compensation earmarked to LPT service providers operating under formalagreements, as well as criteria of public funds allocation to local authorities.The overall Italian regulation setting encourages the local authorities tomore efficient use of public funds and aims to a fairer distribution. Thus, asalready pointed out, substantial savings in public funds could be obtainedby reprogramming the existing services in favor of less expensive andmore efficient transport mode alternatives, according to the distinct contextsituations and without altering passengers' mobility. To this end, thestandard cost models could naturally represent a tool for a meaningful com-parison between modes of transport, mitigating the problem of limitedcomparability in cost structures. Following this idea, we propose a method-ology combining service dimensioning (according to techniques based ondemand behavior), production costs models (making use of the standardcost models adopted by the MIT) and externalities evaluation, creating aneffective framework for a social-economic cost comparison tool.In particular, we focus on the bus versus rail services comparison, whichdue to its potentiality in practical application. The rail services offer highercapacity, reduced time of journey and increased travel comfort; the bus ser-vices benefit of a greater degree offlexibility, usually allowing higher fre-quency and a more widespread network. Therefore, according to thecharacteristics of the demand and the existing tracks, each of the alternativemodes would result in offering a different overall performance. Indeed, inseveral Italian local railway routes, the current level of demand could jus-tify a switch from rail to bus service when the latter is proved to be lessexpensive in providing comparable services. These cases usually concernisolated or terminating railroad tracks,4where demand collapsed in thelast decades. In general, even well-established transport systems shouldbe reviewed, if interested by enduring structural changes such as, for exam-ple, those due to macroscopic changes in the socio-economic environment.Before proceeding further, we clarify the conditions under which ouranalysis is performed.Theinvestment costsfor rail and road infrastructures are assumed to besunk. This assumption avoids a high penalization over the rail service alter-native (which requires an expensive dedicated infrastructure) and makesour tool especially suitable for transport system re-planning.Also, we considerexogenous demand, namely, the demand level is givenindependently of the transport mode. The bus and rail services can varylargely on quality (e.g. different frequencies, load factor, comfort) and beperceived by the users as imperfect substitutes. The effects potentially pro-duced by the difference in the level of service are modal split between thetwo activated modes and/or level of diversion of users from/to privatemodes (changes of daily demand level for public transport). These effectsare usually taken into account in the transport planning analysis by includ-ing the user costs, that allow for the adoption of an endogenous demand.The tool proposed by the present paper focuses on a type of demand thatcould be considered captive on the path. The element of modal split insidepublic transport offer is not considered, since the transport modes arecompared only as alternative solutions. Furthermore, the tool is dedicatedto the optimization of existing services to respond to structural changeson the demand level. Based on these points of discussion, the use of anendogenous demand is considered not suitable and beyond the scope ofthe paper. Nevertheless, since the most important difference perceived byusers is usually the difference in travel time, it was decided to include inthe social-economic cost computation themonetary value of timefaced bypassengers (as a proxy for theusers' cost). Finally, the possible presence ofdiversion from/to private mode is, instead, assumed to have a not signifi-cant effect on our results, mainly due to the“captive”nature of the demand.This assumption is a limitation. The diversion to private modes has nor-mally impacts on public transports profitability (e.g. reducing the averageload factor) and on the externalities (travels by car are usually more pollut-ing, induce congestion problems in road infrastructure and are associatedwith a higher risk for accidents). Furtherresearch could cover these aspects,extending the range of application for our tool.The present paper is contributing to the literature in transport modes ef-ficiency comparison, that to the best of our knowledge is still scarce to thisday. Especially in the Italian context, a tool to support decision/policymakers in choosing which of two alternative modes is the most efficientcould be useful in transport system optimization. As already underlined,the paper considers for the comparison a broad perimeter of costs, includ-ing in the analysis the externalities produced in transport modes production(in particular, air quality, climate change, well-to-tank, congestion, acci-dents, noise, habitat