit u to milg rution, pssngrs n rivr will shr this nit s on rtio ynmilly ust y th supply n mn rltionships in txi ntwork. Our vlution ort is omprhnsiv. W tst ori on rl worl 1 GB tst onsisting o 1 wk o GPS trs rom mor thn 14, txis in Chins ity Shnzhn with popultion o 1 million. Th vlution rsults show tht ompr with th groun truth, our rpool srvi n ru th totl milg y s muh s 33%, n our win-win r mol n lowr pssngr rs y 49% n inrs rivr proit y 76% t th sm tim. Th rst o th ppr is orgniz s ollows. Stion 2 introus th rlt work. Stion 3 proposs th motivtion or th sign. Stion 4 prsnts th ori systm ovrviw. Stion 5 sris our ustomiz vi, Txi- Box. Stion 6 xplins th lgorithms or rpool rout lultion. Stion 7 prsnts win-win rpool r mol. Stion 8 vlits our srvis with ig tst, ollow y th onlusion in Stion 9. 2 Rlt Work Th prmis o txi rpooling is not nw, ut in rl worl it is normlly ngotit privtly y rivrs n pssngrs in n ho mnnr. W lk systmti sign to ln nits o ll th involv prtis,.g., rivrs, pssngrs, n txi oprtors. Two typs o prvious work r irtly rlt to our work: rsrh on txi systms n on ho rpools. 2.1 Txi Systms Th inrsing vilility o GPS vis hs nourg surg o rsrh intn to improv th iiny o lrg-sl txi ntworks. First, svrl systms r propos or th nit o pssngrs or rivrs,.g., llowing pssngrs to qury th xpt urtion n r o pln txi trip s on th history o prvious trips [4] n qury rl-tim txi vilility to mk inorm trnsporttion hois [19], s wll s rommning optiml pikup lotions or routs [8] [9] [23]. Son, txi trs n lso hlp txi ntwork oprtors ttr ovrs txis n provi iint srvi to pssngrs,.g., isovring sptil n tmporl usl intrtions to provi timly n iint srvi in rtin rs with isquilirium [1] [11], n tting nomlous txi trips to isovr rivr ru or ro ntwork hngs [24]. Thir, trs rom xprin txi rivrs n hlp othr rivrs improv thir riving prormn,.g., nvigting nwr rivrs to smrt routs s on thos o xprin txi rivrs [17] [21]. Fourth, lrg sl txi trs nl us to ttr unrstn tri onitions o itis,.g., smntis o origin-stintion lows [25], tri ongstion n volums [3], n tri pttrns twn rgions with irnt untions [2]. Finlly, lrg sl trs lso n hlp in ity plnning,.g., tting lw urn plnning [26] or improving mp inrn [5] [12]. Yt xisting rsrh on txi systms ouss on shuling iniviul txis, ssuming tht on txi n ommot only singl livry rqust t tim. In ontrst, our systm llows shr livry. Thnilly, w ous on rpool rout lultion n win-win r mol, nithr o whih hs n invstigt or. 2.2 A Ho Crpool Limit ho txi rpools xist in oth vlop n vloping ountris. For xmpl, in Nw York City, up to our pssngrs n rpool togthr in singl txi ri uring 6 AM to 1 AM on wky, long thr prst routs in Mnhttn t lt r o $3 or $4 pr pssngr, signiintly lss thn th rgulr mtr rts [16]. In Biing, ho txi rpooling is lso llow with th onsnt o oth pssngrs n rivrs, n vry pssngr pys 6% o th rgulr r. Furthr, som oor to oor shuttl srvis r lso vill in mor irports, n n nl shr ris to or rom irports [1]. Howvr, in th ormntion rpool srvis, oth tim n lotions r prst n th srvis r rrng on th spot y pssngrs or rivrs in smll-sl ho mnnr, n no inrstrutur is provi to improv th iiny o rpooling.

3 3 3 Motivtion In this stion, s on two tsts out trs n rs o 14, txis in Chins ity Shnzhn with popultion o 1 million, w irst introu th si proprtis o lrg sl txi ntworks in ns urn rs. Thn, w prsnt vin out th iniinis o urrnt txi ntworks, monstrt opportunitis or rpools to rss ths iniinis, n intiy hllngs to ilitting rpooling in urrnt txi ntworks. Dtils o th tsts ppr in Stion Proprtis o Txi Ntworks In vlop ountris suh s US, txis r usully us to srv pssngrs to irports, n prsonl vhils r us or othr tivitis, xpting xtrm lrg itis suh s Nw York City. But in vloping ountris, u to high osts o owing prsonl vhils, txis n othr puli trnsporttion r populr or ily tivitis. In ns urn rs suh s Biing, txis r orl or lol trvling with n initit r out 2 USD or 3 KM trip, n r mor omortl thn othr puli trnsporttion with hpr rs (suh s uss or suwy). Du to th populrity n th orility o txi srvis, th numr o txis in txi ntwork o lrg ity is typilly mor thn 1,. Thus, ths txis n sily oun on strts t th most o tim n lotions (xpt in rush hours or in hot pikup spots) n r ommonly us or shopping, trvling to n rom th work or shools, n othr ily tivitis. 3.2 Iniinis o Txi Ntworks For soity, th ky iniiny o txi ntworks is th lrg gs onsumption o long-trvl istn. Figur 1 summrizs sttistis out txi ntwork stui. W osrv tht ths txis trvl totl o 1.2 illion k- ilomtrs pr yr, onsuming out 1 million litrs o gs to livr 2 million pssngrs n using hrmul tilpip missions. Txi Ntwork Summry Colltion Prio 6 Months Colltion Dt 1/1/12-6/3/12 Num o Txis 14,453 Numr o Pssngrs 98,472,628 Totl Trvl Distn 594,31,428 (KM) Totl Fr 2,255,52,932 (CNY) Avrg Trvl Distn 6.32 (KM) Avrg Fr 22.9 (CNY) Dlivry Distn (KM) Dytim Fig 1. Sttistis Fig 2. Dlivry Distn For rivrs, th ky iniiny is low proits, whih r i minly y livry istns (i.., th milg with pying pssngrs). Intuitivly, rivrs shoul rn mor proit in rush hours, ut this is not th s in lrg itis with svr ongstion. In rgulr hours without ongstion, th totl istn (i.., lso inluing totl milg without pying pssngrs) is high, ut th prntg o livry istn is low, sin it is not sy to in pssngr. In rush hours with ongstion, in ontrst, th prntg o livry istn is high (i.., sy to in pssngr), ut th totl istn is low u to th slow p o tri. Figurs 2 shows th vrg livry istn. It shows livry istns t irnt tims o y (i.., rush n non-rush hours) r not signiintly irnt. For pssngrs, ky iniinis r high rs n low vilility. Aoring to sttistis out Nw York C- ity [6] [15], th vrg r is USD or 2.8 mil trip with n 11-minuts trvl tim, whih