COST EXTERNALITIES AND ROAD PRICING EVALUATION: EXPERIMENTAL FINDINGS FROM NETWORK ANALYSIS

Transcription

1 COST EXTERNALITIES AND ROAD PRICING EVALUATION: EXPERIMENTAL FINDINGS FROM NETWORK ANALYSIS André Dnts* John Mo Aln Nicholson Deprtment of Civil Engineering, University of Cnterbury, New Zelnd Abstrct The nlysis of cost externlities in the evlution of rod pricing schemes bsed upon network nlysis in Christchurch (New Zelnd) is presented. Results indicte tht current prctices do not suit the specil chrcteristics of rod pricing nlysis nd evlution. Rod chrging my crete negtive benefits for society nd its min purpose (incresing trnsporttion efficiency) my not reched s well. 1. Introduction The prospects of implementing rod pricing schemes in urbn res hve ttrcted gret del of ttention in recent yers. Reports of the Singpore nd London experiences hve encourged mny trnsporttion plnning gencies to exmine the prospects of rod pricing implementtion (Trnsport for London, 2003). Bsed on the results of these experiences, it hs been rgued tht rod pricing constitutes plnning instrument, which cn be used to rech trnsporttion plnning objectives, becuse it directly ffects rod user behviour. On the other hnd, concerns hve been expressed bout the long-tem impcts nd relibility of rod pricing project evlutions. In the scientific literture, recent rod pricing modelling efforts cn be clssified s theoreticl or prcticl studies. On the theoreticl side, studies such s Yn nd Lm (1996), Yng nd Hung (1998), de Plm et l (2005), Ypermn et l (2005), Meng et l (2005) nd Zhng nd Levinson (2005) hve concentrted in nlysing mrginl cost chrging either for first best rod pricing (generl network) or second nd third best chrging schemes (bridges, tunnels, motorwys, etc) considering hypotheticl rod networks. On the other hnd, vrious prcticl pricing cse studies such s Gupt et l (2005), My nd Milne (2005), Spirov (2005) nd Sumlee et l (2005) hs mostly contemplted vlution nd ssessment of trvel time, trvel cost nd trvel distnce benefits ssocited with chrging schemes by pplying lrge vriety of optimistion techniques (e.g.: genetic lgorithms, gme theory, etc). Although there re severl prcticl motivtions nd considerble scientific progress hs been chieved, the implictions of cost externlities ssocited with trvel demnd behvior modelling hve still to be exmined in detils. Current project evlution prctices estimte the benefits minly from the minimiztion or the reduction of the network-wide trvel time, which is obtined through the estimtion of trffic flows on the network (Meyer nd Miller, 1994). For the evlution of rod pricing schemes, it is ssumed tht the rod network cn be controlled in order to rech the best use of the rod cpcity, through chrging the mrginl cost in order to minimise the rod system trvel time (cost). However, it is essentil to verify whether economic efficiency is reched through the minimiztion of the system trvel time. This specificlly implies tht the trffic ssignment modelling nd forecsting results hve to be exmined for the specil cse of rod pricing schemes. It is lso importnt to expnd the *Contct detils: ndre.dnts@cnterbury.c.nz, Phone: , University of Cnterbury, Privte Bg 4800, Deprtment of Civil Engineering, Christchurch, New Zelnd.

2 nlysis to incorporte the socil impcts generted by rod pricing schemes. The considertion of externl costs tht re not currently prt of the nlysis my ffect the results of the evlution of rod pricing schemes. This pper presents the nlysis of cost externlities in the evlution of rod pricing schemes bsed upon network nlysis. After this brief introduction, we exmine the stte-of-the rt network modelling concepts in order to ssess the impct of cost externlities in rod pricing evlution. An ppliction of these modelling concepts to cse study in Christchurch, is described. Conclusions re summrized in the finl section. 2. Modelling cost externlities impcts in rod pricing evlution This section presents the min modelling definitions, ssumptions nd procedures s well s the formultion of cost functions to nlyse the impcts of cost externlities in the evlution of rod pricing Modelling definitions To conduct the modelling of network users behviour under rod chrging conditions, two distinct principles re enuncited: - All users mke their route choices in order to minimise their perceived trvel time (cost) up to point of equilibrium t which the trvel time (cost) on ll used routes is less thn or equl to tht on the unused routes (i.e. Wrdrop s first principle), which cn be expressed mthemticlly s n optimiztion problem s: subject to h =, p P; q Q L r d pq f = h δ, A r pq r R pq r T e = f L 0 c ( f )dx Where e T = totl network cost t the point of equilibrium e; h = trffic flow from origin p to destintion q on the route r; pqr c ( f ) = trvel cost on the link for flow f d pq = demnd for trips from origin p to destintion q; δ pqr = 1 (if the link is on the route r from p to q) or 0 (otherwise); L= set of links in the network; P= set of origin nodes; Q= set of destintion nodes; nd A= set of links s prt of route; - With control of the rod network, the best use of rod cpcity is reched through chrging the mrginl cost in order to minimise the system totl cost (i.e. Wrdrop s second principle). This cn be expressed mthemticlly s: (1) (1) (1b) f o m T = c ( f )dx L 0 Subject to conditions expressed in equtions 1 nd 1b, where: (2)