damage), that are usually overlooked (Catalanoet al., 2019). Furthermore, an important element of novelty in our paperis specifically the inclusion of the standard cost models in the methodology.The standard cost models have been until now used exclusively as tools forthe quantification of subsidies to transport operator; to the best of ourknowledge, this will be thefirst attempt to utilize the standard cost modelsaspart of a tool for transport system planning. In fact,the coordinated use ofbus standard cost model and rail standard cost model, allows a more robusttransport mode comparison, since both the cost estimation methodologiesfollow the same structure.The rest of the paper is organized as follows.Section 2displays the liter-ature review on the topic.Section 3presents the methodology to performthe transport modes comparison.Section 4describes the application ofthe methodology to a real case study (regarding an Italian region), toshow its practical potential; whileSection 5contains the concluding re-marks of our analysis.2. Literature reviewA vast literature explores the cost structure of LPT companies, for criti-cal reviewsDaraio et al. (2016)andCatalano et al. (2019)can be consultedfor, respectively, bus LPT services and rail LPT services.In the following we provide a short review of the literature related toour paper considering the previous works that analyze only one mode(bus or rail services);finally, we consider the existing literature that com-pares the two modes under the efficiency viewpoint.2.1. Bus servicesThe literature that analyzes the cost efficiency of bus services has fo-cused mainly on three aspects, thefirst (also from a chronological perspec-tive) refers to costs measures and input-output relations; the second widelydebated topic refers to which output is the most appropriate when consid-ering cost efficiency; the third issue refers to the existence of scaleeconomies5and scope economies.62.1.1. Costs measures and input-output relationsAtfirst, papers studying LPT costs (e.g., among othersKoshal, 1970;Miller, 1970;Pucher et al., 1983) focused on input-output relations; then,the literature has mainly focused on estimating variable and total costs(e.g., among others,Obeng and Sakano, 2002;Fraquelli et al., 2004;Ottoz and Di Giacomo, 2012).2.1.2. Output measuresWhen analyzing the efficiency of LPT services, an appropriate measureof output is crucial. Usually, researchers adopt one of the two following ap-proaches: reference tosupply-side indicators, such as vehicle-kilometers orseat-kilometers, or reference todemand-oriented indicators, such aspassenger-trips or passenger-kilometers.The academic debate on which approach is more relevant has not yetbrought to an agreement (seeBerechman and Giuliano, 1985;De Borger4An isolated railroad branch is a direct connection origin-destination which is completelydisconnected by other railroad branches, while a terminating railroad truck is characterizedby one head station close to or interconnected with a station of another railroad branch.5Namely an observed reduction in the average cost function due to an increase in output.6Namely an increase in cost efficiency due to the variety of offered services rather than anincrease in output of one service.A. Avenali et al.Transportation Research Interdisciplinary Perspectives 7 (2020) 1002002
and Kerstens, 2000;De Borger et al., 2002). However, when the analysis fo-cuses on costs as in this paper, supply-side output measures are assumed tobe the bestfitting.2.1.3. Scale and scope economiesA third widely discussed subject that is central in our paper, relates tothe presence of scale economies in transport services production. The liter-ature concerning this topic also appears to have not reached yet a univocalposition.On one side,Cambini et al. (2007)identified economies of networkdensity7and scale economies in studying LTP bus services, and especiallyfor Italian urban context. Intercity LPT services shreds of evidence in sup-port of both scale and scope economies were identified (Fraquelli et al.,2004).Filippini and Prioni (2003)find economies of scale comparing Ital-ian and Swiss companies.Conversely,Bhattacharyya et al. (1995),Levaggi (1994),Matas andRaymond (1998),Jha and Singh (2001)andBoitani etal. (2013)allfind ev-idence of scale diseconomies.Finally,Fraquelli et al. (2001)find that the average cost per seat-kilometers is U-shaped; similarly, alsoAvenali et al. (2016)find that theunit cost per vehicle-kilometers is U-shaped.2.2. Rail servicesConsidering specifically the rail LPT services, researchers atfirst aimedat describing the industry and estimating the cost functions (Borts, 1960;Griliches, 1972;Meyer and Morton, 1975;Brown et al., 1979).Other studies have focused on productivity efficiency (Caves et al.,1980;Dodgson, 1993;McGeehan, 1993;Loizides and Giahalis, 1995;Hensher et al., 1995). Finally, also methodological aspects in estimatingthe cost functions have been analyzed (Hasenkamp, 1976;Braeutigamet al., 1982;De Borger, 1991, 1992). Gradually, the focus moved to thestudy