Enhanced Parametric Railway Capacity Evaluation Tool

Enhanced Parametrc Ralway Capacty Evaluaton Tool Yung-Cheng (Rex) La and Chrstopher P. L. Barkan Many ralroad lnes are approachng the lmts of practcal capacty, and estmated future demand s projected to ncrease 84% by 2035. Therefore, dentfyng a good multyear capacty expanson plan has become a partcularly tmely and mportant objectve for ralroads. An enhanced parametrc capacty evaluaton tool has been developed to assst ralroad companes n capacty expanson projects. Ths evaluaton tool s bult on the Canadan Natonal Ralway Company parametrc model by ncorporatng enumeraton, cost estmaton, and mpact analyss modules. Based on the subdvson characterstcs, estmated future demand, and avalable budget, the proposed tool wll automatcally generate possble expanson alternatves, compute lne capacty and nvestment costs, and evaluate ther mpact. For a partcular subdvson, there are two outputs from ths decson support tool: a plot that depcts the delay volume relatonshp for each alternatve and an mpact and beneft table that shows the mpact of the future demand on the subdvson wth dfferent upgradng alternatves. The decson support tool s hghly benefcal for budget management of North Amercan ralroads. Ralways all over the world are ncreasngly experencng capacty constrants. In North Amerca, ralway freght traffc has ncreased nearly 30% over the past 0 years, and ths demand s projected to ncrease another 84% by 2035 (). Ths growth n demand would not be as sgnfcant f alternatve modes were able to handle the traffc, but hghway constructon s not keepng up wth the growth n demand ether. Even f the capacty were avalable, much ral traffc cannot be economcally transported by truck. Ral s also generally recognzed as safer and more effcent n terms of land use and energy effcency. Therefore, publc offcals ncreasngly see ral as an alternatve transport mode needed to handle the ncreasng freght traffc that wll accompany sustaned economc growth (, 2). Effectve capacty management s the key to a ralroad company s success, but t s not a trval task. On the one hand, capacty planners work on multyear capacty plannng projects amng to provde enough network capacty to accommodate customers future demand at a desred servce level; on the other hand, they must try to maxmze the use of assets (trackage and related nfrastructure) because overcapacty may be as harmful as nsuffcent capacty to company Y.-C. La, Department of Cvl Engneerng, Natonal Tawan Unversty, Room 33, Cvl Engneerng Buldng, Number, Roosevelt Road, Secton 4, Tape, Tawan, 067. C. P. L. Barkan, Department of Cvl and Envronmental Engneerng, Unversty of Illnos at Urbana Champagn, 203 Newmark Cvl Engneerng Laboratory, 205 North Mathews Avenue, Urbana, IL 680. Correspondng author: Y.-C. La, ycla@ntu.edu.tw. Transportaton Research Record: Journal of the Transportaton Research Board, No. 27, Transportaton Research Board of the Natonal Academes, Washngton, D.C., 2009, pp. 33 40. DOI: 0.34/27-05 performance. The frst step n capacty management s usually measurng and montorng capacty and congeston; however, ralway capacty s a loosely defned term that has numerous meanngs. In general, t can be stated as a measure of the ablty to move a specfc amount of traffc over a defned ral lne wth a gven set of resources under a specfc servce plan, known as level of servce (LOS). Ths capacty s hghly dependent on a number of nfrastructure and operatonal factors (3, 4), such as Length of subdvson; Sdng length, spacng, and unformty; Intermedate sgnal spacng; Percentage of sngle, double, or multple track; Peak tran counts; Average and varablty n operatng speed; Heterogenety n tran types (tran length, power-to-weght ratos); Dspatchng prortes; and Schedule. Numerous approaches and tools have been developed to determne ral lne capacty; however, unlke the hghway capacty analyss doman, there s no commonly accepted standard for ralway capacty measurement n North Amerca (5). Each model has ts strengths and weaknesses and s generally desgned for a specfc type of analyss (6). Ralway capacty tools can be categorzed nto three groups: theoretcal, smulaton, and parametrc. In general, smulaton s best suted to analyss of local problems because t becomes computatonally ntensve when appled at the network level. Theoretcal models can often be computed manually but are sometmes too smple to be vald for anythng more than hgh-level comparsons. Parametrc capacty models fll the gap between detaled smulaton and smple formulas; they focus on key elements of lne capacty to quckly hghlght bottlenecks n the system (3). Parametrc models are sutable for strategc capacty plannng because they can account for the dynamc nature of lne capacty and provde systemwde capacty measurement of subdvsons n a ral network. Two parametrc ralway capacty models have been developed to help capacty planners manage track assets by measurng track capacty. Prokopy and Rubn (7) developed the frst parametrc model for ralway lne capacty. Ther model uses formulas that reflect tran delay or capacty as a functon of physcal plant tran operatons and control systems, whch were derved through multvarable regresson analyss of many dfferent smulaton runs usng the Peat Marwck Mtchell model. Krueger (3) appled a smlar method to develop the Canadan Natonal Ralway Company (CN) parametrc lne capacty model; however, hs model was new wth dfferent parameters. Smulatons were conducted usng an n-house tool, the route capacty model (RCM), to develop the CN parametrc model. 33