is 5.8 tims highr thn th vrg puli trnsit r (us or suwy) on vrg. In our sttistis, th vrg r o 22.9 Chins Yun (CNY) or txis is 11 tims o us r o o 2 CNY on vrg. Ths two tsts lso provi som vin out th low vilility o txi srvis. First, in th tim intrvls twn livris prsnt in y Figur 3, smll intrvl inits tht txi will pik up nw pssngr right tr it rops o n ol pssngr, i.., low vilility. In Figur 3, th vrg tim intrvl in rush hours is smll, lss thn 3 minuts, initing low vilility o txi srvis. Son, low vilility n lso sn in th txi oupny rtios in Figur 4, whr high oupny rtio inits wr mpty txis. Th rtios in Figur 4 init tht mor thn 8% o txis r oupi on vrg uring rush hours. Thus, Figurs 3 n 4 init th low vilility o txis uring rush hours. Intrvls twn Dlivris (mins) Hours o Dy Fig 3. Dlivry Intrvls Txi Oupny Rt (%) Hours o Dy Fig 4. Oupny Rt 3.3 Opportunitis or Txi Crpool W show th opportunitis tht rpools provi to rss th ov iniinis. A ky tor nsuring th suss o rpooling is th rquny with whih pssngrs rom th sm origin go to similr stintions, whih n shown y (i) trvl istns o shr routs n (ii) istns twn stintions. Both long-istn shr routs n smll istns twn pssngrs stintions init goo rpool opportunitis. W irst show som xmpls o shr routs n los stintions. Bs on th tsts, w show 2 ontinuous livris rom n irport in Figur 5 whr in orinry srvis, most pssngrs go owntown n othrs go to svrl hot spots. Airport Dlivry Strt Dlivry En Hot Spot Common Rout Downtown Fig 5. Dlivris From Airport

4 4 Furthr, with 1, txi livris rom th irport, Figur 6 shows th prntg istriution o istns o shr routs, whr w osrv tht mor thn 9% o livris shr t lst 5 KM with nothr livry, n tht mor thn 5% o livris shr t lst 2 KM with nothr livry. Th prntg istriution o istns twn stintions is givn in Figur 7, whr w osrv tht lmost 6% o livris hv stintion losr thn 1 KM to tht o nothr livry, n lmost 8% o livris hv stintion losr thn 5 KM to nothr stintion. From Figur 6 n 7, w osrv tht ir mount o livris shr long istns, n hv stintions los to h othr. CDF (%) Distn o Shr Routs (KM) Fig 6. Shr Distn CDF (%) Distn twn Dstintions (KM) Fig 7. Clos Dstintions 3.4 Bnits or Txi Crpool From th ov igurs, w osrv goo opportunity or rpools to nit multipl prtis. For pssngrs, txis rpool n inrs th vilility o txi srvis in xtrm wthrs, pk hours or hot pikup lotions, ruing th witing tim or pssngrs; in ition, multipl pssngrs in rpool n shr th r togthr, ruing th r pi y iniviul pssngrs. For txi rivrs, txi rpool n inrs proits, sin th ggrgt rpool r is highr thn rgulr srvi r with th sm trvl istn. For oprtors, txi rpool n provi mor trnsporttion pity n nl mor iint gs onsumption. Not tht txi rpools o not im to ompltly rpl th tritionl txi srvis, ut srv s ky supplmnt or th situtions whr rgulr txi srvis r insuiint in pk hours or xtrm wthrs, or situtions whr som pssngrs woul lik to tk trnsporttion tht is hpr thn tritionl txi srvis yt mor onvnint thn us n suwy. 3.5 Pssngr Snsitivity or Txi Crpool Aoring to rpool survy tking t Biing [7], 75% o intrviws r willing to rpool; 57% o intrviws hv rpool t lst on; 73% o intrviws pt simpl rpool r mol tht vry pssngr pys 6% o rgulr srvi r or th shr istn, ling to mor proits or rivrs; svrl ky onrns out rpooling point out y mor thn hl o intrviws r s ollows (i) prolong trvl tim (64%), (ii) hr to in pssngrs to rpool (5%), n (iii) unl to print uplit ripts or ll pssngrs (5%). Bs on th ov survy, w in tht most pssngrs r willing to pt rpools n to shr th nits o rpools with o-rirs n th rivr, ut w still svrl hllngs to nl prtil rpool srvi in lrg-sl txi ntworks, whih w will introu nxt. 3.6 Chllngs or Txi Crpool W prsnt thr hllngs n som possil solutions or implmnting rpool srvis in th urrnt txi ntworks. Aquisition o Dtil Sttus out Txis: To in th most suitl txi, ispthing ntr shoul quir til inormtion out txis,.g., how mny sts r lt, whih is iiult to otin in urrnt txi ntworks, whr only th gnrl txi sttus (.g., lotions, sps, with pssngr or not, t) n otin y ispthing ntrs through rl-tim GPS ror uploing. Thus, n onor vi shoul instll in txis to lt ispthing ntrs monitor th til sttus o txis n in th most suitl txi. Crpool Rout Clultion: Atr ining th most suitl txi, ispthing ntr shoul lult th optiml rpool rout s on multipl riv rqusts in ntrliz wy, n sn th lult rout to rivr. This rout shoul iint in trms o th totl istn to livr ll ssign pssngrs. In ition, th lultion o routs shoul st nough to nl rsponsiv txi rpool srvi. Fr Estimtion n Clultion: With rpool rout shul, ispthing ntrs shoul notiy pssngrs with r tils o svrl rpool options or thir pprovl. A win-win rpool r mol tht stimts rs is missing in th txi usinss. Furthr, urrnt r mtrs n lult only singl r, n mor vn r mtr tht n ror multipl onurrnt trips is sirl or rpooling. To rss th ov hllngs, w im to vlop rpool systm, ori, s hrwr n sotwr o-sign with n ront-n onor vi, TxiBox, n k-n lou srvr to upgr urrnt txi ntworks. ori mploys multipl snsors n xtrnl vis tth to TxiBox to tivly mng txi ntworks. W will provi n ovrviw o ori n th TxiBox sign in Stions 4 n 5, rsptivly. 4 Th ori Systm Ovrviw In this stion, w prsnt systm ovrviw o ori, whih onsists o thr ky prts: lou srvr, pssngrs lint, n th onor TxiBox s shown in Figur 8. Pssngr Clints Phon Cll Moil App ori Dlivry Rqusts Crpool Sltion Clou Srvr Rout Clultion (Stion 6) Fr Estimtion (Stion 7) Crpool Shuls Physil n Dlivry Sttus Onor TxiBox Cntrl Control Onor Snsing Extrnl Dvis (Stion 5) Fig 8. ori Systm Ovrviw 4.1 Pssngr Clints Pssngr prtiiption is rquir y our sign, whih n nourg y our win-win r mol isuss ltr. Assuming tht pssngrs will willing to prtiipt, thy will provi livry rqusts to th ispthing ntr.