of scale economies, density economies (Harris, 1977;Keeler, 1974;Caves et al., 1980, 1981, 1985;Braeutigam et al., 1984;Preston andNash, 1993;Savage, 1997), and scope economies (Kim, 1987). It is worthnoting that many papers jointly evaluated passenger and cargo servicesand only relatively more recent papers have focused on passenger serviceonly (Viton, 1981;Marumo, 1984;Miyajima and Lee, 1984;Filippini andMaggi, 1992, 1993;Mizutani, 1994;Nakamura, 1994;Savage, 1997). Inthe last decade, some studies have estimated the costs of passenger servicesby analyzing cost data provided different operators in some European coun-tries, South Korea and Japan (Cantos Sànchez, 2000;Cantos Sánchez, 2001;Christopoulos et al., 2000, 2001;Cantos Sànchez and Villarroya, 2000;Cantos and Maudos, 2001;Loizides and Tsionas, 2002;Cowie, 2002;Mizutani, 2004;Mizutani et al., 2009;Daniel et al., 2010;Avenali et al.,2020). These studies mainly target the causes of inefficiencies and thecost structure offirms to identify the proper configuration of a network,or else they enquire to what extent the cost model and different type of reg-ulatory contracts affect company performance.2.3. Intermodal comparisonsDespite the vast amount of papers that analyze the cost of a single mode,the literature that compares costs and benefits of alternative modes isscarce. Notably,Tirachini et al. (2010)propose a model to compare thetotal performance, on a radial urban network, of light rail, heavy rail andBRT (bus rapid transit), with the aim of minimizing the total cost associatedwith public transport service provision by taking into account the users(demand) preferences (e.g. access time, waiting time, in-vehicle time).Liand Preston (2015)develop a spreadsheet cost model which simulatespublic transport modes (twelve different urban alternatives) operated ona 12-km route on UK context, considering the total social costs generatedby each alternative and considering the effects produced by an endogenousdemand.Grimaldi et al. (2014)applied the modes comparison to the Italiancontext, proposing a bottom-up model that analyzes the economic costs andbenefits associated with an upgrade from an existing urban bus service to alight rail transit system. Somehow, the purpose of our paper is the oppositesince we assume that the infrastructures costs (railways and motorways)are sunk and investigate on which mode is the most efficient under thesecircumstances.3. MethodologyFig. 1summarizes our methodology framework to determine which ofthe bus or rail alternative is the most efficient to be activated on a specificscenario. Thefirst step is the demand behavior analysis. It is assumed to an-alyze the transport service on a single binary origin-destination path. Thedemand is considered exogenous: externallyfixed and not influenced bytransport mode type and/or level of service. The transport mode servicesare required to totally cover the demand (i.e. unsatisfied demand is notacceptable). From the policy maker point of view, in applying our method-ology, the demand behavior would be an input observed in a specificscenario. To different demand behavior would be associated differentcosts and results from thefinal comparison.The demand is the input for the dimensioning of the service process; aminimum level of transport capacity needs to be activated to cover all thepassengers' requests. Considering the distribution of the demand alongthe day (e.g. peak/off-peak percentages, the percentages on the two direc-tions–“AtoB”and“BtoA”are important drivers), andfixing the load fac-tor to a realistic average value,8the minimum required frequency and theefficientfleet's size are calculated, for each mode separately (e.g. themodes differ for vehicle's capacity and ride's travel time). In the literaturethe service dimensioning can be carried out through a theoretical approach(e.g. applying heuristic methodologies or vehicles routing andfleet size al-gorithms, while no formal optimization instruments are available;Nilsson,2015), or expert based approach.The calculated frequencies andfleet sizes are used as input for the costs'estimation. The overall social cost associated with each transport mode'sservice is then computed summing: standard costs for production, costsfor the infrastructure usage, costs of externalities and proxy for the users'cost component (based onvalue of travel time).Table 1displays the perime-ter of costs, specifying for each one the unit of measure and the data sourcesused.The comparison is performed by considering the resulting overall socialcost values. The transport mode associated with the lower overall cost isthen considered the most efficient to be activated in the consideredscenario.The considered costs categories can mainly be divided between: coststhat increase with increment in traffic (unit of measure:vehicles-km; usedfor production and infrastructure costs), and costs which increase alsowith increment in load factor, even if the level of generated vehicles trafficdoes not change (unit of measure:passenger-km; used for externalities andusers' cost component).The