SIDT Scientific Seminar 2012

Transcription

1 Available online at ScienceDiect Pocedia - Social and Behavioal Scienc es 87 ( 2013 ) SIDT Scientific Semina 2012 Evaluation of tavel demand impacts in the case of ail system failue Luca D Acieno a, *, Maiano Gallo b, Buno Montella a, Antonio Placido a a Fedeico II Univesity of Naples, Depatment of Civil, Achitectual and Envionmental Engineeing, via Claudio 21, Naples 80125, Italy b Univesity of Sannio, depatment of Engineeing, piazza Roma 21, Benevento 82100, Italy Abstact Rail o meto systems ae geneally chaacteised by high pefomance in tems of maximum tavel speeds and/o educed headways between two successive convoys. Howeve, in the event of beakdowns, since faulty tains cannot usually be ovetaken and thei emoval could pose exteme difficulties especially in metopolitan systems with two sepaate tunnels, eestablishing the egula sevice could involve inconveniently long tavel times. Hence, ou poposal is to analyse effects on tavel demand of diffeent levels of degaded sevices in the case of meto system failue in ode to define the best stategy to adopt so as to minimise use discomfot. In paticula, we popose to simulate a ail system though the inteaction of fou models (failue, sevice, supply and tavel demand) by extending ideas poposed elsewhee in the liteatue. Finally, the poposed methodology is tested in the case of an Italian meto system by poviding fo each failue scenaio the selection of the best stategy to minimise impacts on uses. Initial esults show that inteactions among ail system components (infastuctue, olling stock, signalling and timetable) and tavel demand ae complex, and theefoe the optimal stategy to be implemented may be affected not only by ail system beakdowns but also by tavel demand conditions The Authos. Published by Elsevie by Elsevie Ltd. Ltd. Open access unde CC BY-NC-ND license. Selection and pee-eview unde unde esponsibility of SIDT2012 of SIDT2012 Scientific Scientific Committee. Committee. Keywods: tavel demand analysis; capacity constaints; ail passenge systems; public tanspot management; micosimulation appoach 1. Intoduction The management of tanspotation systems is a key issue which can affect both life quality and economic development. In lage uban aeas, an efficient public tanspot system can help to educe the negative extenalities of pivate ca use without excessively penalising use tavel times o zone accessibilities (as shown by Goi et al., 2012, 2013). * Coesponding autho. Tel.: ; fax: addess: luca.dacieno@unina.it The Authos. Published by Elsevie Ltd. Open access unde CC BY-NC-ND license. Selection and pee-eview unde esponsibility of SIDT2012 Scientific Committee. doi: /j.sbspo

2 76 Luca D Acieno et al. / Pocedia - Social and Behavioal Sciences 87 ( 2013 ) Moeove, high-density contexts epesent the ideal famewok in which to adopt ail systems. Although they equie geate building, opeating and maintenance costs than othe public tanspot systems (such as buses, tolleybuses and taxis), high pefomances stemming fom the use of exclusive facilities, constained diving and the signalling system allow ail systems to achieve lowe unit costs pe seat-km (i.e. vehicula capacity multiplied by tavel distances) o pe caied passenge-km (i.e. tavel demand multiplied by tavel distances). Likewise, in the case of ail systems, extenalities such as ai pollution o fuel consumption ae also lowe than those of othe public tanspot systems. Positive pefomance in tems of maximum tavel speed o educed headway between two successive convoys is patly offset by geate vulneability to system failue. Indeed, in the case of beakdowns, since the faulty tain cannot geneally be ovetaken and could be extemely had to emove especially in metopolitan systems with two sepaate tunnels, e-establishing egula ail schedules could entail vey substantial passenge delays. Hence, in dealing with emegencies, ail netwok manages have to take into account effects of intevention stategies on tavel demand. In tems of methodology, it is woth noting that, as shown by Gibson (2003), Abil et al. (2008) and Lindne (2011), the pefomance of ail systems and thei elated capacities has mainly been analysed by neglecting effects on tavel demand. Indeed, the fist papes actually consideing that the main pupose of a ail system is to satisfy tavelle equiements wee the contibutions of Hamdouch et al. (2011), Kanai et al. (2011) and Zheng et al. (2011). In paticula, Hamdouch et al. (2011) poposed an assignment model that