OPTIMIZING LOCATION AND LENGTH OF PASSING SIDINGS ON SINGLE-TRACK LINES FOR LONG HEAVY-HAUL FREIGHT TRAINS

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1 OPTIMIZING LOCATION AND LENGTH OF PASSING SIDINGS ON SINGLE-TRACK LINES FOR LONG HEAVY-HAUL FREIGHT TRAINS Me-Cheng Shh Graduate Research Assstant Unversty of Illnos, Urbana-Chamagn, IL, USA P.E. C. Tyler Dck Senor Research Engneer Unversty of Illnos, Urbana-Chamagn, IL, USA SUMMARY Dr. Yung-Cheng La Assocated Professor Natonal Tawan Unversty, Tawan Oeraton of long freght trans n heavy haul servce can hel mrove the oeraton effcency and reduce the unt cost, but the current ral nfrastructure n North Amercan can t fully suort ths tye of oeraton. In North Amercan, whch the majorty of ral network s sngle-track lnes, the otental benefts of long freght trans are constraned due to the nsuffcent length of many assng sdngs on many exstng sngle-track lnes. As a resonse to the nfrastructure condton, ralroads can oerate long trans n a sngle drecton [1] or fleet the long freght trans. However, ncreasng the length of exstng short sdngs s a more fundamental soluton for the growng number of long freght trans. Constructng addtonal sdngs wth suffcent length s also a soluton to facltate the long freght oeraton. The trade-off between extendng lengths of exstng sdngs and constructng new sdngs wth suffcent length could be very comlcated when the budget s lmted and alternatves are numerous. Ths study roosed an Otmal Project Selecton Model (OPSM) to hel the ralroad lanners select the most effectve combnaton of avalable rojects n order to maxmze the return from the nvestment of ralroads. Moreover, the develoed tool s demonstrated by a hyothetcal sngle-track scenaro n the case study. The result of case study also roved the benefts from oeraton of long freght trans. 1 INTRODUCTION The ntenton of long tran oeraton of ralroad ndustry as well as the assocated economc and oeraton effcency has been covered n a revous study. Newman et. al. [2] exlaned the economc and oeratonal benefts of longer unt trans on one Class 1 Ralroad. There s also a lterature done by Martland [3] whch stated the benefts of sdng extenson rojects. He ndcated the otental contrbutons of sdng extenson rojects by showng a conservatve estmaton that 2/3 of the unt trans n oeraton are lmted by the length assng sdngs. On the other hand, constructng addtonal sdngs wth suffcent length on the exstng sngle-track lnes can also facltate the oeraton of long freght trans. Ths strategy s used by at least one Class 1 ralroad to accommodate long tran oeraton and reduce traffc congeston [4]. Snce the overall budget avalable for nfrastructure mrovement s always lmted, a comrehensve lannng rocess to balance the nvestment allocated to each tye of rojects s an essental element to hel ralroads maxmze ther return from nvestment. Currently, ralroad ndustry n North Amercan reles on the exerenced racttoners to fnd the solutons for the nfrastructure constrants. Ths ales to the case to fnd soluton for long freght tran oeraton too. However, the exerenced racttoners can dentfy feasble and effectve nfrastructure rojects, but may not be able to consder all the related factors before determne an otmal selecton of rojects. In ths study, an Otmal Project Selecton Model (OPSM) s roosed to hel ralroad lanners determne the otmal selecton of avalable rojects under lmted budget. The result from OPSM, an otmal sdng constructon and extenson lan whch ndcates the otmal selecton of avalable rojects, can hel ral network to accommodate the oeraton of long freght trans. Ths can hel the ralroads to boost ther economc and oeraton effcency. Perth, Australa