34 Transportaton Research Record 27 The three most mportant elements of the CN parametrc model that make t partcularly useful are (a) the ablty to calbrate each parameter for partcular scenaros; (b) the ablty to produce a graphcal delay versus volume relatonshp; and (c) a what-f ablty to quantfy the senstvty to and sgnfcance of parameters ndvdually and n combnaton. However, t does not have the ablty to create possble alternatves, estmate the constructon cost, and evaluate the trade-offs among captal nvestment, delay, and operatng costs. Thus, there s ncentve to develop an enhanced parametrc capacty evaluaton tool that ncorporates these features. Consequently, the authors have developed a new decson support model, the Ralway Capacty Evaluaton Tool (RCET), whch bult upon the CN parametrc model by ncorporatng enumeraton, cost estmaton, and mpact analyss modules. On the bass of subdvson characterstcs, estmated future demand, and avalable budget, RCET s able to help capacty planners generate possble expanson alternatves, compute lne capacty and nvestment costs, and evaluate ther mpact. ENHANCED PARAMETRIC CAPACITY EVALUATION TOOL Fgure shows the decson support process usng RCET. By nputtng the lnk propertes, avalable budget, and estmated future demand, RCET wll frst enumerate possble expanson alternatves (enumeraton module), and then compute the cost and capacty ncrease for each alternatve (cost and capacty evaluaton module), followed by evaluaton of the trade-off between captal nvestment and delay cost to determne f each partcular captal nvestment s cost-effectve (mpact analyss module). The outputs of RCET wll be a graph showng relatonshp between traffc volume and delay for each alternatve, and an mpact and beneft table contanng a set of optons that the capacty planner can use to gude decson makng. One of the most mportant components of RCET s the CN parametrc model, whch s located n the cost and capacty evaluaton module and s used to determne the delay volume relatonshp and lne capacty. In the followng sectons, the CN parametrc model s revewed, and then the three RCET modules are descrbed. Revew of CN Parametrc Model The CN parametrc model (3) provdes a systemwde measure of subdvson capacty n a ral network and enables evaluaton of the effect of mprovements for varous alternatves. The model measures the capacty of a subdvson by predctng ts relatonshp between tran delay (hours per trp) and traffc volume (trans per day). In general, the more trans that run on a subdvson n a gven tme perod, the more delay each tran experences (7). The CN model calculates ths relatonshp usng several key parameters that affect the traffc handlng capablty of a subdvson. These parameters are categorzed nto plant, traffc, and operatng parameters. Plant Parameters Length of subdvson (SL) Meet and pass plannng pont spacng (MPPPS). MPPPS s the mean spacng of locatons used to meet or overtake trans, namely sdng spacng. Sdngs are crucal for operatng bdrectonal, mxed prorty, and dfferent speed trans. MPPPS for a subdvson s computed as MPPPS = Meet and pass plannng pont unformty (MPPPU). MPPPU s the measure of unformty n sdng spacng (MPPPS). It s a rato of the standard devaton versus average sdng spacng: SD of MPPPS MPPPU = MPPPS A unformty value of zero represents a subdvson wth equally dstrbuted sdngs. In general, the hgher the unformty of sdng spacng, the more the lne capacty. Intermedate sgnal spacng rato (ISSR). Intermedate sgnals reduce the requred headway between adjacent trans, thereby ncreasng lne capacty. Ths parameter accounts for the rato of sgnal spacng to sdng spacng. The parametrc expresson for ISSR s ISSR = SL number of MPPP + ( ) SL MPPP + + no. of sgnals 00 MPPPS Percent double track (%DT). Addng a second track has a sgnfcant mpact on lne capacty (more than double the capacty of a sngle track manlne). %DT s calculated as the rato of double track versus SL: mles of double track %DT= 00 SL Lnk (sub) Propertes Budget Estmated Demand Alternatves Enumeraton Cost & Capacty Computaton Ralway Capacty Evaluaton Tool (RCET) Impact Analyss Delay-Volume Relatonshp Impact & Beneft Table FIGURE Decson support process usng RCET.