diffeentiates the discomfot level expeienced by sitting and standing passenges in the case of public tanspot systems, Kanai et al (2011) poposed an algoithm fo educing use waiting times in the case of a ail (multi-line) netwok by modifying tain timetables, while Zheng et al. (2011) povided the definition of capacity eliability of a ail netwok and developed a model fo calculating it. Likewise, Canca et al. (2011, 2012) focused on key aspects of ailway netwok management by taking tavel demand into account in the case of sevice disuptions, such as an incease in tavel demand o a eduction in fleet size. Recently, Mazzeo et al. (2011) and Quaglietta et al. (2011), neglecting capacity constaints, poposed joint analysis of ail pefomance (i.e. ail entepise efficiency) and elated effects on uses (i.e. sevice effectiveness and quality) in the case of ail systems failue. In this context, ou poposal epesents an extension of Mazzeo et al. (2011) and Quaglietta et al. (2011), intoducing capacity constaints of ail vehicles in ode to povide moe ealistic simulated effects. Indeed, although these contibutions might be consideed an innovative appoach to ail system analysis because they adopt a multi-objective appoach in evaluating opeational stategies, thei assumptions on capacity allow each use to boad the fist aiving tain. They do not conside that in failue contexts some tains might not have enough space to accommodate all passenges wishing to boad. Theefoe, the simulated failue effects tend to be calmed moe apidly than in eal cases. It is woth pointing out that, as shown by Montella et al. (2000), in any design o eal-time management poblem it is necessay to adopt simulation models which should be able to identify netwok pefomance and featues fo each altenative poject and/o management stategy. These models can be classified as macoscopic, mesoscopic o micoscopic accoding to the assumption on the level of detail consideed. Macoscopic simulation models (Pinz et al., 2001; Kettne & Sewcyk, 2002) adopt a high abstaction level of ailway infastuctue and opeations. They ae mainly adopted in long-tem planning to detemine at a maco level some netwok o sevice featues (such as the numbe of stations, numbe of lines, aveage sevice fequencies, aveage speed o equied olling stock). Likewise, mesoscopic simulation models (Mainov & Viegas, 2011) ae able to simulate a simplified system by means of a multi-scale famewok consisting of both macoscopic and micoscopic elements. Finally, micoscopic simulation models (Nash & Huelimann, 2004; Siefe & Radtke, 2005) epesent the system elements (such as signalling systems, adiuses of cuvatue, slopes, timetables, locomotive types, numbe of passenge cas, numbe of feight cas o adhesion values) in ode to povide a moe pecise desciption of ail opeations. In paticula, ecently, Wang et al. (2011), Coapi et al. (2013) and De Matinis et

3 Luca D Acieno et al. / Pocedia - Social and Behavioal Sciences 87 ( 2013 ) al. (2013) poposed to adopt a micoscopic appoach fo analysing effects of diffeent diving stategies in tems of enegy consumption. Ou pupose is to analyse effects on tavel demand of diffeent levels of degaded sevices in the case of meto system failue in ode to define the best stategy to adopt so as to minimise use discomfot. Indeed, in these contexts, as shown by Batley et al. (2011), due to high quality sevices (fo instance in tems of fequency), in the case of beakdowns which educe the quality of sevice without inteupting it, passenges may decide to incease thei tavel times athe than modify thei planned tips in tems of path (i.e. by choosing to change thei depatue station) o mode choices (i.e. by choosing altenative tanspot modes). Hence, in ode to detemine tavel times of passenges in non-stationay contexts (i.e. two successive ail convoys may povide diffeent levels of sevices such as values of esidual capacity, tavel times, etc.), although high calculation times could be equied, it is woth adopting mico-simulation tools, fo instance, implemented by means of off-line pocedues. In paticula, in simulating ail and/o meto systems, adoption of a micoscopic model equies the solution of a system of diffeential equations by means of a numeical appoach. Hence, we popose to adopt OPENTRACK softwae (Nash & Huelimann, 2004), developed by the Swiss Fedeal Institute of Technology (ETH) of Zuich, fo integating the system of diffeential equations in the case of a micoscopic simulation appoach. The pape is oganised as follows: Section 2 descibes the famewok of the poposed appoach fo defining the best stategy in the case of ail system failue; Section 3 applies the stategy in the case of a eal dimension meto netwok; finally, Section 4 summaises the conclusions and outlines eseach pospects. 