standard costs for production, manly composed by costs associatedto operation,fleet maintenance, administration and capital, also includethe depreciation of the rolling stock. The cost of the net invested capital isconsidered only regarding the investment in transport operation activities,while the investments in infrastructure construction are assumed as sunk.The only costs associated with infrastructure included in our analysis areusage costs (i.e. payments to access to the infrastructure, infrastructuremaintenance, operating infrastructure costs for lines and stations). Finally,the externalities impacts are considered, including the dimensions of airpollution, accidents, congestion, noise, climate change, well-to-tank andhabitat damage. Also other categories of externalities are usually associatedwithtransport services operation (suchaslandscape damage,soil and water7Economies of network density exist when the total cost to transport passengers decreasesby increasing the usage of the existing rolling stock and infrastructure within a definednetwork.8For example, a typical value for load factor associated with rail services in the Italian con-text is 35%, for economically sustainable scenarios.A. Avenali et al.Transportation Research Interdisciplinary Perspectives 7 (2020) 1002003
pollution), nevertheless, the effect of these adjunctive external impacts arestrongly related with the specific context of the application, and requirespecific data that are usually lacking. Since their inclusion would havenot be associated with significant changes in our results, we decided to ex-clude them from our analysis. We also excluded from the perimeter of coststhe effects generated onland useby transport systems. Indeed, the stationsand stops position, the path itself and the demand level generated by thetransport services have a clear influence on urban planning, householdvalue, commercial activities position and so on. The inclusion of thesetypes of effects requires a careful examination of the area interested bythe transport service and thus beyond the scope of the present work. Never-theless, it is an interesting element that could be considered in future worksas an adjunctive feature for the developed tool.In the next subsections, we provide details on the methodologies anddata sources used in estimating each cost category.3.1. Standard cost modelsThe standard cost for transport production is thefirst cost category in-cluded in the analysis, it encompasses:(i) operation and maintenance (concerning thefleet's vehicles only);(ii) administrative costs and other overheads; and(iii) the pre-tax cost of capital.The estimation is obtained applying the cost models proposed inAvenali et al. (2016)andAvenali et al. (2020).Avenali et al. (2016)esti-matean average-efficient standard costof local bus transport services if pro-vided by Italian operators, given a specific level of demand. Similarly,Avenali et al. (2020)define a standard cost model to identify an average-efficient standard cost for regional rail public transport services production,under the same conditions.Both the standard cost models do not include the costs for investmentsin infrastructure construction.Operation and maintenance costsincludelabor costs, direct and indirectcosts of spare parts, materials and goods, contracted services to third parties(e.g. outsourced maintenance), depreciation offixed assets and the relatedcapitalized maintenance. Overheads and general administrative costsmainly concern overall management, economic planning and controlcosts, business consulting costs and information systems costs.Finally, the cost of capital represents the minimum money amount to re-ward the investments in rolling stock for the bus system, and the invest-ments in rolling stock and maintenance facilities for the railway system.The standard costmodels have been developed through regression anal-ysis by using certified economic data and real transport services informa-tion collected from Italian private and public-owned LPT operators. Thedata were gathered through questionnaires carried out by the NationalObservatory9on Local Public Transport Policies (from here on the Observa-tory) and covers overall>500 million of bus-kilometers (about 30% of theoverall offer), and>220 million of train-kilometers (above 90% of the pro-duction of regional rail public transport services). The variable consideredin the standard cost models evaluation represents both elements partiallyunder providers' control (e.g. thefleet composition and quality) and ele-ments endogenous to the scenario, on which instead the provider is mostlyjust subjected (e.g. the commercial speed).3.1.1. Bus service standard cost modelIn this section, we describe the standard cost model for local bus ser-vices production.The model identifies the standard cost associated with the production ofa single unit of bus transport and it was proposed byAvenali et al. (2016).For the bus services, the unit of transport considered as reference is the bus-kilometer (from here on bkm). The variables considered in the standardmodel are the following:CSb(km/h):Commercial Speed for buses, a qualitative (hedonic) charac-teristic of the service, which can be barely controlled by the operator.9The Observatory is in charge of building a complete, certified and constantly updated da-tabase to monitor of the Italian local public transport industry.Fig. 1.The methodologyflowchart.A. Avenali et al.Transportation Research Interdisciplinary Perspectives 7 (2020) 1002004