5 5 Th most ommon wy to provi livry rqusts is to ll th ispthing ntr y phon to provi th numr o pssngrs, pikup tim, origin, stintion, n possil livry lin. Furthr, moil pps n us to provi livry rqusts without lling th ntr. Bs on th livry rqusts provi y pssngrs, th ispthing ntr will rturn rpool option with ru r or thir pprovl, long with non-rpool option with rgulr r or omprison. 4.2 Onor TxiBox Whn rpool is pprov y pssngrs, ispthing ntr will lot suitl txi or th rpool s on th urrnt sttus o txis n thn sn rpool rout shul to this txi s TxiBox. Th rivr will rspon to this rpool rqust y hnging th sttus o th txi n thn prorming th rpool rout shul. Ths untions r prorm y thr ky omponnts o TxiBox, whih will introu in til in Stion Dispthing Clou Srvr In this ppr, w will ous on untion signs or lou srvr t ispthing ntrs with n mphsis on txi rpool srvis rthr thn rgulr srvis. In our rpool srvi sign, lou srvr is minly in hrg o (i) riving livry rqusts rom pssngrs; (ii) lulting rpool routs s on livry rqusts; (iii) stimting rpool rs or pssngrs to pprov; (iv) sning rpool routs to suitl txis; (v) otining th physil n livry sttus o txis. In th rst prt o th ppr, w prsnt th til Txi- Box sign in Stion 5; or th ispthing lou srvr, w sri two ky untions, th rpool rout lultion n r mol in Stions 6 n 7, rsptivly. 5 TxiBox Hrwr In this stion, w prsnt our hrwr sign, n thn show th ploymnt out TxiBox, n inl propos th pility o txis with TxiBox. 5.1 TxiBox Dsign As shown y Figur 9, our onor vi, TxiBox, onsists o thr min prts: ntrl ontrol systm, onor snsing systm, n xtrnl vis. Th ntrl ontrol systm hs two ky prts, th powr moul n th CPU moul. For th powr moul, w mploy TPS5416 rom Txs Instrumnts, whih is 6V, 1.5A, stp own SWIFT DC/DC onvrtr with n intgrt high-si MOSFET. For th CPU moul, w us 32 it 72 MHz prossor STM32F13 rom ARM Cortx-M3 prossors with A/D Convrtors o 12-it ury. Th onor snsing systm hs opn intrs to multipl snsors, n th urrnt hrwr is tth with (i) lohol n smok snsors, (ii) ± 2g trixil lrtion snsor, n (iii) mr n mirophon. Bs on th ov onor snsors, ispthing ntr is pl o monitoring th omprhnsiv physil sttus o txi on strts. Vrious xtrnl vis n intgrt into our Txi- Box. Som xtrnl vis in th urrnt TxiBox sign inlu (i) isply n spkr intgrt to th isply; (ii) tritionl r mtr or r lultion n ript printing; (iii) kup powr or sitution in whih th min powr is not vill; (iv) n mrgny utton; (v) GPS moul with sprt GPS ntnn; n (vi) CDMA 1X ommunition moul with sprt ntnn. In som xisting txi ntworks, th ommunition mouls usully us GPRS (.g., or GPS oorints uploing) twn txis n ispthing ntrs. But in our sign, txis typilly hv lrgr tst to uplo to or ownlo rom ispthing ntr. Thus, CDMA 1X, inst o GPRS, ommunition moul is tth to TxiBox, sin CDMA mploys irnt hnnls or voi n t ommunitions, whih lrly hs vntgs in trms o ommunition sp n stility, ompr to G- PRS tht mploys th sm hnnl or t ommunitions. 5.2 TxiBox Dploymnt W hv ploy our TxiBox in 98 txis s shown y Figur 1. Th lohol n smok snsors r instll in th iling o txis or ttr snsor untion. Th mr is in ront o pssngrs so s to tk piturs rom ttr ngl. Th min prt o TxiBox is hin ov th glov ox. Th isply is instll ov th ir-onitionr ontrol pnl or sir ss y rivrs. Th 3 xis lrtion snsor is hin unr th glov ox. Fig 9. TxiBox Hrwr Dsign Fig 1. TxiBox Dploymnt

6 6 5.3 TxiBox Cpility In this stion, s on th hrwr w ploy in txis, w introu th pilitis o TxiBox. Txi Physil Sttus Snsing: Dispthing ntrs shoul ully wr o th sttus (.g., lotion, sp, t.) o txis to provi ttr rpool srvi. With GPS n CDMA 1X mouls onor, txi n prioilly uplo its rl-tim physil sttus to ispthing ntr. Th onor tritionl r mtr n TxiBox with isply n untion togthr s smrt mtr tht n ror th sttus o svrl trips, i.., th livry istn n r or irnt pssngrs onor, whrs th tritionl r mtr n only ror singl livry istn. Furthr, spkr is intgrt into th isply so ispthing ntrs n issu voi shul or voi nvigtion. Txi Dlivry Sttus Snsing: In ition to txi s physil sttus, ispthing ntr is lso intrst in th rl tim sttus o its livris. Th sttus o livris inlus livry istn, with pssngrs or not, r, urtion, strt tim, n tim, pikup n ropo lotion, whih ll n otin y TxiBox n uplo to ispthing ntrs. 6 Rout Clultion in Clou Srvr In this stion, w irst propos prliminris out our rpool work, thn in rpool rout lultion prolm, n inlly propos its solution. Crpools n lssii into our tgoris, (i) on o- rigin to on stintion (1 1); (ii) on origin to mny stintions (1 N); (iii) mny origins to on stintion (N 1); n (iv) mny origins to mny stintions (N N). For th sk o prsnttion, w will ous on 1 N us (i) 1 1 is spil s o 1 N; (ii) N 1 n solv with 1 N y rvrsing origin n stintion; n (iii) N N n solv with spil 1 N with onstrints on th orr in whih to visit ll origins n stintions. Without loss o gnrlity, w us 1 N mol (.g., rpool pssngrs rom n irport) s n xmpl or th sign. 6.1 Prliminris For rpool, pssngr will provi livry rqust with n origin, stintion, strt tim n n optionl n tim (A possil n tim srvs s lin or livry, ut our mol works with n unknown n tim). Thus, givn svrl rqusts or rpooling rom th sm origin s in Figur 11(), w shll nlyz istns twn thir stintions, whih n shown s omplt grph. W onstrut this omplt grph s shown in Figur 11() y (i) trting oth origin n stintions s vrtis, n (ii) linking ll vrtis to h othr with irt gs, ssoit g wights with pirwis milg osts. Suigurs () n () in Figur 11 giv n xmpl o how to rt omplt grph s on 9 livry rqusts rom th origin. A wight on n g (.g., M i ) inits th rl worl milg twn two lotions. Givn th omplt grph, w n otin rpool rout s on livry grph, whih is in s ollows. D1:[, ]; D2:[, ]; D3:[, ]; D4:[, ]; D5:[, ]; D6:[, g]; D7:[, h]; D8:[, i]; D9:[, ]; () Rqusts M i i h g Origin () Complt Grph G i h Fig 11. Complt