3 O T = Totl network cost t the point of system equilibrium O; m c ( f ) = mrginl trvel cost on the link for flow f ; On one hnd, Eqution 1 expresses the current prctice dopted in project evlution, which considers the minimiztion of trvel costs to estimte benefits. On the other hnd, Eqution 2 supports Bell nd Iid s (1997) observtion tht rod pricing is the mechnism for pplying mrginl chrges tht re the difference between mrginl nd verge costs. Furthermore, the economic theory suggests tht the most efficient lloction of resources results when trvellers py the mrginl cost inclusive of the externlities Modelling ssumptions The min ssumption dopted here is tht users cn be chrged in terms of their direct usge of the rod network nd/or in terms of indirect costs such s noise, ir pollution nd ccidents. This ssumption is mbitious in nture nd mybe unrelistic to certin degree, becuse its implementtion would be lmost impossible using the technology nd knowledge currently vilble. Nevertheless, it reltes to relity to the extent tht direct nd indirect impcts occur every time rod user mkes trip, but they re not ctully ccountble for the impcts of their ctions Modelling procedure This comprises four steps. Firstly, relevnt dt bout both supply nd demnd re prepred for nlysis. For simplicity the demnd (i.e. origin-destintion or OD flows) is ssumed to be fixed within the study network. On the supply side, physicl network chrcteristics, such s free flow speeds nd link cpcities, hve to be defined priori. The second step involves the selection of the pproprite cost functions nd ssignment methods, in order to estblish the interction between supply nd demnd. Two descriptive types of cost functions re employed: perceived cost nd socil cost. In trnsporttion prctice nd reserch, perceived cost is often represented by trvel time only, due to its simplicity nd mjor contribution to the totl perceived cost. The Bureu of Public Rods (BPR) trvel time function is the best known nd mostly commonly pplied in trnsporttion studies (Thoms, 1991). On the other hnd, socil cost consists of three spects: efficiency, energy nd environment effects. In the socil cost function, totl trvel time represents the economic efficiency of trnsporttion system nd totl fuel consumption represents energy sustinbility, while ccidents, pollution nd noise costs tke ccount of environmentl sustinbility. Among ssignment methods, user equilibrium (UE) ssignment with the clssic BPR cost function is initilly used to estimte the unregulted trffic pttern. Then rod pricing is ssumed to be implemented throughout the network by chrging users the mrginl cost, which Bell nd Iid (1997) defined s the user optimum (UO), becuse the minimum trvel cost (time) is chieved from the users point of view. From the public perspective, the socil optimum (SO) is estimted by minimising the totl socil cost. The socil equilibrium (SE) ssignment pproch (where users re ssumed to minimise the perceived socil costs of their own trvel) is used merely for comprison purposes. In the fourth step, the ssignment types re estblished on the bsis of the combintions of cost functions nd trffic ssignment methods, s shown in Tble 1. It cn be seen from the lst column of Tble 1 tht ll the ssignments re conducted using the UE pproch, since it hs been mthemticlly proven tht the system optimum ssignment cn be identified through user equilibrium ssignment with mrginl costs (Newell, 1980; Mo, 2004). For