BKM(mln of bkm):million of Bus-Kilometers, the overall transport capac-ity offered by the operator. In our specificcase,BKMwould indicate theoverall bkm offered on the binary path A to B and B to A on a yearlybase.Abkm(€/bkm):degree offleet renewal. This variable is defined as theratio between a monetary value of the rolling stock (busfleet) and theoffered bus-kilometers (BKM). If the rolling stock is completely ownedby the operator, the monetary value corresponds to the sum of all thedepreciations of the owned vehicles (over an assumed lifetime of15 years), including their capitalized maintenance. This variable iden-tifies a qualitative characteristic, which can be controlled by theoperator.In the following lines, we report the equation used forAbkmcalculation;for an extended description of how this equation is obtained and how it canbe used (including practical examples), seeAppendix A. Notice that, themonetary value of the rolling stock strongly depends on vehicles character-istics. The MIT has provided standard market values (including the ex-pected capitalized maintenance through their life cycle) of several newlyequipped bus types (Annual depreciation). These values are then adjustedto represent the costs associated with the single produced unit of transport(Abkm), that is then calculated as follow:Abkm¼Annual depreciationSMQNBS1Average annual BKMð1Þwhere,SMQ(seats/m2), is the number of seats per square meter for the bus ve-hicle type used to carry out the service. It is used to express the differ-ence in bus types capacities (usually, it ranges between one and two);NBS, number seats per bus (according to the type of vehicle);Average annual BKM(mln of bkm), million of bus-kilometers producedon average by a bus vehicle in one year.The standard unit cost model combines the aforementioned three mainvariables in order to calculateCTSbkm, the cost per produced unit of bkm(see theAppendix Bfor statistical details of the model). Then, the unitcost is multiplied for the produced bkm to determineACTSb, namely, thetotal cost associated with the production (Eq. 3):CTSbkm€=bkmðÞ¼1:538þ34:183CSb−5−0:186DTb1BKMþ0:015DTb2BKMþ1:651Abkmð2ÞACTSb¼BKM106CTSbkmð3ÞAvenali et al. (2016)proved that the impact of the commercial speed onthe production costs can be modelled through a hyperbolic function. Thedummy variablesDTb1andDTb2are introduced to model the nonlinearrelationships that stands between the unit costCTSbkmand the scale of theserviceBKM(Eq. 4):DTb1¼1i f BKM≤4mln bkm0otherwiseDTb2¼1i f BKM>4mln bkm0otherwiseð4ÞThe standard cost model for bus services reports the existence of scalediseconomies after 4 millions of bkm. Indeed, according to the appliedunit transport cost model(2), the minimum efficient scale for a LPBTservices is about 4 million of bus revenue kilometers. In order to minimizethe overall production cost in the case the scale of service is larger than 4million of bus revenue kilometers, the service production has to be opti-mally allocated to two or morefirms whose individual output vectorssum to the overall service size (for instance, it could be assigned to distinctoperators of a temporary association of enterprises or to independent busi-ness units of a single operator;Braeutigam, 1989). However, a good proxyof the optimal (in terms of minimizing the cost) allocation consists ofequally dividing the overall size of the service among thefirms. Therefore,a rational policy maker would try then to avoid diseconomies by dividingthe service in smaller fragments, to be assigned in separated contractsand/or to different operators. Therefore, we assume that if a service largerthan four million of bus-kilometers per year is needed to satisfy the overalldemand, the maximum subsidies payment recognized by the local publicadministration to the transport operator would be equal the one obtainedwith a fragmentation of the service into several service lots, each onewith a size lower or equal to four million of offered bus-kilometers. For in-stance, the overall standard cost of a service of 15 million of bus-kilometersis equal to four times the overall standard cost of a service of 3.75 million ofbus-kilometers.Thus, for real allotmentsof LPT services, the standard trans-port cost can be written as follows:CTSbkm¼1:538þ34:183CSb−5−0:186BKMþ1:651Abkmð5ÞACTSb¼BKM106CTSbkmð6ÞVariableBKM¼BKMNis used in the case of a service larger than four mil-lion of bus revenue kilometers, whereN¼dBKM4e. Obviously,BKM¼BKMfor any service whose sizeBKMis lower than or equal to four million of busrevenue kilometers. Therefore, variableBKMis by construction lower thanor equal to four million of bkm.3.1.2. Rail