Grph g M () Dlivry Grph (no rpool) Dinition 1: Dlivry Grph: With omplt grph G givn y livry rqusts, livry grph is sugrph o G whr (i) th origin vrtx n rh ll stintion vrtis; n (ii) no rnhs xist t ny vrtx othr thn th origin vrtx (i.., spok topology) With th ov inition, w n s tht livry grph uniquly inits rpool rout whr th totl rpool milg is qul to th sum o ll its gs wights. In Dinition 1, th onition (i) is to mk sur tht with rpool rout, ll pssngrs n livr rom th origin to thir stintions; th onition (ii) is to mk sur tht vry pssngr will tk only on txi uring th rpool, i.., without rly. Suigur () in Figur 11 givs n xmpl o livry grph without rpool, i.., ll pssngrs r livr y sprt rivrs with sprt milgs,.g., M. Txi 1 g h i Txi 2 Txi 3 () Dlivry Grph () Sugrph g h i Origin Txi 1 Rly () Rly Fig 12. Dlivry Grph with Crpool Txi 2 Dstintion Th xmpls o livry grph DG with rpool r givn in Suigur () o Figur 12. In DG, th origin vrtx n rh ll stintion vrtis, n no rnhs xist t ny stintion vrtx. A livry grph (.g., DG) inits rl worl rpool y spiying (i) pssngr ssignmnts or txis, n (ii) livry orr or txi s pssngr ssignmnt. For xmpl, DG shows tht thr txis ulill pssngr rqusts with stintions on thr pths (th totl wight on gs o pth inits th rl worl milg): Txi 1 livrs pssngrs to, with milg M ; Txi 2 livrs pssngrs to,, n, with milg M + M + M + M ; Txi 3 livrs pssngrs to g, h, i n, with milg M g + M gh + M hi + M i. Suigur () o Figur 12 givs n xmpl o rpools prohiit y ori. To rpool y this sugrph, w hv to t lst us two txis to livr pssngrs to,, n : th irst txi livrs pssngrs with stintion

7 7,, n, ut rris only th pssngr with stintion rom origin to n intrmit vrtx ; th son txi hs to pik up this pssngr t vrtx ( rly), n thn livr him or hr to stintion s shown in Suigur (). W rgu tht th rpool srvi with rly is not prtil in rl worl snrios, us (i) th rly pssngr hs to py multipl tims to irnt rivrs, n (ii) th oorintion twn txis woul l to lrg lyovr ly. Thror, in our work, ori supports only th livry grphs with spok topology to init prtil rl worl rpool rout shul or rivrs to livr pssngrs without rly. 6.2 Crpool Rout Clultion Prolm Bs on th livry grph propos in th lst sustion, w propos our rpool rout lultion prolm: Givn omplt grph s on livry rqusts, in th minimum wight livry grph. Th omplt grph n sily onstrut s on livry rqusts provi y pssngrs; s sugrph, livry grph spiis pssngr ssignmnts n livry orrs to ulill ll livry rqusts; th minimum totl wight o livry grph inits it ulills ll rqusts with rpool spning th minimum totl milg. To prorm prtil rpool, w lso onsir thr onstrints or our sign. (i) Txi Cpity ; it shows how mny pssngrs n pool into on txi. (ii) Numr o Avill Txis n; it shows how mny txis n us or rpool t th origin. (iii) Trvl Prio [ti s,t i ]; it shows th rlist pikup tim ti s n th ltst ropo tim ti or livry rqust i. Bs on th ov isussion, our rpool rout lultion prolm is rlt to multipl trvling slsmn prolm (ll mtsp whr multipl slsmn strt rom pot to visit irnt itis with th minimum totl istn [14]) yt with th spil rpool onstrints. An mtsp is gnrlly solv with Intgr Linr Progrmming to th optiml solution. But or our lrg sl rpool rout lultions, th optiml solution rsults in long running tim, sin it is NP-Hr. Thus, prtil pproximtion lgorithm shoul us to otin livry grph within rsonl tim. Anothr ky tur o our rpool rout lultion prolm is tht inst o ooking rpool trip y or two in vn, som pssngrs my provi onlin livry rqusts ust tns o minuts or th strting tim o thir livris. So n onlin lgorithm shoul mploy to pool nw pssngrs into xisting rpools or to strt nw rpool. Thror, th sign gn out our solution to th rpool rout lultion prolm givn s ollows: (i) w us Intgr Linr Progrmming to ormult our rpool rout lultion to otin th optiml solution in Stion 6.3; (ii) or prtil (quikr) solution, w propos 2-tor pproximtion lgorithm to otin su-optiml solution in Stion 6.4; (iii) to onsir onlin rqusts, w prsnt our onlin lgorithm in Stion Optiml Solution In th litrtur, th optiml solution or mtsp is givn y Intgr Linr Progrmming. Thus, w ormult our Crpool Rout Clultion with ollowing initions. (1) G =(V,A): wight omplt grph whr vrtx is th origin vrtx whr rpool strts n V = V {} is th st or stintions, n wight on A init s i is th rl worl milg ost rom vrtx i to vrtx ; (2) x i = 1 i g (i, ) A is us; x i = othrwis; (3) [ti s,t i ]: trvl prio or pssngr to vrtx i; (4) n: th numr o vill txis; (5) : th txi pity; (6) y i : totl numr o ropp pssngrs or vrtx i; (7) q i : totl numr o ropp pssngrs t vrtx i; (8) p i : tim rriving t vrtx i; (9) w i : ltst strttim o ropp pssngrs or vrtx i; (1) T (i, ): trvl tim twn vrtx i n vrtx. min (i, ) A i x i s.t. x i = 1 V (1) i V x i {,1} i V (2) V V x n x i = i V (3) y i + q i i V (4) I x i = 1 y i + q i y i, V (5) p i ti i V (6) I x i = 1 p i + T (i, ) p i, V (7) mx{w i,ti s } + T (,i) ti i V (8) I x i = 1 w i w i, V (9) x i 1 S V (1) i/ S S x i {,1} i, V (11) whr (1) nsurs tht xtly on txi visits stintion; (2) nsurs tht xtly on txi lvs on stintion or th nxt livry, or th rpool is ovr n no livry ns to m; (3) is out th onstrint on th numr o vill txis; (4) n (5) r out th txi pity onstrint; (6), (7), (8) n (9) r out th trvl prio onstrint; (1) is to prvnt th ormtion o sutours not inluing origin vrtx. Not tht lthough vry txi hs isoint vrtis in livry grph, thy n shr th sm rout in th rl worl whn prorming th rpool. Sin th tritionl trvling slsmn prolm is NP-Hr, s gnrliz vrsion, our prolm is lso NP-Hr (u to sp onstrint w omit th orml proo). Thror, whn th numr o stintions inrss, th running tim to solv th ov intgr progrmming inrss xponntilly. Although intgr linr progrmming is suiint or smll numr o stintions, w n to ommot th s whr th numr o stintions is lrg with n iint lgorithm.