2 Me-Cheng Shh Unversty of Illnos, Urbana-Chamagn Otmzng Locaton and Length of Passng Sdngs on Sngle-track Lnes For Long Heavy-Haul Freght Trans 2 PROBLEM DESCRIPTION Usng the mathematcal rogramng technues, OPSM focuses on the determnaton of the otmal sdng constructon and extenson lan. OPSM coordnates the deas of both caacty lannng and tran dsatchng models through a seres of constrants [6] to acheve ths goal. For the caacty lannng art, the nfrastructure constrants consder the constructon cost, length and the caacty of the sdngs [7]. In addton to the nfrastructure constrants, those related to oeraton ssues are consdered through traffc constrants. Traffc constrants guarantee the necessary headway between two adjacent trans [8] and take the effect of tran seed, length and commercal schedule nto consderaton. Fgure 1 below shows the concetual framework for OPSM together wth the nuts and oututs. The nut arameters of the otmzaton model are track nfrastructure roertes and traffc characterstcs. Based on the nut arameters, the feasble rojects wll be dentfed and the travel tme of each segment wll be calculated, these data wll then be use by the OPSM. OPSM follows the rncles mentoned to generate two tyes of outut (tran aths and an otmal sdng locaton lan) that deend on three cost categores (euvalent nvestment cost, meet and ass delay cost, and late dearture cost). Infrastructure roertes Inuts Traffc characterstcs Traffc characterstcs o Average seed of trans on manlne n each segment (mh) o Average seed of trans on each exstng and rosectve sdng (mh) o Scheduled dearture tme for trans (hr) o Lost tme er acceleraton and deceleraton (hr) o Safety headway for adjacent trans (hr) Infrastructure roertes are assocated wth the exstng track confguraton, grade, and curvature. Traffc characterstcs nclude the traffc mxture, tran seed, commercal schedule, and the lengths of trans. Moreover, the effect of grade and curvature can be consdered by adjustng the average seed of trans. OPSM uses these two dfferent tyes of data to generate an otmal sdng constructon and extenson lans. 3 NOTATION In ths study, the orgnal track confguraton and the relatve locatons of avalable rojects are reresented by three basc tyes of ndces. Fgure 2 below llustrates the relatonsh of these three tyes of ndces. In ths fgure, notaton reresents all the nodes, notaton stands for the segments between any two adjacent nodes, and notaton c ndcates the tye of sdngs. A more detaled notaton lst s dslayed n Table 2. Identfy feasble sdng constructon and extenson rojects Budget Constrant Tran aths Cost of late dearture Oututs Calculate segment travel tme Cost of meet and ass delay Otmal sdng constructon and extenson lan OPLM Fgure 1 : Concetual framework for OPSM The detals of the nut data are dslayed n the followng lst: Infrastructure roertes o Mleosts of sdng constructon or extenson rojects (mle) o Total length of manlne (mle) o Constructon costs assocated wth sdng constructon or extenson rojects (USD) o Locatons and lengths of exstng sdngs (mle) Fgure 2 : Illustraton of basc ndces Table 2 : Indces, sets and arameters used n OPSM Indces (, j) N (, r) P (, s) Q c C Sets b + b - κ ε (a) Indces and sets Descrton Indces referrng to trans runnng through the lne Indces reresentng sectons of the lne Indces stand for sdngs and statons (nodes) Index referrng to standards of sdng length (short or long) Descrton Set of any two trans wth same drecton Set of any two trans wth ooste drecton Set of exstng and rosectve sdng nodes Set of orgns to tran Perth, Australa

3 Me-Cheng Shh Unversty of Illnos, Urbana-Chamagn Otmzng Locaton and Length of Passng Sdngs on Sngle-track Lnes For Long Heavy-Haul Freght Trans Sets η + η - k ψ δ ϑ π Parameters β t f σ U,c g,c φ e + e - h j L c v W M Ε B (b) Sets and arameters Descrton Set of rosectve sdngs Set of exstng sdngs (otental objectve for extenson) Set of destnatons to the trans Set of short sdngs Set comosed of all secton and the adjacent node to enter the secton Set comosed of all secton and the adjacent nodes (, s ) Set of orgns and ther adjacent sectons Descrton Euvalent weght for nvestment cost Extra travellng tme for tran to across