service operating cost modelIn this section, we describe the standard cost model for rail servicesproduction.The model identifies the standard cost associated with the production ofa single unit of transport and it was proposed byAvenali et al. (2020).Forthe rail services, the unit of transport considered as reference is the train-Table 1Perimeter of costs description.Costs categoriesUnit of measurement Source (rail)Source (bus)Standard cost models OperationFleet maintenanceAdministration and other overheadsPre-tax cost of capitalVehicles-kmAvenali et al. (2020)Avenali et al. (2020)Infrastructure usageCosts associated with the increment ininfrastructure usage (e.g. access to theinfrastructure, maintenance) and operationVehicles-kmNumber of stationsEU(2019)andOriginal methodology based on data from the Italian contextEU(2019)ExternalitiesTotal costs for externalities (accidents,congestion, air pollution, climate change,well-to-tank, noise, habitat damage)Passengers-kmEU(2019)EU(2019)Users' costProxy:Differences on trip duration,reported as saved time for passengers.Passengers-kmEU(2019)EU(2019)A. Avenali et al.Transportation Research Interdisciplinary Perspectives 7 (2020) 1002005
kilometer (from here on tkm). The main variables considered in the stan-dard model are the following:NTS:number of seats per train (according to vehicle type).CSt(km/h):commercial speed, a qualitative (hedonic) characteristic of aservice, which can be barely controlled by the operator.T:rail turnover or network turnover, indicating the intensity in the usageof rail tracks. Ifskmare the offered seat-kilometers (in millions) andRkmare the kilometers of rail tracks used to produce the rail service,the rail turnoverTis the ratio betweenskmandRkm.Di:percentage of seat-kilometers powered by diesel.Itistheratiobetweenthe diesel-powered seat kilometers and the overall offered seat kilome-ters (skm), and it is used to model the existing differences in operatingcosts associated with diesel-driven or electric-driven train services.Askm(€/skm):degree offleet renewal. This variable is defined as the ratiobetween a monetary value of the rolling stock (trainfleet) and the of-fered seat-kilometers (skm). If the rolling stock is completely ownedby the operator, the monetary value corresponds to the sum of all thedepreciations of the owned vehicles (over an assumed lifetime of30 years), including their capitalized maintenance. This variable iden-tifies a qualitative characteristic, which can be controlled by theoperator.We report the equation used forAskmcalculation; for an extended de-scription of how this equation is obtained and how it can be used (includingpractical examples), seeAppendix A. Notice that, the monetary value of therolling stock strongly depends on vehicles characteristics. The MIT has pro-vided standard market values (including the expected capitalized mainte-nance through their life cycle) of several newly equipped bus types(Annual depreciation). These values are then adjusted to represent thecosts associated with the single produced unit of transport (Askm), that isthen calculated as follow:Askm¼XiAnnual depreciationiNTSiXiAverage annual SkmiNTSið7ÞThe standard unit cost model combines the aforementioned variablesin order to computeCTSskm(€/skm), the cost to produce a unit of railtransport, measured as seat-kilometers (see theAppendix Bfor statisticaldetails of the model). Then, unit cost is multiplied byNTSto determineCTStkm(€/tkm), namely, the cost per offered unit of tkm:CTSskm¼0:02716þ0:24975CSt−28−0:00349Tþ3:52342Askmþ0:02816D2ið8ÞCTStkm¼NTSCTSskmð9ÞAgain, the impact of the commercial speed on the unit cost is modelledthrough a hyperbolic function. Furthermore,Avenali et al. (2020)showedthe presence of scale economies10in the standard cost model.Now, let TKM denotes the millions of offered train-kilometers (what-ever the trains are powered). Obviously, TKM =(Skm/NTS). Therefore,the standard transport cost for the train system is as follows:ACTSt¼TKM106CTStkmð10Þ3.2. Marginal infrastructure cost for usageThis section is dedicated to the marginal infrastructure cost descriptionand estimation.In our analysis, the marginal infrastructure costsfor usage are defined asboth the increment in costs due to the higher maintenance, repair, renewaland operation activities associated with an increment in vehicles traffic,and, in railway case, as the operating cost component for stations andtracks, associated with the service activation.Even if there is not a univocal definition of the usage costs of the infra-structure in the literature, it is well established that part of the maintenancecost (that represents the main part of the infrastructure costs) have to behandled also in the absence of traffic. Nevertheless, the distinction betweenvariable andfixed costs is rarely considered, preferring the assumption of alinear variation with the traffic volume. This output is usually expressedthrough vehicle-km or passenger-km (or gross-tons-km, for freight trans-port). We adopted this approach for the bus servicesmarginal infrastructurecosts.The operating