8 8 6.4 Approximtion Algorithm In this stion, w irst propos n pproximtion lgorithm, n isuss th impts o th thr onstrints Approximtion Algorithm without Constrints An pproximtion lgorithm without onstrints is unr snrio whr ll pssngrs trvl prios r not onsir; th origin is with unlimit txis or rpooling; vry txi hs unlimit pitis. W irst prsnt som rtionls. Any rpool rom th sm origin n prorm with two ky stps: (i) w shll ssign pssngrs to irnt mpty txis; (ii) w shll lult livry orr or givn pssngr ssignmnt or prtiulr txi. In th ollowings, w will sri how to mk us o this rtionl or our pproximtion lgorithm in two stps n provi its pproximtion rtio. (i) Pssngr Assignmnt: Bs on omplt grph G rt with livry rqusts, w will show how to ssign pssngrs in Figur 13. i Origin h g () Complt Grph G Sutr 1 Sutr 2 Sutr 3 g h i () Minimum Spnning Tr T o G Txi 1 Txi 2 Txi 3 g h i () Pssngr Assignmnt y T Fig 13. Pssngr Assignmnt To ssign pssngrs to irnt txis, w shll tk into ount th istns twn stintions givn y G in sugrph (). Th otiv is to in minimum wight sugrph o G to ssign stintion vrtis to irnt pths (vry pth is us y n uniqu txi). Sin th minimum spnning tr (MST) is th minimum wight sugrph o G, in this ppr w try to mploy n MST to otin pssngr ssignmnt. Sugrph () givs G s MST T with thr sutrs root t origin vrtx. Bs T,w ssign th pssngrs, who hv stintion vrtis in th sm sutr, into th sm txi. For xmpl, pssngrs with stintions,, n r ssign into Txi 2, s in Sugrph (). Not tht T is not livry grph w try to otin, us T hs rnhs t stintion vrtis. Thus, w hv shown how to onut pssngr ssignmnt s on givn omplt grph. (ii) Dlivry Orr Clultion: Bs on th pssngr ssignmnt in stp (i), in Figur 14 w will show how to lult livry orr mong pssngrs ssign into th sm txi. () Sutr ST rom MSP T () Douling to nl trvrsl () Trvrsl Orr Fig 14. Dlivry Orr Clultion As in stp (i), pssngr ssignmnt or prtiulr txi is givn y sutr root t th origin vrtx. Thus, w mploy Sutr 2 (nm ST) in th MST T in suigur () s n xmpl to show how to otin livry orr. With n osrvtion on ST, w oun tht ST only givs pssngr ssignmnt, ut not ix livry orr sin ST hs rnh tht rquirs pssngr rly, whih is prohiit y ori. Thus, nw sugrph trnsorm rom ST shoul rt to lult n orr without rly. In this ppr, w us pth-irst trvrsl rom root vrtx to i livry orr. But s w n s in suigur (), ST is irt grph, n nnot trvrs s on urrnt gs. Thus, s in suigur (), w oul th gs in ST to rt loops to nl trvrsl. This orr is not livry orr sin it involvs uplit vrtis, i..,, thus longr totl milg M + M + M + M + M. To otin livry orr, w us shortut strtgy to limint uplit vrtis in trvrsl. In Figur 15, w show how to shortut som gs out uplit vrtis, thus urthr ruing livry milg. () Shortutting g n () Shortutting g, n () Dlivry Milg M +M +M +M Txi 1 g h i Txi 2 Txi 3 () Dlivry Grph Fig 15. Shortutting out Duplit Vrtis As in suigur () n (), w shortut g n with nw g, n thn shortut g, n with nothr nw g. Not tht s on tringl inqulity, th lngth o n g (.g., M ) is lwys shortr thn th sum o gs it shortutting (.g., M + M ). Furthr, w lt th g to otin th livry orr n th totl milg ost o 4 gs (M + M + M + M ) s in suigur (). Thror, with trvrsl, w hv shown tht how to lult livry orr s on givn pssngr ssignmnt. With th ov two stps, w inish our pproximtion lgorithm to otin our livry grph in suigur (). Proo o Approximtion Rtio: W hv prov tht our trvrsl lgorithm hs onstnt prormn rtio o 2, i.., th totl milg otin y our rpool shul, is t most 2 tims th optiml milg w otin y th optiml solution using intgr progrmming. This is us (i) with shortutting, th wight o our livry grph W(S) is smllr thn wight o Trvrsl W(T ), i.., W(S) < W(T ); (ii) trvrsl is xtly two tims o MST, W(T )=2W(T ); (iii) th MST is smllr thn or - qul to th Optiml solution sin th optiml solution is spnning tr n MST is th smllst spnning tr, 2W(T ) 2W(O). Thus, W(S) < W(T )=2W(T ) 2W(O), thror W(S) W(O) < 2. During th onstrution o th minimum spnning tr, thr onstrints, i.., Txi Cpity, Numr o Avill Txis, Trvl Prio, hv spil impts, whih will introu in th ollowing thr sustions.

9 Impt o Numr o Avill Txis n In this stion, w show how to solv rpool prolm with onstrints on th numr o vill txis n. W n ru th totl milg y livring pssngrs sprtly, i thy r hing in signiintly irnt irtions. In livry grph G, vry sutr root t th origin is ssoit with sprt txi, whih stisis ll livry rqusts in this sutr. For xmpl, in Figur 16, th spnning tr hs thr sutrs (ox), n thror w n thr txis to stisy th livris. g Txi 1: ; Txi 2: ; h i Txi 3: g h i ; Fig 16. Minimum Numr o Txis or Dlivris Whn onstruting spnning tr, w hv to in on s- pnning tr whos numr o sutrs root t origin is not iggr thn n. Figur 17 shows how to impos suh onstrint uring spnning tr onstrution. Aing g inits 2 txis Aing g inits 1 txi Fig 17. Constrints on Numr o Avill Txis n In Figur 17, givn n = 1, i.., thr is only on txi vill or origin, suppos tht tr ing g, urrntly th minimum g tht shoul to th tr is g oring to Prim s lgorithm. But ing g inits tht w n two txis to ulill th livris, whih is ginst to n = 1. Altrntivly, w n g n it will still ulill th livris yt with on txi Impt o Txi Cpity In this stion, w onsir how to solv rpool prolm with onstrints on th txi pity. Sin th txi pity is limit (.g., 4 or sn n 6 or vn), livry grph shoul not hv ininit pth or ny livry rnh. It is lr tht givn ix s- pnning tr, th minimum txi pity is qul to th siz o its iggst sutr root t origin, us txi hs to livr ll pssngrs in this sutr rom origin. Figur 18 givs n xmpl, whr th iggst sutr hs our vrtx, thror th minimum txi pity is 4. Txi 1: 1 g ; Txi 2: ; h i Txi 3: g h i ; Fig 18. Minimum Txi Cpity or Dlivris Whn onstruting spnning tr, w hv to ontrol th sizs o sutrs to mk sur th siz o th lrgst sutr lss thn givn pity onstrint. Figur 19 shows how to onsir it uring th onstrution o spnning tr. Aing g rquirs pity o 2 Aing g rquirs pity o 1 Fig 19. Constrints on Txi Cpity In Figur 19, suppos = 1 or simpliity, n suppos tht tr ing g, urrntly th minimum g shoul to th tr is g oring to Prim s lgorithm. But ing g inits tht w n txis with pity o 2 to ulill th livris, whih is ginst to = 1. Altrntivly, w n g n it will still ulill th livris yt with pity o Impt o Trvl Prio In this sustion, w nlyz th rpool prolm with onstrints on th trvl prios o livris. A trvl prio o livry i is spii y [ti s,t i ], whr ti s is th rlist tim tht livry i n strt, n ti is th ltst tim tht livry i must inish. Th rson to onsir trvl prios is tht in prti, two livris with non-ovrlpping prios nnot rpool togthr, vn though thy hv th sm origin n stintion. To impos this onstrint, or minimum spnning tr T n livry i with trvl prio [ti s,t i ] rom origin vrtx to stintion vrtx i, w n to nsur tht spnning tr T n ommot livry i y stisying: mx k p ts k + T (,i) t i, whr p is pth on T rom to i, hn mx k p tk s is th s- trt tim o lst pssngr, n T (,i) is th trvl tim rom to i in p o T. Th lt-hn si is xpt rrivl tim o livry i oring to this rpool, n th right-hn si is th ltst n tim o livry i, givn y th pssngr. Thus, i th lt-hn si is smllr thn or qul to th right-hn si, it inits tht T n ommot i. Figur 2 givs n xmpl o how to vlit whthr th minimum spnning tr n ommot livry or not. Miniml Spnning Dlivry Rqusts Tr T D1:[,, t s =2, t =7]; D2:[,, t s =2, t =6]; D7:[,, t s =3, t =8]; Trvl Tim T(,)=3; T(,)=1; T(,)=3; T(,)=.5; T(,)=3; T(,)=1; Fig 2. Vlition on Trvl Prio In Figur 2, suppos tht uring th onstrution o s- pnning tr, th nxt minimum g shoul to th spnning tr oring to Prim s lgorithm is n g. Bs on livry rqusts n trvl tim in Figur 2, mx k p tk s = mx{2,2,3} = 3; T (,) = = 4.5; thus, mx k p={ } tk s + T (,)=7.5 t = 8. Thror, th g is s g n n to th spnning tr.