La and Barkan 35 The CN parametrc model can handle %DT up to 75%; ths lmt was found to retan the exponental characterstcs and fall wthn the parametrc range of most of CN s subdvsons. Traffc Parameters Traffc peakng factor (TPF). TPF represents the concentraton of traffc wthn a short tme frame (4 h), often called bunchng or peakng. It has a sgnfcant mpact on capacty, because when the traffc level s greater than the sustanable capacty, t causes lengthy system recovery tme. TPF s calculated as the rato between the maxmum number of trans dspatched n a 4-h perod versus the average number of trans wthn the same tme duraton. maxmum trans n 4 h TPF = average trans n 4h Dspatchng prorty factor (DPF). Dspatchng prortes for dfferent types of trans dctate whch trans wll experence delay. Hgher prorty reduces transt tme for hgher-prorty trans by penalzng trans of lower prorty. Generally the greater the number of prorty classes, the less capacty s avalable. DPF s quantfed usng a probablty functon that calculates the chances of a tran meetng another tran of a hgher prorty, whch s calculated as DPF = T where N = number of prorty classes (passenger, express, freght, and unt), T = daly number of trans, C = number of th prorty class trans, and C j = number of jth prorty class trans. Speed rato (SR). Besdes DPF, SR s another parameter reflectng the traffc mx over the subdvson. The dfference n speed among trans can sgnfcantly ncrease delay because of overtakes, trans beng held n the yard, or both. SR s calculated as the rato of the fastest tran speed to the slowest tran speed: SR faster tran speed = slowest tran speed Average speed (AS). Average tran speed plays a vtal role n lne capacty because the hgher the tran speed the lower the delay and transt tme. AS s measured as the average mnmum run tme of all trans n each drecton, as obtaned from a tran performance calculator. N AS = = N t= N = 2 nv n C ( T ) j= C j where V = speed of th class, n = number of trans n th class, and N = total number of classes. Operatng Parameters Track outage (TO). Track outage accounts for the planned and unplanned events that take a track out of servce. TO drectly reduces the avalable servce tme of a subdvson as well as lne capacty. Capacty s senstve to the occurrence and duraton of TO. Ths parameter s defned as the number of hours the subdvson s out of servce: total duraton of outages TO = N t = nd where n T s the total number of outages per day and d s the duraton of each outage (h). Temporary slow order (TSO). TSO has a negatve mpact on lne capacty because of the tme loss from operatng at slower than normal speed, and acceleraton and deceleraton tme (V tme ). It s often mantenance related and can be appled to a dstance or at a sngle pont on the lne. TSO s computed as follows: TSO = V + travel tme V tme tme ( ) + ( ) VK m V = A TSO L L travel tme = + V 60 TSO VK m where V m = maxmum freght speed (mph), V TSO = TSO speed (mph), K = % of tme runnng at max speed (85%), A = acceleraton rate (20 mph/mn), D = deceleraton rate (30 mph/mn), and L = length of TSO + average tran length. The relatonshps between the delay volume curve and key parameters were developed on the bass of a seres of regresson analyses and smulaton results from the RCM. The relatonshp between tran delay and traffc volume was found to be best expressed by the followng exponental equaton: BV tran delay = Ae o o T VK m V D TSO where A o = parametrc plant, traffc, operatng coeffcent, B o = constant, and V = traffc volume (trans/day). Coeffcent A o depcts the relatonshp between tran delay and the parametrc values. A o s a unque value for each combnaton of parameters defned by the plant, traffc, and operatng condtons of a subdvson. A dfferent A o wll defne a new delay versus volume curve (Fgure 2). Ths parametrc model was verfed by comparng ts output wth the RCM output of the CN network, and the results show that the accuracy was on average wthn 0% (3). The followng three sectons cover the development of the three modules (enumeraton, cost and capacty evaluaton, and mpact analyss) n RCET.