infrastructure cost category for railways, instead, is alsocomposed of all the costs necessary to keep the infrastructure open fortraffic. It includes, for example, lightning, signaling, expenses for stationsactivation (utilities, heating system, cleaning). Indeed, the costs associatedwith stations activation are also the main component, and thenumber ofstationsalong the line can usually be used as unit of measures for this costcategory, as approximation.The measurement of the marginal infrastructure cost could be carriedout using different methodologies, as described inLink and Nilsson(2005). As in other costs categories, it is possible to choose betweenbottom-uportop-downapproaches. In general, different classes of vehicleshave different impacts on infrastructure damages and also on the actual ac-cess capacity (i.e. associated with different minimum safe headway). Forexample, the difference in axle weight or types of tires in the road vehiclesmay affect the wear and tear in different ways (e.g. heavier vehicles tend tocause more damage). Similarly, passenger/freight service or high/conven-tional speeds for the trains may affect the magnitude of infrastructures' de-terioration. The econometric methods often fail to represent in a significantway the described phenomena. A solution could be to create differentmodels for each vehicle category, but this independent estimation risks tounderestimate their joint impact (the interaction among different catego-ries operating on the same infrastructure).In the present paper, the marginal infrastructure costs are estimated re-ferring to EU best practices, for the bus transport system, and referring to anoriginal bottom-up estimation model that we proposed specifically for Ital-ian LPT rail services. TheEC (2019)reference included an indication of EUbest practices also concerning the railway infrastructure usage, that we re-port in the following sub-paragraph. Nevertheless, the suggested marginalcosts are national (or even European) average values; where possible,values specific for the context at exam could improve the estimation ofthe real external effects produced by the transport services.3.2.1. Bus service marginal infrastructure costs for usageAs regards to bus services, we consider the method of estimationdescribed in the European Handbook on the external costs of transport(EC - European Commission, 2019), that bases the cost evaluation on astudy conducted on the structure of the trafficflow and variable cost com-position in Germany for the year 2007 (Link et al., 2009).In general, the magnitude of the generated effects differs by vehicleclass, country (e.g. peculiar characteristics on construction road) and roadtype. For example, high quality roads are less affected by the damagesdue to the vehicles' operations, but their construction requires higher initialinvestments. To produce validcountry-specific unit costs,EC (2019)appliessome adaptation based on the price variation on average construction costs.As regards the technical characteristic of the roads, instead, it is assumed tobe the same in all countries; even if this represents a strong assumption, it isconsidered acceptable respect to the aim of the present analysis.Table 2re-ports the unit infrastructure costs (in€/vehicle-km) for buses. Values for10Avenali et al. (2020)highlights that the model should not be applied to predict the cost ofservices with>10,000 million of seat-kilometers as it has been trained on a database where thelargest-size instances have mostly 10,000 million of seat-kilometers.A. Avenali et al.Transportation Research Interdisciplinary Perspectives 7 (2020) 1002006
marginal costs for infrastructure usage due to rail services are also added intheTable 2, as alternative reference (at Italian national level and EU aver-age) to the methodology estimation proposed in this paper in the nextsubsection.Thus, referring to the Italian case, the Standard Infrastructure usageCost for the bus mode (SICb) is as follows:SICb¼0:39€bkm106ð11Þ3.2.2. Rail service marginal infrastructure costs for usageAs regards rail services, we elaborated a simple model aiming to esti-mate the infrastructure usage marginal costs, making use of data gatheredby the Italian MIT from 9 local railways operators. This methodology repre-sents an original proposal for the Italian context.It is well known that the estimated impact on the railways' assets couldvariate with the amount of traffic, the type of track (e.g. electrified or not),type of trains (e.g. passengers or freight, the latter being usually less expen-sive, according toWheat et al., 2009andGaudry and Quinet, 2013) andspeed regime. Our estimatesfind evidence that in the Italian context thenumber of produced tkm and the capillarity of the network (namely, the in-verse of the average distance between two subsequent stations) representthe main drivers of the infrastructure maintenance unit cost (€/tkm). Inparticular, the capillarity of the network is an important factor due to its in-fluence on the acceleration/deceleration needed in departing/approachingto a train