10 Put All Constrints Togthr A prtil pproximtion lgorithm shll onstrut minimum spnning tr tht (i) ommots ll trvl prios o its livris, (ii) hs th iggst siz o sutrs not iggr thn, n (iii) hs numr o sutrs not iggr thn n. Th tils out how to impos th thr onstrints hv n givn in prvious stion. W not tht th orr o imposing onstrints shoul not hng, sin it is sist to in mor txis to ulill rqusts, rltivly sir to in iggr txis to ulill rqusts, n hrr to rquir pssngrs to hng thir shuls. I th onitions onlit with h othr, w n lwys in sil solution y using mor txis. Not tht with highly ivrs trvl prios or smll txi pity, lots o txis will us to stisy livris iniviully, whih is livry shul s on t spnning trs with smll yt mny sutrs. In ontrst, with smll numr o vill txis, lots o livris will pool into on txi n thn ulill on y on, whih is livry shul s on thin spnning trs with ig yt wr sutrs. 6.5 Algorithm or Onlin Rqusts Inst o proviing livry rqusts y or two or th livry strt tim, som pssngrs my ll ispthing ntr hour, or vn svrl minuts, or th livry strt tim to provi onlin rqusts. In ori, w rspons to onlin rqusts y ing thm to n xisting rpool shul, or strt nw rpool shul s on tils o rqusts. Givn n onlin rqust k n livry grph DG out xisting rpool rout shuls t n origin, w n intgrt k to DG y two mthos: (i) As nw l to n xisting sutr o DG: w k to th l o sutr o DG (k s th nw n th only l or this sutr), only i () this nw sutr n ommots th trvl prio o k n () th siz o this nw sutr is not iggr thn th txi pity. This mtho inits tht w pool this nw pssngr with pssngrs o n xisting rpool. (ii) As nw sutr o DG: w k to DG y onstruting nw sutr (k s th only on vrtx in this sutr) rom th origin vrtx o DG. This mtho inits tht w strt nw sprt rpool or this nw pssngr. Onlin Rqust k Existing Crpool Rout Shuls g h i Onlin Algorithm k Option 1 g h i g h i Option 2 g h i Option 3 Option 4 g h i k Fig 21. Onlin Algorithm or Onlin Rqusts In Figur 21, givn th xisting rpool rout shuls n n onlin rqust, ori otins our irnt rpool options or th pssngr to slt y pooling this pssngr to xisting txis (option 1, 2 n 3) or strting nw rpool (option 4). Th ky ritri or pssngrs to slt rpool is th rpool r s w prsnt nxt. k k 7 Th Win-Win Fr Mol Gnrlly, txi r onsists o thr min prts: n initil hrg or vry srvi; surhrg or luggg, witing tim, t; n min hrg s on trvl istn. In our mol, w ous on how to onsir rpool nit into lultions o th min hrg. Suh rpool nit shll shr twn th pssngrs (s group) n th rivr, s wll s mong th pssngrs thmslvs. Th rtionl hin shring th rpool nits with rivrs is tht w hv to nourg rivrs to prtiipt in th non-mntory rpool pplition. W liv tht ngotiting privtly y pssngrs lon n shring th nits only twn pssngrs will svrly hurt th intrsts o rivrs, sin th totl proit or ll rivrs will rs signiintly. 7.1 Crpool Bnit A rpool nit B twn th totl non-rpool r n r pi or rpool istn is givn s ollows: B = i=1 τ i τ, whr is th totl numr o pssngrs in this rpool; τ i is th sprt non-rpool r or pssngr i; τ is th rgulr r or istn qul to th rpool istn (not th rpool r). Thus, th totl non-rpool r o ll pssngrs is givn y τ i, n th rgulr r or th rpool istn is givn y τ, n thir irn is rpool nit B. Givn rpool shul, ll thr prmtrs r otinl, n thus B is lso otinl. For xmpl, Figur 22 shows thr pssngrs (with non-rpool r τ 1 = 17, τ 2 = 32, τ 3 = 45) rpool togthr with istn o rgulr r τ = 52, ling to B = 42. Not tht τ = 52 is rgulr r or istn - qul to th rpool istn, n is not th tul rpool r ll pssngrs will py togthr unr our mol. Origin τ 1 =17 τ 2 =32 τ i =94 τ=52 τ 3 =45 Iniviul Rout Crpool Rout Crpool Bnit B =(τ 1 +τ 2 +τ 3 ) τ = ( ) 52 =42 Fig 22. Crpool Bnit To uil win-win r mol, w n to (i) shr rpool nit twn th rivr n ll pssngrs s group n (ii) shr th nit within th pssngr group. 7.2 Shring % twn Drivr & Pssngr W us ρ to init th shring prntg o th pssngrs (ll pssngrs s group) or givn rpool nit B, n hn 1 ρ is th shring prntg o th rivr. (i) For rpool nit B, ll pssngrs s group py: Totl Fr Pi y Pssngrs = i=1 τ i ρ B, whr τ i is th sum o rgulr rs y ll pssngrs in non-rpool sitution; ρ B is th nit to pssngr group.