2. Famewok of the poposed appoach The aim of the pape is to define the best opeational stategy which minimises use discomfot in the case of ail system failue. Hence, the poblem can be fomulated with a multidimensional constained optimisation model, as follows: ( y, fc, np, unf ) ˆ y = ag min Z (1) y S y subject to: ( np unf ) Λ( y, fc, np, unf, pt), = (2) with: Z ( y, fc, np, unf ) = β tw ( y, fc, np) fw ( unf ) + β waiting on boad s= station p= platfom = un l= link = un tb l s,p ( y, fc, np) fb ( unf ) l s,p + (3) whee y is the vecto of paametes which identify the intevention stategy; ŷ is the optimal value of vecto y (i.e. the vecto of paametes identifying the optimal stategy); fc is the vecto of paametes identifying the failue context; np is the vecto of paametes identifying the netwok pefomance; unf is the vecto of paametes identifying use flows on the tanspotation netwoks; pt is the vecto of paametes identifying the planned timetable; Z is the objective function to be minimised depending on y, fc, np and unf; S y is the feasible

4 78 Luca D Acieno et al. / Pocedia - Social and Behavioal Sciences 87 ( 2013 ) set of vecto y (i.e. the set identifying all feasible opeational stategies); Λ is the simulation function which povides netwok pefomance (np) and use netwok flows (unf) as a function of y, fc, np and unf; β waiting is a paamete which expesses the elevance (i.e. elative weight) given by uses to waiting times; tw s, p is the aveage use waiting time at station s on platfom p between un ( 1) and un ; fw s, p is the numbe of passenges waiting at station s on platfom p between un ( 1) and un ; β is a paamete which on boad expesses the elevance (i.e. elative weight) given by uses to on-boad time; tb is the time spent by the convoy l associated to un fo tavelling on link l; fb is the numbe of passenges who tavel on the convoy associated l to un while cossing link l. Constaint (2) epesents the consistency constaint between tanspotation system pefomance and tavel demand flows, whose fomulation equies the analysis of fou kinds of models: failue, sevice, supply and tavel demand models. In paticula, the implementation of the optimisation model (1) equies the calculation of objective function (3) whose input paametes have to be detemined by means of the following pocedue which allows the fixed-point poblem (descibed by constaint 2) to be solved, that is: fo each failue context, it is necessay to povide effects on the ail system in tems of educed pefomance o unavailability of a tain o a tack section (failue model); the use flows on platfoms (pe-platfom model) is the esults of use choices depending on pefomances of all tanspotation systems (supply model), including the ail system (sevice model); the pefomance of the ail system (sevice model implemented via OPENTRACK softwae) is elated to intevention stategy (vecto y), use flows on the netwok (vecto unf) and beakdown seveity (outputs of the failue model); finally, the numbe of boading passenges (on-platfom model) can be calculated by means of passenges on platfom (pe-platfom model), olling stock (vecto s) and ail system pefomance (sevice model). In the following, we popose a detailed desciption and elated fomulation of the adopted models fo implementing the methodology. Moeove, we povide suitable efeences whee eades can delve into the analytical specifications of the models and numeical values of paametes adopted in the liteatue. The failue simulation model povides pefomance of the ail systems elated to each possible beakdown. Model output in this case may consist, fo instance, in eduction in maximum speed o the unavailability of a tain o a tack section. This model is based on the cause-effect elation between the faulty element and the opeations of all systems. Details on the management of beakdowns ae analysed by RAMS (Reliability, Availability, Maintainability and Safety) pocedues as shown by Mazzeo et al. (2011) and Quaglietta et al. (2011). Analytically, the failue model consists of a function, indicated as FSM, which povides paametes descibing infastuctue (in), olling stock (s) and signalling system (ss) as depending on thei non-petubed values (in 0, s 0 and ss 0 ) and failue context (fc), that is: ( in, s, ss) = FSM( in, s, ss, fc) (4) The sevice simulation model descibes ail system pefomance depending on ail infastuctues, olling stock, signalling system, timetable and use flows on the netwok. Unde the assumption of a micosimulation appoach, this model can be solved though a system of diffeential equations whose numeical solution can be tackled by means of suitable commecial softwae. In ou case, we popose to adopt OPENTRACK softwae (see Nash & Huelimann, 2004) by adding an extenal tool fo adopting also tavel demand as input data (i.e. fo simulating the vaiation in dwelling times at stations due to vaiations in use flows on the platfom).