sdng than a arallel secton on manlne (hr) Lost tme due to an acceleraton and a deceleraton of tran (hr) Runnng tme of tran on segment Cost of constructng sdng wth tye c length standard (USD) The tye of standard length of the exstng sdng Locaton of exstng and rosectve sdngs (mleost) Earlest ossble dearture tme of tran (hr) Latest ossble dearture tme of tran (hr) Safety headway between adjacent tran abd j on secton (hr) Ablty for sdng wth tye c legnth standard to accommodate trans, eual to 1 f c s long sdng tye, 0 f short sdng tye Length standard of tran, eual to 1 f s a long tran, eual to 0 f s a short tran Delay cost, the cost generated by an dlng tranhour, t also reflects the rorty of tran An arbtrary bg number Total dsatchng duraton (hr) Avalable budget (USD) 4 MODEL FORMULATION Three basc tyes of decson varables are used n OPSM: tran tme varables, nfrastructure varables and tran dsatchng varables. Tran tme varables reresent the arrval and dearture tme of trans. Obtanng the values of tme varables s eual to obtanng the tran aths. D = dearture tme of tran at node A = arrval tme of tran at node y = tme for last tran to arrve ts destnaton The nfrastructure varables determne the selecton of feasble rojects. An otmal sdng constructon and extenson lan can be derved from the values of nfrastructure varables. z = eual to 1 f sdng s n the standard length of tye c Tran dsatchng varables are used to ensure the logc behnd tran dsatchng mechansm n OPSM. x j = eual to 1 f tran assng through segment before tran j, 0 otherwse o = eual to 1 f tran stays on sdng durng the dsatchng erod, 0 otherwse θ j = eual to 1 f and only f tran stays on sdng before tran j, 0 otherwse Euaton (1) shows the objectve functon of OPSM. It mnmzes the total cost durng the lannng horzon, whch ncludes euvalent nvestment cost, meet and ass delay cost, and the late dearture cost. The euvalent weght β for nvestment cost can be determned by followng the rncle mentoned n the study by La and Barkan [9]. Snce W s the delay cost for dfferent tye of trans, the dsatchng result could reflect the busness objectves of North Amercan ralroads [10]. Objectve: Mn U ( z g ) N N cc W ( D A ) W D ( e ) (1) Ths objectve s subject to a set of constrants (euatons (2)~(24)), ncludng dsatchng constrants, commercal schedule constrants, sdng length and caacty constrants, track confguraton constrants and envronmental constrants. The tran dsatchng constrants mantan a reasonable logc of the tran dsatchng rocess. They are shown n euatons (2) to (7). The basc rncle followed by ths tye of constrant to dsatch trans s to ensure a reasonable headway between any two adjacent trans. Euatons (2) and (4) mantan a headway between the dearture tmes of any adjacent trans toward the same drecton and euatons (3) and (5) mantan a headway between the arrval tmes of any two adjacent trans. Euatons (6) and (7) guarantee the headway between two adjacent trans n ooste drectons. M(1 x ) D D h j j j (, j) b, j,, P (2) M(1 x ) A A h j j j (, j) b, j,, P (3) Mx D D h j j j Perth, Australa

4 Me-Cheng Shh Unversty of Illnos, Urbana-Chamagn Otmzng Locaton and Length of Passng Sdngs on Sngle-track Lnes For Long Heavy-Haul Freght Trans (, j) b, j,, P (4) Mx A A h j j j (, j) b, j,, P (5) M(1 x ) D A h j j j (, j) b, j,, P (6) Mx D A h j j j (, j) b, j,, P (7) Based on the commercal freght tran schedule, euaton (8) enforces that trans deart from the orgn before ther latest allowable tmes. e D e N, (8) Euatons (9) to (14) are sdng length and caacty constrants. Euaton (9) ensures that a dwell of a tran lnk to varable o. Euatons (10) and (11) dentfy the stong seuence of trans on the same sdng. Euaton (12) hels elmnate all ossble conflcts between two trans on the same sdng. Euaton (13) s the sdng length constrant. It forbds a tran to use a sdng f the length of the tran s longer than the standard length of the tye of the sdng. Euaton (14) catures the extra