11 11 (ii) For rpool nit B, rivr ollts: Totl Fr ollt y Drivrs = τ +(1 ρ) B, whr τ is th r rivr ollts or th rpool istn; (1 ρ) B is th nit or rivr to rpool. Not it is sy to hk tht th totl rpool r pi y pssngrs quls th mount ollt y th rivr in our mol. In rl worl snrios, ρ n ynmilly i s on vrious tors out th supply n rqust rltionship in txi ntwork. In this ppr, w giv n # o oupi txis xmpl to in ρ = # o totl txis in rtin r uring tim winow to ln th rpool inntivs twn th rivr n th pssngr. Thus, or lrg ρ, i.., mor oupi txis, th mor nit will givn to th pssngrs to nourg pssngrs to rpool; or s- mll ρ, i.., mor mpty txis, th mor nit will givn to th rivr to isourg pssngrs to rpool, lning livris mong othr mpty txis. In Figur 22, givn ρ = 1 2, totl rpool r ollt y rivrs is = 73, whih is qul to th totl rpool r or ll pssngrs, i.., = Shring % mong Pssngrs Among th totl rpool nits or ll pssngrs, i.., ρ B, w shll i shring prntg to show rpool nit or prtiulr pssngr i, n thus mol th rpool r or pssngr i. It is givn s ollows. Crpool Fr Pi y Pssngr i = τ i ρ B τ i, τ i whr τ i is th non-rpool r pssngr i hs to py t non-rpool sitution; ρ B τ i τ i is th rpool nit or prtiulr pssngr i. In Figur 22, givn ρ = 1 2, th rpool r pi y pssngr 3 is Currntly, w us τ i τ i to shr th rpool nit mong pssngrs s on thir non-rpool r. In othr wors, w irntit pssngrs y thir stintions to th ommon origin, not th livry orr. But th lst ropp o pssngr typilly will hv rthr stintion thn othr pssngrs (sin our rpool grph is s on th minimum spnning tr), so h/sh will shr mor rpool nit thn othr rlir ropp o pssngrs in our r mol, whih impliitly ompnsts to th pssngrs with longr trvling tim. In mor vn signs, th shring prntgs mong pssngrs n lso irtly i y th priority o srvis,.g., s on th livry orr μ i o pssngr i in rpool, th shring prntg n in s μ i Σμ. 7.4 Crpool Fr Mol Evlution In this sustion, w numrilly vlut our r mol. Bs on thr livry rqusts in Figur 22, Figur 23 shows th impt o irnt shring prntgs ρ on th r tht vry pssngr pi n th r th rivr ollts. It shows whn ρ inrss rom to 1 (initing trn o n unrsuppli txi srvis in th rl worl), th rpool inntiv or th pssngr inrss rom % r svings to 44% r svings, whrs th rpool inntiv or th rivr rss rom 8% mor proit to % mor proit. By usting shring prntg ρ oring to txi supply, our mol n ynmilly ln th rpool inntivs or rivrs n pssngrs. 1 9 Inrs Proits or Drivr 8 Ru Fr or Pssngr # o Oupi Txis Shring Prntg o Pssngr ( ) # o Totl Txis Prntg (%) Prntg (%) Inrs Proits or Drivr Ru Fr or Pssngr Crpool Rout Distn Fig 23. Inntiv Blning Fig 24. Win-Win Mol Givn rqusts with ix non-rpool rs, short rpool istn will inrs th rpool nit (th sm τ i, ut smllr τ), whih rsults in win-win sitution (i.., mor proits or rivrs n lowr rs or pssngrs). Tking th pssngrs with τ 1 = 17 n τ 2 = 32 in Figur 22 s xmpls, physilly, th lowr oun o r pi or th rpool istns shoul τ min = mx{τ 1,τ 2 } = 32. In ition, pssngrs my not s- lt rpool livry whr thy py r togthr mor thn th sum o thir rgulr non-rpool rs. So, logilly, th uppr oun or τ is τ mx = τ 1 + τ 2 = 49. Figur 24 show impts o irnt rpool rout istns (y irnt τ rom τ mx to τ min ) on th svings prntgs o pssngrs n proiting prntgs o rivrs. First, it shows win-win sitution s long s τ < τ mx. Son, th smllr τ, th highr th proit or rivrs, th lowr th r or pssngrs. 8 Evlution o th ori Srvi W hv instll th ustomiz TxiBox in smll portion (98 txis) o th txi ntwork o Chins - ity Shnzhn with popultion o 1 million to tst th untionlity o TxiBox. W quikly lrn tht it tks tim to instll hrwr in urrnt txis, n tht it is muh mor iiult thn w h ntiipt. Although th txi oprtors rqust tht thir rivrs ooprt with th ploymnt, rivrs still wr not nthusisti out instlling vis to txis with no immit nits to thm. During th ploymnt, it ws usul or rivrs to not ppr or to rriv lt n lv rly u to usinss or prsonl mttrs. It ws lso hr to prsu rivrs to mor involv in systm tsting,.g., logging pssngr numrs or vry livry. How to provi n inntiv or thm to involv in systm ploymnt n tsting is ky qustion w n to rss. For lrg sl ploymnt o rpool srvis, through th oprtors rom whih w otin tsts, th ispthing ntr to ollt livry rqusts vi phon ll hs n stlish. But th til rgultion lw out txi rpool r still unr progrss to ing pss, n hop to omplt within this yr. Thus, lrg sl rpool srvi vlution is hr to onut or urrnt sitution. Inst, w prorm lrg sl tr-rivn - vlution o rl worl tst out on wk o GPS rors o 14, 453 txis longing to irnt txi ompnis in Shnzhn. 32

12 Dtsts Th irst tst ontins ily GPS tr t o th txi ntwork, n th son tst is out livris. Th GPS tst ws ollt y ltting h txi uplo its rors 3 sons on vrg to ntrliz s sttion, n th livry tst ws otin y n olin mtho. Figur 25 givs tils out ths tsts. Dsription o Dtsts GPS Dtst Dlivry Dtst Colltion Prio 1/1/12-6/3/12 Colltion Prio 1/1/12-6/3/12 Num o Txis 14,453 Num o Txis 14,453 Dt Siz 45GB Dt Siz 18GB Ror Numr 3,888,, Ror Numr 95,, Formt Formt Plt Mumr Dt n Tim Plt Mumr Bgin & En Tim Sttus Sp Dlivry Distn Dlivry Durtion Dirtion GPS Coorints Dlivry Fr Unlo Distn Fig 25. Dtils o Dtsts In th GPS tst, ky ttriuts r txi sttus n GPS oorints, whih n init whthr txi t rtin lotion is mpty or not. In livry tst, th ky ttriuts r livry istn, urtion n r, whih n sri txi livry vnt. Furthr, th unlo istn inits th istn twn th n lotion o th lst livry n th gin lotion o this livry. By omining ths two tsts, w n ully unrstn th ily oprtionl sitution o th ntir txi ntwork n onut vli vlution. Du to th lrg siz o th tsts, w minly oun two kins o rrors. (i) Lotion Error: GPS oorints show tht txi is o th ro. (ii) Missing Rors: ir mount o GPS rors r missing. Th rrors my rsult rom irnt rsons,.g., GPS vi mluntions, sotwr issus, t. W prorm prprossing to ln tsts to rul out txis with mor thn 1% o missing or rrnt rors. Du to surity n privy rsons, w r llow to slt on wk o tr t rom th hl yr tst s smpl or vlution purposs. 