5 Luca D Acieno et al. / Pocedia - Social and Behavioal Sciences 87 ( 2013 ) In paticula, OPENTRACK is a mico-simulation softwae which epoduces in high detail the motion of the tains by a mixed simulation pocess. This means that the simulation is a combination of continuous and discete events. The fome epesent the motion of the tains which is simulated by solving a system of diffeential equations (basically Newton s equation), while the latte ae all the netwok modifications due to signalling system o delays. Since it is not possible to evaluate the solution by an analytical fomula, it is necessay to adopt a numeical appoach. Fo this eason, this softwae uses the Eule Method (see, fo instance, Butche, 1987) which estimates the new value of a vaiable by means of the pevious one. Analytically, the sevice model can be fomulated as a function, indicated as SSM, which povides ail netwok pefomance (np) as depending on intevention stategy (y), infastuctue (in), olling stock (s), signalling system (ss), planned timetable (pt) and use netwok flows (unf) paametes, that is: ( np ) = SSM( y, in, s, ss, pt, unf ) (5) The supply model povides use genealised costs on all tanspotation systems in the analysed aea depending on the outputs fom sevice and tavel demand models. Details on these kinds of models can be found in Cascetta (2009). Analytically, this model can be fomulated as a function, indicated as SM, which povides tanspotation netwok pefomance (tnp) as depending on use netwok flows (unf), that is: tnp = SM( unf ) (6) Finally, the tavel demand model descibes the use behaviou conditioned by the pefomance of tanspotation systems (i.e. supply and sevice simulation models). Geneally, this model can be fomulated by a classic fou-step demand model (Cascetta, 2009). It is woth noting that in the case of failue of the ail system with the assumption of convoy capacity constaints it is necessay to adopt two kinds of tavel demand models: a pe-platfom model and an on-platfom model. The fome descibes use choices in the case of egula sevice and can be implemented by means of the abovementioned fou-step models. Outputs of the pe-platfom model ae use flows on each ail platfom. The on-platfom model analyses fo each appoaching tain whethe the esidual capacity (which is equal to the tain capacity minus the on-boad passenges plus the alighting passenges) is geate than the numbe of boading passenges. If this condition is not satisfied, only a potion of tavel demand (i.e. waiting passenges), equal to the esidual capacity, is able to boad the tain while the suplus has to wait fo the following tains. Ou poposal is to adopt a Fist In Fist Out (FIFO) appoach fo simulating the sequence of uses boading tains. Indeed, although in eal cases passenges geneally tend to mingle on the platfoms, in the case of high levels of cowding the feedom of movement is limited and hence the pioity in being seved (i.e. in boading) is stongly coelated with the sequence of aivals on platfom, especially if pat of the uses ae unable to boad the fist appoaching tain. Hence, in ou opinion, the adoption of a FIFO ule could geneate moe ealistic simulations. Obviously, the FIFO appoach has to take into account that on the same platfom passenges may have diffeent destinations and hence diffeent alighting stations. In tems of futue eseach, the compaison of esults could be consideed with the adoption of a Random In Fist Out (RIFO) appoach fo taking into account effects of mixing of passenges on platfoms. Obviously, this appoach would change waiting times of passenges on platfom and the elated detemination of objective function values into andom vaiables with the effect that the optimal stategy would not be detemined with an absolute cetain but it would be associated to a confidence inteval (i.e. pobability which expesses the eliability of the value).