travel tme exerenced by trans due to acceleraton, deceleraton, sdng seed lmt whle travelng on sdngs. Mo D A N, Q (9) o o x 2 j j j N, j N, j,, P (10) 3 j o oj xj N, j N, j,, P (11) A D h M(1 ) j j j N, j N, j, { }, P (12) v o c ( L z g ) N, (13) cc D A o ( f t ) N, Q (14) The followng constrants are the track confguraton constrants. Euaton (15) mantans the lengths of the orgnal long sdngs. Euaton (18) mantans the locaton of exstng sdngs at ther orgnal locatons. Euaton (16) revents trans from meetng or assng at a non-exstng sdng. Euaton (17) ensures that a rosectve sdng can only has one tye and euaton (18) ensures the model to select one tye for all resent sdngs. Moreover, snce the current sdng constructon rojects are usually desgned as long sdng tye. Euaton (19) enforces the tye of new constructed sdngs to be long sdng. The reason to have ths constrant s because long sdng s the new standard length of new constructed sdngs n North Amercan. cc N cc c c v g v z Q (15) cc o M z Q (16) cc z 1 z 1 cc z 0 c (17) (18) (19) Euaton (20) s the budget constrant. Euaton (21) ensures OSLM to comlete the dsatchng rocess wthn a tme erod. Euaton (22) fxes the tran runnng tme between any two adjacent nodes as average tran runnng tme along the secton. c cc U z B (20) A E N k (21), s A D N, (, s), P (22) 5 CASE STUDY The use of OPSM s demonstrated n a hyothetcal case (Fgure 3) n the case study. It s a 100 mles long sngle-track lne wth 5 exstng short sdngs for sdng extenson rojects and 4 locatons of rosectve sdng rojects. There s a 20 mle sacng between any two exstng and adjacent sdngs. Furthermore, the dstance between an exstng sdng and a rosectve sdng roject s 10 mles. The result of ths case study not only show the caablty of the tool to determne an otmal sdng constructon and extenson lan, but dslay the otental benefts of usng long freght trans. Perth, Australa

5 Me-Cheng Shh Unversty of Illnos, Urbana-Chamagn Otmzng Locaton and Length of Passng Sdngs on Sngle-track Lnes For Long Heavy-Haul Freght Trans 1 20 mle sdng sacng between the 2 exstng short sdngs e Adjacent termnals New sdng rojects (locaton for new sdngs) Exstng short sdngs, canddate for extenson rojects Fgure 3 : Hyothetcal case used n the case study The values of the mortant arameters used n the case study are lsted n Table 3. The rorty of freght trans denoted by delay cost, s set accordng to Dngler [10]. These arameters n Table 3 reflect the advantages and dsadvantages of short and long tran oeratons. Long tran oeraton reures fewer trans to fulfl the traffc demand, but decreases the average tran seed. Short tran oeraton need to run more trans to fulfl the demand, but the average tran seed s hgher than the long trans. Parameter Tran length (car) Average tran seed (mh) Total traffc demand er day (car) Prorty of trans (delay cost er hr, n USD) Commercal schedule Maxmum track seed Table 3 : Inut arameters Safety headway between two trans Value Short freght trans: 100 cars Long freght trans: 150 cars Short freght trans: 40 mh Long freght trans: 32 mh 1200 cars er drecton Short freght trans: 586 USD/hr Long freght trans: 879 USD/hr (1.5 tmes as short trans) The dearture tmes of the trans are evenly dstrbuted n 20 hours 40 mh 6 mn Plannng horzon 5 years To evaluate the effect of dfferent traffc mxture of short and long freght trans, four traffc scenaros were tested. The detals are lsted below, noted that the total number of cars through the manlne mantans the same (1200 cars n total) n all scenaros. Scenaro 1: 9 short trans, 0 long trans Scenaro 2: 6 short trans, 2 long trans Scenaro 3: 3 short trans, 4 long trans Scenaro 4: 0 short trans, 6 long trans OPSM was coded nto GAMS and solved by CPLEX. Deendng on the scenaros, the number of varables ranges from 3,500 to 7,000, the number of euatons ranges from 10,500~20,400, s and the soluton tme ranges from 1 to 3 hours. Two tyes of oututs were generated from OPSM: the