4 exmple, the SO ssignment involves the optiml lloction of trffic bsed on the socil cost, nd cn be ccomplished by the UE ssignment method with mrginl socil costs. Bsed on the UO trffic ssignment, the implementtion of rod pricing scheme is simulted. For ll ssignment types (UE, UO, SO nd SE), the totl trvel time vlue nd socil cost re clculted nd compred. The totl trvel time vlues indicte whether the rod pricing is efficient in monetry terms, while the socil cost is used to exmine whether it cretes benefits to the society. This will lso be used to verify the impct of the cost externlities in the ssessment of rod pricing schemes. Tble 1 Assignment definitions Assignment type Description Accomplished by UE with UE minimising users perceived costs (time) perceived costs UO minimising totl user trvel cost (time) mrginl costs SE minimising users socil costs socil costs SO minimising totl socil cost mrginl socil costs 2.4. Formultion of cost functions User costs differ from the user perceived costs, which re often represented by time cost functions or generlised cost function. Insted the economic vlues of time nd fuel consumption cn be clculted dynmiclly ccording to verge trvel speeds on individul links. The list of externl costs, however, is lmost endless. For instnce there re twelve components in environmentl ssessment recommended by HMSO (1993) in the UK, nmely ir qulity, culturl heritge, disruption due to construction, ecology nd nture conservtion, lndscpe effects, vehicle trvellers, wter qulity nd dringe, geology nd soils, nd policy nd plns. Since it is impossible to consider them ll, some mjor components should be tken into ccount, which re costs of ccidents; rod construction, mintennce nd services; nd environmentl externlities such s ir pollution nd noise (Smll, 1992). Tking into considertion Trnsfund NZ s Project Evlution Mnul (PEM) (Trnsfund 2002), the following sub-sections describe the cost functions for user s perceived cost, socil cost nd mrginl costs Perceived cost The clssic BPR cost function is shown in Eqution 1, where the free flow time is t 0, nd the link flow is f nd the link cpcity is C. The prmeters α nd β re estimted to fit the reltionship to the observed trffic flow chrcteristics in the bsence of rod pricing. β f t = t 0 1+ α (3) C

5 Socil cost Socil cost (SC) is the summtion of the trvel time cost (TTC), operting cost (OC), ccident cost (AC), ir pollution cost (APC) nd noise cost (NC) in monetry terms (NZ$), s represented in Eqution 4. SC = TTC + OC + AC + APC + NC (4) The trvel time cost is defined by Trnsfund (2002) s the bse vlue of trvel time in uncongested conditions ($16.27/vehicle/hour) plus the dditionl vlue of trvel time due to congestion ($3.95/vehicle/hour). Therefore, fter pplying these two vlues to Eqution 3, the trvel time cost of vehicle on link is t 0 f TTC = α 60 C As for the vehicle operting cost on link, Trnsfund s Mnul (2002) recommends the ppliction of Eqution [ln() v ] [ ln( v) ] [ ln( v) ] + OC = / 100L (6) 2 exp( [ vc] [ vc] ) where L link length (km); v trvel speed (km/hour) on link; nd f vc minimum vlue in the rnge 1.0; C. For the third component (ccident cost), the verge cost for vehicles trvelling on link is estimted using the following eqution AC = 0.03 f L (7) The ir pollution cost is the most imprecise one mong the socil costs, with Trnsfund (2002) suggesting tht light vehicle trvelling t 40 km/hour hs n ir pollution cost of 1 cent per km. It is not unresonble to ssume the verge speed is 40 km/hour in the pek hour given tht trffic in the network is slightly congested. Hence, the ir pollution cost of vehicle on link is clculted s follows. APC = l (8) where l is the length of the link. As for the lst component of socil cost, the verge noise cost per vehicle per hour on link is clculted s shown in Eqution 9, ssuming tht the mbient noise level is 55 db networkwide (HMSO 1975) nd the monetry vlue for link is determined ccording to Trnsfund (2002). 500 NC = log10 QT + 33log10 v NH / f (9) v where NH is the number of households long the link; nd Q T is the dily trffic volume (AADT, vehicles per 18 hours dy) Mrginl costs On the bsis of Eqution 3, the mrginl cost is s follows. β (5)