6 80 Luca D Acieno et al. / Pocedia - Social and Behavioal Sciences 87 ( 2013 ) In tems of analytical fomulation, the pe-platfom model can be fomulated as a function, indicated as PPM, which povides use platfom flows (upf) as depending on tanspotation netwok pefomance (tnp) including ail netwok pefomance (np), that is: ( np) upf = PPM tnp, (7) Likewise, the on-platfom model can be fomulated as a function, indicated as OPM, which povides use flows on the netwok (unf) as depending on use platfom flows (upf), olling stock (s) and ail netwok pefomance (np), that is: (, s np) unf = OPM upf, (8) Thus, by adopting the abovementioned vaiables, constaint (2) can be obtained by combining eqns. (4)-(8) whee tem np can be expessed as: np = [ np;tnp] T (9) Hence, by solving poblem (1), it is possible fo each possible failue scenaio (fc) to associate the best opeational stategy ( ŷ ) which minimises effects on tavel demand, that is: fc poblem (1) ŷ (10) 3. Application to a eal-scale netwok The poposed methodology was applied to Line 1 of the Naples meto system in southen Italy. This line, opeated by METRONAPOLI, consists of 16 stations, as shown in Fig. 1. Impotantly, the line povides two sevices: a meto sevice (indicated in black in Fig. 1) between Piscinola and Dante; a shuttle sevice (indicated in gey in Fig. 1) between Dante and Univesità, which is povided by using a single tack and a single tain. Depot Univesità Piscinola Colli Aminei Medaglie d Oo Dante Fig. 1. Line 1 of the Naples meto system (Italy)

7 Luca D Acieno et al. / Pocedia - Social and Behavioal Sciences 87 ( 2013 ) Theefoe, since the two sevices ae completely independent and the tain depot is next to Piscinola, we analyse only the meto sevice, neglecting the shuttle. In this application, we analysed failue scenaios duing the moning peak-hou (i.e a.m.) fo simulating when discomfot effects ae geatest. Obviously, we consideed a wide time peiod fo analysing netwok loading (people and tains on the netwok at 7.00 geneally stated befoe) and discomfot duation (failue effects could last well beyond the peak-hou). We thus consideed the time peiod between 6.00 am and pm. In this application, we popose to analyse jointly eight failue scenaios whose diect effects ae a degadation in tain pefomance: at 7.00 in the Chiaiano station, the second station afte the depot, a convoy expeiences a beakdown which limits the maximum tain speed in each scenaio to a value between 10 % and 80 %. Since thee ae only thee maintenance tacks on the netwok (at Colli Aminei, Medaglie d Oo and Dante), thee ae six feasible stategies: the tain continues the sevice until Colli Aminei o Medaglie d Oo and then, afte unloading passenges on the platfom, it is diven onto the neaest maintenance tack; the tain continues the sevice until it eaches the following teminus, i.e. Dante, and is then diven onto the maintenance tack; the tain completes the outwad tip and stats the etun tip until Medaglie d Oo o Colli Aminei and then, afte unloading passenges on the platfom, it is diven onto the neaest maintenance tack; the tain completes the whole sevice until it eaches the depot, i.e. Piscinola. Obviously, just befoe allocating the tain to the maintenance tack, it is necessay to unload passenges on the platfom who should wait fo a following tain. Numeical applications wee pefomed by applying in the same contexts both the pevious model poposed in the liteatue (Mazzeo et al., 2011; Quaglietta et al., 2011), which was based on neglecting capacity constaints of ail convoys, and ou poposal based on taking into account this kind of constaint. In both cases, ou analysis of the simulation esults shows