tran dsatchng result and the otmal sdng constructon and extenson lan. Fgure 4 shows the tran dsatchng result of scenaro three as an examle. Snce there are no conflcts, the tran dsatchng mechansm n OPSM s logcally reasonable. Hours Mleost (mle) Long trans Short trans Fgure 4 : Traffc dsatchng result Table 4 s the otmal sdng constructon and extenson lans for all scenaros. It shows that the ncrease n rato of long tran n traffc decreases the number of sdng constructon rojects and ncreases the number of sdng extenson rojects. An exlanaton for ths fact s that long tran oeraton reures the exstence of long sdngs to execute meet and ass rocess. Also, the use of long trans decreases the number of trans that needs to be dsatched er day. The orgnal track confguraton wth some sdng extenson rojects s caable enough to handle the traffc under ths crcumstances. Table 4 : Otmal sdng constructon and extenson lans Scenaros Selected sdng constructon rojects Selected sdng extenson rojects Total nvestment cost (mllon 1 6, , 5, , 5, Fgure 5 shows the euvalent nvestment cost, delay cost and total cost of all scenaros. For all scenaros, the total cost s less f the rato of long trans s ncreased. Ths roves that the oeraton of long trans hels save the catal nvestment and reduces the total traffc delay. For ths reason, the benefts of the long freght tran oeraton are further strengthened. Perth, Australa

6 Me-Cheng Shh Unversty of Illnos, Urbana-Chamagn Otmzng Locaton and Length of Passng Sdngs on Sngle-track Lnes For Long Heavy-Haul Freght Trans Mllon USD Scenaros Total delay cost (m. USD) Euvalent Investment Cost (m. USD) Fgure 5 : Euvalent nvestment, delay, and total cost n all scenaros 6 CONCLUSION The use of longer freght trans benefts both economcal and oeratonal effcences. However, the oeraton of long freght trans s constraned by the length of exstng sdngs. Ralroads rely on the exerenced racttoners to dentfy some effectve and feasble rojects as the solutons but may not be able to select the otmal collecton of the solutons to solve the roblems. Snce human decson may not fully evaluate all the related factors whle selectng the rojects that need to be conducted, ths study resents an OPSM to hel ralroads determne the otmal sdng constructon and extenson lan. A case study was used to demonstrate the ablty of OPSM. Result from the case study ndcates that the ncrease n use of long freght trans can reduce nvestment and delay cost thus can hel the ralroads to maxmze ther return from nvestment and enhance the freght servce ualty. 7 REFERENCES [1.] Atanassov I, Dck CT. Caacty of Sngle- Track Ralway Lnes wth Short Sdngs to Suort Oeraton of Long Freght Trans. In: Proceedng of Transortaton Research Board [2.] Newman RR, Zarembsk AM. and Resor RR. Economc mlcatons of heavy axle loads on eument desgn oeratons and mantenance, In: Proceedngs of the Amercan Socety of Mechancal Engneerng, WAM, 1991; 4. [3.] Martland CD. Introducton of Heavy Axle Loads By the North Amercan Ral Industry. Journal of the Transortaton Research Forum. 2013; 52(2): [4.] Canadan Natonal Ralway (CN). BCNL Long Sdng Reurements, [5.] Shh MC, La YC, Dck CT, and Wu MH. Otmzaton of Sdng Locaton for Sngletrack Lnes. Acceted In Trans Res Rec, [6.] Ahuja RK, Magnant TL, and Orln JB. Network Flows: Theory, Algorthms, and Alcatons. Prentce Hall, New Jersey, 1993 [7.] Qang LS, and Kozan E. Schedulng Trans As a Blockng Parallel-machne Job Sho Schedulng Problem. Comuters & Oeratons Research. 2009; 36(10): [8.] Jaumard B, Le TH, Tan H, Akgunduz A, and Fnne P. An Enhanced Otmzaton Model for Schedulng Freght Trans. Proceedng of the 2013 Jont Ral Conference, Knoxvlle, 2013 [9.] La YCR, and Barkan CPL. Comrehensve decson suort framework for strategc ralway caacty lannng. J Trans Eng. 2011; 137(10): [10.] Dngler MH, La YCR, and Barkan CPL. Mtgatng tran-tye heterogenety on a sngle-track lne. Proc Inst Mech Eng F. 2013; 227( 2): Perth, Australa