6 t = t0 1+ α( β + 1) f C β (10) The mrginl socil cost cn be derived from the socil cost nd the derivtion is not presented here due to the limited spce (see Mo, 2004 for detils). 3. Cse study This section describes the ppliction of the concepts presented in section 2 to conduct network nlysis experiments tht im to ssess the impct of cost externlities in the evlution of rod pricing scheme in Christchurch, New Zelnd. The following sub-sections describe the study re, the dtbse, modelling results nd nlysis. 3.1 Description of the study re nd the dtbse The study re comprises the Greter Christchurch Metropolitn re, which gthers n pproximtely 350 thousnd inhbitnts of 130,500 households with pproximtely 200,000 crs. The re is covered by n extensive network, which includes min rteril rods such s the Min North Rod, Min South Rod, Riccrton Rod, Blenheim Rod, Colombo Street, QE II Drive, Southern Motorwy nd Northern Motorwy. Figure 1 shows the study re nd its min urbn elements. Previous plnning nd modelling ctivities (e.g. Christchurch Trnsporttion Study - CTS) hve divided the study re into 559 zones, including 10 externl zones, nd reserving 81 zones for the future usge. Figures 2 nd 3 show, respectively, the zones nd the network used in this study. The network dt ws obtined from the Trffic Model (1996) developed jointly by the Christchurch City Council, Environment Cnterbury nd Trnsit New Zelnd. nd consists of bsiclly residentil zones. The rod network dtbse (rod lengths, cpcity, trvel time, etc) ws obtined from the Christchurch City Council nd ws geo-referenced in Geogrphicl Informtion System (GIS) ccording to the New Zelnd Mp Grid. This study considered n Origin-Destintion mtrix comprising 471 trffic zones, representing totl demnd of trips in the morning pek (8-9 AM).

7 Figure 1 Min elements of the study re Figure 2 Trffic zones

8 Figure 3 Rod Network 3.2. Modelling results The cost functions (Equtions 4-10) were implemented in Trnsporttion Plnning pckge (TrnsCAD) in order to conduct the four ssignments (UE, UO, SE nd SO) s defined in Tble 1. Initilly, the UE ssignment with the BPR cost function (Eqution 3) ws used to reproduce the current trffic flow pttern. After 8 itertions considering convergence rte of 0.01, constntsα nd β in the BPR function were clibrted (Eqution 11). For reltive gp of 0.01, equilibrium ws reched for n observed Root Men Squre Error (RMSE, defined in eqution 12) of trips with mximum flow chnge of trips. The totl number of vehicle*hours ws nd the totl number of vehicle*km ws The ssigned volume/cpcity (VOC) rtios re shown in Figure f t = t C (11) The four ssignments (UE, UO, SE nd SO) were crried out for the current network configurtion, nd the totl trvel times, trvel time costs nd socil costs re listed in Tble 2 nd grphiclly represented in Figure 5. e ( f f ) 2 (12) RMSE = n where f e estimted trffic flow; nd n number of links with observed trffic flow f;

9 Figure 4 Reproduced VOC Tble 2 The results of the four ssignments Assignment UE UO SE SO Totl trvel time (veh-min) 692, , , ,850 (% increse from UE) Totl Socil Cost (NZ$) (% increse from UE) (NA) 305,646 (NA) (-3.2) 304,351 (-0.4) (6.2) 307,080 (0.5) (-1.0) 302,994 (-0.9) NZ $ (Thousnds) UE UO SE SO Trf f ic Assignment () 300 UE UO SE SO Trffic Assignment (b) Figure 5 Trffic Assignment results: () Network Trvel Time; (b) Network Socil Cost

10 It cn be seen tht system-wide rod pricing (UO) results in the minimum totl trvel time (692,113 vehicles-minutes). Its benefit results from the trvel time sving of 22,131veh-min when compred with the ssumed current trvel pttern (UE). The SE ssignment gives the lrgest trvel time (pproximtely 6.2% more thn the UE result), which is mostly due to the incorportion of externl fctors (ccident, noise nd pollution) into the cost functions The SO ssignment does decrese the totl trvel time but not s much s for the UO ssignment. As for the totl socil cost, the SO ssignment provides the lowest socil cost for the system (NZ$302,994). The highest vlue occurs for the SE ssignment, which is pproximtely 0.5% more thn the UE results. Also interesting to note the composition of the socil costs; this is pproximtely the sme proportion of costs for ll four types of ssignments (trvel time cost=56%; vehicle opertionl cost=31%; ccidents costs=9%; ir pollution costs=2%; noise costs=2%) 3.3. Anlysis of the results The results described in section 3.2 indicte tht there is cler reltionship between network performnce mesures (totl trvel time cost nd totl socil cost) nd the four types of trffic ssignment (UE, UO, SE nd SO) reflecting different rod pricing schemes. For ech network performnce mesure, the results re different for ech trffic ssignment (UE, UO, SO nd SE). For instnce, the network performnce results considering trvel time show tht the performnce will be best with the introduction of rod pricing scheme (UO ssignment). Furthermore, using the totl socil cost s the performnce mesure leds to the conclusion tht rod pricing scheme (UO), which excludes socil costs, would not be the best possible policy vilble Consequently, it ppers tht totlly different decisions will be reched depending on which trffic ssignment nd performnce mesures re employed. This is prticulrly interesting, becuse the outcomes present gret del of contrdiction mong themselves. Current prctices of evlution, which convert trvel time costs fter trffic ssignment, my led to decision tht t the sme time disregrd the economic fesibility nd the socil impcts. As shown in Figure 6, the contrdiction between the selection of the totl trvel time nd totl socil costs is obvious, becuse if one tkes the totl trvel time xis s the reference for comprison, the User Optimum (UO) is clerly the best option. However, if the totl socil cost xis is tken, then UO is ctully fr from the best option (SO). In contrst, the Socil Optimum (SO) minimizes the dverse impcts, becuse it simultneously optimizes the trffic pttern while ccounting for the externl costs. On the other hnd, the Socil Equilibrium (SE) option is extremely inefficient, becuse it llows rod users to mke their route choice decisions. 308 Totl Socil Cost ($) Thousnds Totl Trvel Time (veh-mins) Thousnds UE UO SE SO Figure 6 Trffic Assignment results: Network Trvel Time versus Network Socil Cost