that an incease in headway geneally yields an incease in boading passenges. Likewise, a decease in headway yields a decease in boading passenges. Theefoe, the faulty tain tends to be satuated, while following convoys tend to be empty. Moeove, elimination of a faulty tain yields an incease in passenge tavel times since passenges on boad have to alight onto the platfom and wait to boad a following tain, a decease in tavel times because following tains will have tacks fee of any obstacles, and an incease in vehicle cowding and possible incease in waiting times because following tains will be boaded also by passenges fom the faulty tain. Tables 1 and 2 povide objective function values (i.e. total tavel time of passenges), expessed in tems of equivalent monetay costs, fo each intevention stategy and fo each speed eduction espectively without and with convoy capacity constaints. Bold values epesent the minimum value of the objective function fo each beakdown occuing. Hence these values allow the optimal intevention stategy to be identified fo each failue scenaio. Likewise, Fig. 2 povides a compaison of objective function values by adopting, fo each model (i.e. neglecting and consideing capacity constaints), two diffeent scales in ode to highlight tends of the function in the neighbouhood of optimal values. Obviously, since thee is a geat diffeence between the minimum and maximum values of objective function and ou aim is to identify the minimum of the objective function (as descibed by eqn. 1), we epesent only the pat of the objective functions below the theshold of 170,000 (in the uppe pat of the figue) and 140,000 (in the lowe pat of the figue), not indicating highe values in the figue. In tems of data analysis, it is woth noting that in some cases, the objective function has moe than one local minimum (i.e. the objective function is not convex). Moeove, as expected, by consideing capacity constaints, the objective function has values geate than neglecting them since some passenges would not be able to boad

8 82 Luca D Acieno et al. / Pocedia - Social and Behavioal Sciences 87 ( 2013 ) the fist aiving convoy and theefoe have to wait fo the following, inceasing thei waiting times. These diffeences between the two appoaches could povide diffeent optimal stategies. Obviously, the adoption of capacity constaints yields an estimation of use disutility and hence identifies the optimal stategy close to the eal phenomenon. Indeed, only in exteme conditions (i.e. speed eductions lowe than 30% o highe than 70%) do both appoaches povide the same optimal stategy. Table 1. Total tavel passenge costs by neglecting capacity constaints of ail convoys (Mazzeo et al., 2011; Quaglietta et al., 2011) Speed eductions Stations 10% 20% 30% 40% 50% 60% 70% 80% Colli Aminei (fowad) 130, , , , , , , ,900 Medaglie d Oo (fowad) 130, , , , , , , ,676 Dante 128, , , , , , , ,171 Medaglie d Oo (backwad) 128, , , , , , , ,950 Colli Aminei (backwad) 127, , , , , , , ,778 Piscinola (depot) 127, , , , , , , ,591 Table 2. Total tavel passenge costs by consideing capacity constaints of ail convoys (ou poposal) Speed eductions Stations 10% 20% 30% 40% 50% 60% 70% 80% Colli Aminei (fowad) 134, , , , , , , ,214 Medaglie d Oo (fowad) 132, , , , , , , ,950 Dante 130, , , , , , , ,768 Medaglie d Oo (backwad) 129, , , , , , , ,892 Colli Aminei (backwad) 129, , , , , , , ,826 Piscinola (depot) 129, , , , , , , ,473 Moeove, on analysing esults in the case of speed eductions between 10% and 40% (between 10% and 50 % in the case of the unconstained appoach), the application of the Colli Aminei (fowad) as well as Medaglie d Oo (fowad) stategy povides