station, to which are associated higher tracks wear and tear.The operating costs due to circulation of traffic, instead, mainly dependon both the network capillarity and the total number of stations in the net-work. As already described, this category is composed by all the costs thatare activated when at least one ride run on the infrastructure; includinglightning, signaling, expenses for stations activation (e.g. utilities, heatingsystem, cleaning).Table 3reports the average values estimated from ourdataset of 9 observations, where 3 observations are characterized by ahigh network capillarity (average distance between two subsequent sta-tions lower than 2.9 km), 4 observations by a medium network capillarity(average distance between two subsequent stations higher than or equalto 2.9 km and lower than 4.8 km), and 2 observation by a low network cap-illarity (average distance between two subsequent stations larger or equalto 4.8 km).More in detail, the Standard Infrastructure usage Cost for the rail mode(SICt) is modelled as follows:SICt¼DIt16:42€tkm106þ292;500€NStationsþDIt22:44€tkm106þ113;100€NStationsþDIt31:24€tkm106þ113;100€NStationsð12Þwhere, dummy variablesDIt1,DIt2andDIt3identify the capillarity level ofthe rail infrastructure at issue (i.e. high, medium and low):DIt1¼f1if capillarity is high0otherwiseDIt2¼f1i f capillarity is medium0otherwiseDIt3¼f1if capillarity is low0otherwiseð13Þwhile, parameterNStationsrepresents the number of rail stations wherepassengers can get on or off the trains.3.3. Costs of externalities associated with the transport servicesA series of externalities are associated with transportation production. Forexample, a higher road traffic volume increases the congestion level and, con-sequently, the air pollution and the global warming, while trains and aircraftsgenerate noise. These types of effects generally do not burden only the trans-port users, but society overall. In outline, externalities occur when productionand/or consumption of a good or a serviceimposes external costs to (generateexternal benefits on) third parties outside the considered market.In this section, we present the methodology adopted to evaluate the ex-ternal costs associated with the transport services.FollowingEC (2019), we include in the cost perimeter environmentalimpacts: air pollution costs, fuel (energy) production external costs(well-to-tank), impact on habitat and on climate change. Furthermore, weconsider the social costs associated with noise, congestion and accidents.The most relevant component for the externalities costs are congestion,noise and air pollution. In particular, the latest generates broad negative ef-fects on health and ecosystems (Kampa and Castanas, 2008). Despite positiveimprovements occurred in the last decades, the transportation sector still rep-resents one of the principal air polluters, especially in urban areas with hightrafficvolume.Table 4collects the marginal external costs (in€-cent per passenger-km), divided in sub-categories, by mode. Since rail services run on dedi-cated infrastructure, in the limit of safety capacity (minimum headway be-tween two subsequent rides in the same direction), congestion externalitiesare not generated. The marginal cost of climate change is null for electric-driven rail service, since the only generation of greenhouse gases associatedwith this type of vehicles would be caused by electricity production itself.The electricity production effects on climate change do not impact directlyon the area where the service is run and are strongly related to the produc-tion sources mix, varying largely country by country (and year by year onthe same country); for these reasons, it is not included in our analysis.Notice that, to effectively run the bus services a number of bus-kilometersout of service are required. Referring to the Italian case, a 10% of total serviceBKM is considered an average reference value, while for regional rail servicesonly 2% with respect to the number of TKM in service. Therefore, the externalcosts generated by bus and rail modes have to be computed also by takinginto account vehicle-kilometers produced out of service.Table 2Incremental roads and railways infrastructure costs according to EU (2019).Source:European Commission–EC (2019).Italy(€/vehicle-km)EU-28(€/vehicle-km)Buses0.390.3575Electric trains6.1291.81Diesel train6.1292.075Table 3Track maintenance and rail traffic unit costs for Italian context.Network capillarityUnit maintenance cost(€/train-km)Operating infrastructure(€/station)High (average distance <2.9 km) 6.42292,500Medium (2.9 km≤averagedistance <4.8 km)2.44113,100Low (average distance≥4.8 km) 1.24113,100Table 4Costs for externalities by transport mode in€-cents per passenger-km.Source:European Commission–EC (2019).Cost categoryTrain (€-cent/pkm)Bus (€-cent/pkm)Accidents0.3430.472Air pollution0.0070.780Climate change0.409Noise1.6170.694Congestion3.833Well-to-tank0.6790.177Habitat damage0.3820.068Total cost of externalities3.0286.434A. Avenali et al.Transportation Research Interdisciplinary Perspectives 7 (2020) 1002007