11 4. Conclusions This pper ttempts to contribute to the scientific nd technicl discussion regrding the nlysis nd evlution of rod pricing schemes. Among the mny issues relted to the implementtion of rod pricing schemes tht hve been discussed, the nlysis nd evlution hs criticl role in mesuring, quntifying nd compring the benefits, costs nd impcts tht my be creted from the implementtion of rod pricing. In this pper, we discussed the relibility of current prctices for rod pricing nlysis evlution, bsed on method tht provides comprtive nlysis of the benefits nd costs ssocited with interventionl nd non-interventionl policies, s well s the incorportion of brod socil impcts. It ws found tht the ppliction of current prctices does not suit the specil chrcteristics of rod pricing nlysis nd evlution. Current prctices concentrte on the minimiztion of trvel time, which is contrdictory to the nture of rod pricing schemes, which re hevily bsed on chrging users the mrginl trvel costs. The min consequence of this ssessment of current prctices is tht technicl decisions my be mde bsed on erroneous grounds. In the cse study, the rod pricing benefits climed by efficiently llocting the resources (rod cpcity) re prtilly predicted nd some effects re not included. It ws found tht the implementtion of rod pricing minimising totl trvel time (UO) my mke society worse off by imposing greter totl socil cost thn the noninterventionl trffic (UE). This mens tht form of rod chrging which excludes socil costs my crete negtive socil benefits for society. There is dilemm in tht these ssignments (the UE, UO nd SO ssignments) hve their own dvntges nd disdvntges. The UE hs ner-optiml socil cost nd lrgest totl trvel time. The UO hs minimum totl trvel time but high level of socil cost, whilst the SO minimises the socil cost nd cuses more totl trvel time thn the UO. Nevertheless, the SO is bsed on the monetry evlution of ll mjor costs nd if this evlution is sound, it delivers the best nswer to mximising economic benefits nd minimising the dverse impcts of trnsporttion. The SO clls for socil rod pricing minimising the totl socil cost, rther thn rod pricing to minimise the trvel time. As for future studies, efforts should be mde to llow for elstic demnd. If the cost of trvel is to be incresed, the im would not be to simply chnge the distribution of trffic on network, but to reduce the mount of trvel. Acknowledgements The uthors wnt to express their grtitude to the trnsporttion plnning stff of the Christchurch City Council for the permission to use their dtbse in this reserch. We lso wnt to thnk Mr. Zrko Andjic (Min Rods Austrli) for his vluble help on dt processing nd modelling nd his comments tht contributed to this reserch. Finlly, we would like to thnk Mr. Jim Cox of Gbites Porter, Christchurch, for his vluble support in the modelling efforts. References Bell, M. G. H. nd Iid Y. (1997) Trnsporttion Network Anlysis, John Wiley & Sons, London, UK. Benedek C. M. nd Rilett L. R. (1998) Equitble Trffic Assignment with Environmentl Cost Functions, Journl of Trnsporttion Engineering, Vol. 124, No. 1, Jnury/Februry 1998 Button, K. J. nd Verhoef, E. T., editors (1998) Rod Pricing, Trffic Congestion nd the Environment, Edwrd Elgr; Norhmpton, MA. de Plm et l (2005) A comprison of the second-best nd third-best tolling schemes on rod network; 84 th Trnsporttion Reserch Bord Annul meeting, Wshington, DC, USA. Florin M. nd Hern D. (1999) Network Equilibrium nd Pricing, In Rndolph W. Hll, editor (1999) Hndbook of Trnsporttion Science, Kluwer Acdemic Publishers