a slight eduction in objective function values by inceasing failue seveity. This is due to the fact that an incease in beakdown seveity yields a decease in faulty tain speed which geneates a decease in headway between this tain and the following. Hence, thee is an incease in tavel times fo passenges on the faulty tain combined with a decease in waiting time fo the following ail convoys, once passenges ae unloaded onto the platfom. Since in the objective function paamete β waiting is geate than β, as suggested in the liteatue (see, fo instance, Cascetta 2009), a slight incease in tavel times is moe on boad than compensated by the eduction in waiting times. Howeve, this effect does not take place when beakdown seveities, and theefoe inceases in tavel times, ae significant. Indeed, especially in the case of the constained appoach, waiting times could be highe, since some passenges might not be able to boad the fist aiving tain. A common esult between the two constained appoaches is that, in tems of optimal stategy, when the faulty tain is fast (low eduction in maximum speed), it is best to conclude the tip at the depot so as to avoid passenge discomfot caused by alighting fom the faulty tain and boading the following tain. Likewise, when the faulty tain is excessively slow (geat eduction in maximum speed), it is best to position the faulty tain on a

9 Luca D Acieno et al. / Pocedia - Social and Behavioal Sciences 87 (2013) maintenance tack as soon as possible. Obviously, diffeent speed eductions yield diffeent points of convenience. Fig. 2. Objective function values by neglecting (left) and consideing (ight) capacity constaints of ail convoys 4. Conclusions and eseach pospects In poposing a decision suppot system fo analysing ail systems in the case of tain beakdowns, we showed that, although effects on tavel demand have often been neglected in the liteatue, they can pofoundly affect analytical esults. We expanded contibutions poposed elsewhee (such as Mazzeo et al., 2011; Quaglietta et al., 2011) by intoducing capacity constaints in ode to develop a moe ealistic model which could allow fo the fact that, in a failue scenaio, passenges might not be able to boad the fist aiving tain since the boading flow may be highe than the convoy esidual capacity. Howeve, this assumption made it necessay to split the tavel demand model into two sub-models (the pe-platfom and on-platfom models). Finally, we applied the poposed methodology in the case of a eal ail netwok, compaing esults with the application of pevious appoaches by neglecting capacity constaints of ail convoys and highlighting diffeences in optimal stategy definition. 83

10 84 Luca D Acieno et al. / Pocedia - Social and Behavioal Sciences 87 ( 2013 ) As egads pospects fo futue eseach, the appoach could be fuitfully applied in the case of a wide set of tain beakdowns with diffeent demand levels. It might be used to analyse the effects of beakdowns and elated intevention stategies in the case of diffeent ail netwoks, and geneate timetables by adopting a multimodal appoach fo analysing ail system vulneability in tems of shot-, medium- and long-tem effects on tavel demand. Refeences Abil, M., Babe, F., Ingolotti, L., Salido, M. A., Tomos, P., & Lova, A. (2008). An assessment of ailway capacity. Tanspotation Reseach Pat E, 44, Batley, R., Dagay, J., & Wadman, M. (2011). The impact of lateness and eliability on passenge ail demand. Tanspotation Reseach Pat E, 47, Butche, J. C. (1987). The numeical analysis of odinay diffeential equations: Runge-Kutta and geneal linea methods. Wiley Intescience: New Yok (NY), USA. Cascetta, E. (2009). Tanspotation systems