8.2 Evlution Ovrviw To show th tivnss o rpool srvis, w ompr two rpool rout lultion lgorithms, th optiml rpool n th pproximtion lgorithm, init s ori, with th groun truth, whih is th originl GPS trs rom th tst. To show th prormn o ori to rss onlin rqusts, w lso plot th prormn o ori onlin. Th ov lgorithms r vlut s on thr irnt rl worl onstrints. (i) Txi Cpity to show tht how mny livris n pool togthr in singl txi. (ii) Numr o Avill Txis n to show tht how mny txis n us t n origin to ulill ll livry rqusts. (iii) Trvl Prio [ti s,t i ] to show th livry strt tim n tolrt n tim. For trvl prio onstrints, sin w n otin th tul trvl prio out vry livry in th tst, w us tolrt tour tim t (minuts) plus th tul n tim o trip to show this onstrin. For xmpl, or n tul trvl prio [ti s,t i ] in th tst out livry i, with tolrt tour tim t, th trvl prio w us to tst spnning tr is [ti s,t i +t], inst o th tul trvl prio [ts i,t i ]. From th thr prsptivs o soity, pssngrs, n rivrs, w vlut th prormn o th ov lgorithms y svrl mtris. From soity s prsptiv, with th Prntg o Ru Totl Milg, w invstigt how muh milg w n ru y rpooling, givn th ov onstrints n irnt tim lngths twn th tim to provi livry rqusts n tim to strt livris or onlin rqusts. From pssngrs prsptiv, with th Prntg o Ru Fr pi y pssngrs, w show th minimum r thy n py, givn tolrt tour tims. From rivrs prsptiv, with th Prntg o Inrs Proit rn y rivrs, w prsnt th mximum r thy n ollt, givn tolrt tour tims. In ition, w lso invstigt two prtil mtris, i.., (i) th running tim o th optiml lgorithm to show why this optiml lgorithm is not sil in trms o running tim, n (2) th inrs iniviul milg u to rpooling to show possil ngtiv t o rpooling, i.., inrsing th trvl tim or pssngrs. In th vlution, or tsts out iniviul ys o th wk, w irst pross tsts to otins livry rqusts, n thn s on th livry rqusts w lult th rpool rout y irnt lgorithms. By prossing ths rqusts on ily sis, w show th prormn whn pssngrs provi livry rqusts 24 hours rlir thn th livry strt tim, n or rqusts strting t on y n ning t th y tr, w lssiy thm into th y thy strt. For ori onlin, w show its prormn whn pssngrs provi rqusts t 1, 3, 6 n 12 hours rlir thn th livry strt tim. Th rsults r vrg outoms o 7 ys o vlutions. % o Ru Totl Milg (%) Groun Truth ori Crpool Optiml Crpool Txi Cpity Fig 26. Totl Milg vs. % o Ru Totl Milg (%) Groun Truth ori Crpool Optiml Crpool Numr o Avill Txis n Fig 27. Totl Milg vs. n 8.3 Ru Totl Milg In this sustion, w vlut ori vi th prntg o ru totl milg t irnt prmtrs Txi Cpity Figur 26 plots th t o txi pity on th prntg o ru totl milg with tolrt tour tim t = 5 n numr o vill txis n = 16. With th inrs o txi pity, th prntg o ru totl milg or ori rpool n th optiml rpool lso inrss. For xmpl, in ori rpool, th prntg o ru totl milg inrss rom % to 22%, whn txi pity inrss rom 1 to 4. This is us whn txi pity inrss, livry o txi n pool with mor othr livris, n thus it n ru th totl milg. It implis tht rpool untions mor tivly whn txis n rry mor pssngrs.

13 Numr o Avill Txis n Figur 27 plots th t o th irnt numr o vill txis n on th prntg o ru totl milg with tolrt tour tim t = 5 n txi pity = 4. W osrv tht with th inrs o numr o vill txis n, th prntgs o ru totl milg in ori rpool inrs rom 11% to 27%. Ths r som ngtiv prntgs o ru totl milg whn th numr o vill txis n is smll, n similr sitution is lso shown in th prormn o th optiml rpool. This is us tht with wr txis t n origin, w hv to pool mor unrlt livris in this origin into th sm txi, n rop thm o on y on, n it will inrs th totl milg. But whn th numr o vill txis n is lrgr thn 8, w n ru th totl milg y rpools. % o Ru Totl Milg (%) Groun Truth ori Crpool Optiml Crpool Tolrt Dtour Tim t Fig 28. Totl Milg vs. t % o Ru Totl Milg (%) ori Onlin-24 ori Onlin-12 ori Onlin-6 ori Onlin-3 ori Onlin Tolrt Dtour Tim t Fig 29. Milg (Onlin) Trvl Prio [ti s,t i ] Figur 28 plots th t o irnt trvl prios in trms o irnt tolrt tour tim on th prntg o ru totl milg with th numr o vill txis n = 16 n txi pity = 4. In Figur 28, w osrv tht with th inrs o tolrt tour tim t in trms o minuts, th prntgs o ru totl milg in ori rpool inrs rom % to 33%, whil ths o th optiml rpool inrs rom % to 4%, ling to 7% prormn gin. Whil in rpool, with mor tour tim, mor milg n ru y pooling mor livris togthr. Th inrs o t nls lrgr trvl prio, mking mor livris orrlt with h othr in tim Onlin Rqusts In th ov ori rpool, w pross rqusts y ys, so it mns w pool th livry rqusts tht pssngrs provi y 24 hours in vn (nm ori onlin-24). In Figur 29, w vlut th prormn o ori or onlin rqusts situtions whr (i) th hl o th pssngrs provis rqusts in vn o 24 hours, n s on thm, w uil rpool grphs, (ii) th othr hl o th pssngrs provis rqusts in vn o 1, 3, 6 n 12 hours (init s ori onlin-1, t), n w us our onlin lgorithm to optimlly ths onlin rqusts togthr to th xisting rpool grphs vry 1, 3, 6 or 12 hours, ling to nw irnt rpool grphs. W osrv tht ori onlin-24 outprorms ll othrs, initing th rly th pssngrs provi rqusts, th ttr th prormn. This is us with mor rqusts to gin with, w n uil mor tiv spnning tr, ut or onlin rqusts, w only n rqusts s lvs or strt nw rnh t roots o rpool grphs. Running Tim (s) ori Crpool Optiml Crpool Numr o Pssngrs p Fig 3. Tim vs. p % o Inrs Iniviul Milg Groun Truth ori Crpool Optiml Crpool Tolrt Dtour Tim t Fig 31. Milg vs. t Running Tim o Algorithms Figur 3 shows th running tim o th optiml rpool lgorithm n ori rpool lgorithm t irnt rpool pssngr numrs p t singl origin. W osrv tht s th pssngr numr p inrss rom 2 to 18, th running tim or ori rpool lgorithm is ngligil ompr to th running tim or ori rpool lgorithm. This is us tht our rpool rout lultion prolm is NP-hr, n th optiml rpool lgorithm uss Intgr Progrmming to otin th solution, whih ls to longr running tim, n is not prtil or rl worl rpool rout lultion with lrg numr o pssngrs Prntg o Inrs Iniviul Milg In this sustion, w vlut th prormn o ori rpool y th prntg o inrs iniviul milg u to rpools with irnt trvl prios. This inrs iniviul milg lso provis n inition o th tour tim pssngr will tolrt or rpooling with othrs. Not tht lthough th iniviul milg inrss, th r or iniviul pssngrs is tully ru, sin mor pssngrs will shr th r or ommon routs, ling to lrg rpool nit, s show y our Fr Mol in Stion 7. Figur 31 plots th t o irnt trvl prios in trms o t on th prntg o inrs iniviul milg with n = 16 n = 4. With th inrs o t rom 1 to 1, th prntg o inrs iniviul milg in ori rpool inrss rom % to 3%, whil tht o th optiml rpool hs similr trn. In ori n th optiml rpool, with mor tour tim, high milg is to iniviul livris, sin tr rpool, most o th pssngrs will hv nw yt longr rout ompr to th groun truth. % o Ru Fr (%) Groun Truth ori Crpool Tolrt Dtour Tim t Fig 32. Ru Fr % o Inrs Proit (%) Groun Truth ori Crpool Tolrt Dtour Tim t Fig 33. Inrs Proit 8.4 Ru Fr or Pssngrs In this sustion, w vlut th prormn o ori rpool in trms o mximlly ruing th r or iniviul pssngrs, s on th win-win r mol w propos in Stion 7. Bs on th tsts, w hv th groun truth or rgulr rs o iniviul pssngrs, n