12 Gupt, S., Klmnje, S., Kochelmn, K. (2005) Rod pricing simultion: trffic, lnd use nd welfre impcts for Austin, Texs; 84 th Trnsporttion Reserch Bord Annul meeting, Wshington, DC, USA. Mo, S (2004) Bress Prdox in Relity Cuse, Consequence nd Resolution, A Project Report, School of Civil Engineering, University of Cnterbury, New Zelnd My A. D. nd Milne D. S. (2000) Effects of Alterntive Rod Pricing System on Network Performnce, Trnsporttion Reserch prt A 34, pp Myeres, I., Ochelen S. & Proost, S (1996) The Mrginl Externl Costs of Urbn Trnsport, Trnspn Res. D, Vol. 1, No. 2, pp Meng, Q., Xu, W., Yng, H. (2005) A tril-nd-error procedure for implementing rod pricing scheme; 84 th Trnsporttion Reserch Bord Annul meeting, Wshington, DC, USA. Meyer nd Miller (1984). Urbn Trnsporttion Plnning: A Decision-Oriented Approch. McGrw-Hill, New York, USA. Ngurney, A. (2000) Sustinble Trnsporttion Networks, Edwrd Elgr, Msschusetts, USA. Nsh nd Snsom (2001) Pricing Europen Systems, Journl of Trnsport Economics nd Policy, Vol. 35, Prt 3 Newell, G. F. (1980) Trffic Flow on Trnsporttion Networks, MIT Press, Msschusetts, USA. Ortuzr, J. de D. nd Willumsen, L. G. (1995) Modelling Trnsport (2 nd Ed.), John Wiley & Sons, New York, USA Spirov, E., Gilliinghm, K. Hrrington, W., Nelson, P., Lipmn, A. (2005) Choosing pricing policy cordon tolls versus link-bsed tolls; 84 th Trnsporttion Reserch Bord Annul meeting, Wshington, DC, USA. Sheffi, Y. (1985) Urbn Trnsporttion Networks, Prentice-Hll, New Jersey, USA. Smll, K. A. (1992) Urbn Trnsporttion Economics, Hrwood cdemic publishers, Luxembourg. Smll, K. A. nd Ibnez J. A. G. (1998) Rod Pricing for Congestion mngement: the Trnsit from Theory to Policy, In Button, K. J. nd Verhoef, E. T., editors (1998) Rod Pricing, Trffic Congestion nd the Environment, Edwrd Elgr. Norhmpton, MA. Stenmn O. J. nd Sterner T. (1998) Wht is the scope for environmentl rod pricing; In Button, K. J. nd Verhoef, E. T., editors (1998) Rod Pricing, Trffic Congestion nd the Environment, Edwrd Elgr Norhmpton, MA. Sumlee,A. My, A., Shepherd, S. (2005) Specifying optiml rod pricing cordons for different objectives; 84 th Trnsporttion Reserch Bord Annul meeting, Wshington, DC, USA. Thoms, R. (1991) Trffic Assignment Techniques, Avebury Technicl, Aldershot, Englnd. Trnsfund New Zelnd (2002) Trnsfund NZ s Project Evlution Mnul, Amendment No. 6, 1 September 2002, New Zelnd. Trnsport for London (2003). Congestion Chrging Six Months On. Trnsport for London, London, UK. Yn, H. nd Lm, W. (1996) Optiml rod tolls under conditions of queueing nd congestion; Trnsporttion Reserch A, Vol. 30, No. 5, pp Yng, H. nd Hung,H. (1998) Principle of mrginl-cost pricing: how does it work in generl rod network?; Trnsporttion Reserch A, Vol 32, No. 1, pp Ypermn, I, Logghe, S., Immers, B. (2005) Strictly Preto-improving congestion pricing in multi-destintion network with Queue splillover; 84 th Trnsporttion Reserch Bord Annul meeting, Wshington, DC, USA. Zhng, L. nd Levinson, D. (2005) Rod princing with Autonomous links; 84 th Trnsporttion Reserch Bord Annul meeting, Wshington, DC, USA.