analysis: Models and applications. Spinge: New Yok (NY), USA. Canca, D., Zazo, A., Algaba, E., & Baena, E. (2011). Confontation of diffeent objectives in the detemination of tain scheduling. Pocedia Social and Behavioal Sciences, 20, Canca, D., Baena, E., Zazo, A., Otega, F., & Algaba, E. (2012). Optimal tain eallocation stategies unde sevice disuptions. Pocedia Social and Behavioal Sciences, 54, Coapi, G., Sanzai, D., De Matinis, V., D Acieno, L., & Montella, B. (2013). A simulation-based appoach fo evaluating tain opeating costs unde diffeent signalling systems. WIT Tansactions on the Built Envionment, 130, De Matinis, V., Gallo, M., & D Acieno, L. (2013). Estimating the benefits of enegy-efficient tain diving stategies: a model calibation with eal data. WIT Tansactions on the Built Envionment, 130, Gibson, S. (2003). Allocation of capacity in the ail industy. Utilities Policy, 11, Goi, S., Nigo, M., & Petelli, M. (2012). The impact of land use chaacteistics fo sustainable mobility: The case study of Rome. Euopean Tanspot Reseach Review, 4, Goi, S., Nigo, M., & Petelli, M. (2013). A new method to ecove the coect land use and public tanspot inteaction. WIT Tansactions on the Built Envionment, 130, Hamdouch, Y., Ho, H. W., Sumalee, A., & Wang, G. (2011). Schedule-based tansit assignment model with vehicle capacity and seat availability. Tanspotation Reseach Pat B, 45, Kanai, S., Shiina, K., Haada, S., & Tomii, N. (2011). An optimal delay management algoithm fom passenges viewpoints consideing the whole ailway netwok. Jounal of Rail Tanspot Planning & Management, 1, Kettne, M., & Sewcyk, B. (2002). A model fo tanspotation planning and ailway netwok evaluation. Poceedings of the 9th Wold Congess on Intelligent Tanspot Systems, Chicago (IL). Lindne, T. (2011). Applicability of the analytical UIC Code 406 compession method fo evaluating line and station capacity. Jounal of Rail Tanspot Planning & Management, 1, Mainov, M., & Viegas, J. (2011). A mesoscopic simulation modelling methodology fo analyzing and evaluating feight tain opeations in a ail netwok. Simulation Modelling Pactice and Theoy, 19, Mazzeo, A., Mazzocca, N., Nadone, R., D Acieno, L., Montella, B., Punzo, V., Quaglietta, E., Lambeti, I., & Mamo, P. (2011). An integated appoach fo availability and QoS evaluation in ailway systems. Lectue Notes in Compute Science, 6894, Montella, B., Gallo, M., & D Acieno, L. (2000). Multimodal netwok design poblems. Advances in Tanspot, 5, Nash, A., & Huelimann, D. (2004). Raiload simulation using OpenTack. Computes in Railways, 9, Pinz, R., Sewcyk, B., & Kettne, M. (2001). NEMO: Netwok Evaluation Model fo the Austian aiload (ÖBB). Eisenbahntechnische Rundschau, 50, Quaglietta, E., D Acieno, L., Punzo, V., Nadone, R., & Mazzocca, N. (2011). A simulation famewok fo suppoting design and eal-time decisional phases in ailway systems. Poceedings of the 14th Intenational IEEE Confeence on Intelligent Tanspotation Systems (ITSC), Washington (D.C.), USA, at. no , Siefe, T., & Radtke, A. (2005). Railway simulation: key fo bette opeation and optimal use of infastuctue. Poceedings of the 1st Intenational Semina on Railway Opeations Modelling and Analysis, Delft, The Nethelands. Wang, Y., De Schutte, B., Ning, B., Goot, N., & van den Boom, T. J. J. (2011). Optimal tajectoy planning fo tains using mixed intege linea pogamming. Poceedings of the 14th Intenational IEEE Confeence on Intelligent Tanspotation Systems (ITSC), Washington (D.C.), USA, at. no , Zheng, Y., Zhang, Z., Xu, B., & Wang, L. (2011). Caying capacity eliability of ailway netwoks. Jounal of Tanspotation Systems Engineeing and Infomation Technology, 11,