36 Transportaton Research Record 27 FIGURE 2 Delay volume curve from CN parametrc model (3). Enumeraton Module The purpose of the enumeraton module s to automatcally generate conventonal capacty expanson alternatves for each subdvson beng evaluated. In the model descrbed here, three common types of capacty expanson alternatves are bult nto ths module addng passng sdngs, ntermedate sgnals, or a second man track but other optons could be ncluded f desred. For the sngle-track scenaro, ncreasng the number of sdngs can reduce meet and pass delay, and shortenng block length and the consequent decrease n sgnal spacng can reduce the headway between trans, thereby ncreasng lne capacty. Beyond that, accordng to Rolln Bredenberg, Vce Presdent of Servce Desgn at Burlngton Northern Santa Fe Ralway, f the combned total number of trans n both drectons averages 60 trans per day wth a peak of 75, double track must be added to sngle-track segments (4, 8). For each subdvson, the enumeraton module calculates all possble combnatons of expanson alternatves untl t reaches the lmt of mnmum sdng spacng or maxmum number of sgnals per spacng specfed by the user. For example, consder a 00-m subdvson wth centralzed traffc control (CTC), nne exstng sdngs, and no ntermedate sgnals. The mnmum sdng spacng s set to 8 m and the maxmum number of ntermedate sgnals between sdngs s two. The largest number of sdngs that can be placed on ths subdvson s ( 00/8 ), and the largest number of ntermedate sgnals that can be placed (between two sdngs) s two. Table shows the possble alternatves for ths example ordered by ascendng constructon cost. Snce addng sgnals s usually less expensve than addng sdngs, these are consdered frst (up to the lmt) before addng another sdng; therefore, the frst and second alternatve for each sgnal spacng s to ncrease the number of ntermedate sgnals by one and by two, respectvely. Because two ntermedate sgnals s the upper bound for the sdng spacng consdered n ths example, the next (thrd) alternatve s to ncrease the number of sdngs (by one). Cost and Capacty Evaluaton Module After the enumeraton, the next step s to determne the capacty ncrease and constructon cost of each alternatve (Fgure ). For each subdvson, the cost and capacty evaluaton module wll frst compute the current lne capacty on the bass of the exstng parameters. Capacty planners usually have an dea of the current lne capacty based on emprcal experence. These emprcal values can be used to determne the current LOS by adjustng the acceptable delay to match the capacty values from the delay volume relatonshp. If emprcal values are not avalable, the default settng s to use the maxmum trp tme of 0 h or an acceptable delay of 2 h to calculate the capacty (Fgure 2) (3). Users can specfy ther own sutable lmts, dependng on the context. After obtanng the base case (current condton), the cost and capacty evaluaton module wll then compute the capacty ncrease of each alternatve by changng the plant parameters (e.g., MPPPS and ISSR), assumng the traffc and operatng parameters reman the same. The CN parametrc model cannot handle subdvsons wth %DT more than 75%; consequently, the authors assgned a capacty of 80 trans per day for a double-track segment, accordng to typcal freght ralroad practce (4, 8). The unt constructon cost of each type of expanson opton s needed to compute the cost of expanson alternatves. Users can specfy these values n advance or use the default cost estmates. TABLE Possble Capacty Expanson Alternatves for Hypothetcal 00-m Subdvson Alternatve Sdngs Sgnals Spacng + 0 + 0 2 + 0 + 3 + 0 + 2 4 + + 0 5 + + 6 + + 2 7 + 2 + 0 8 + 2 + 9 + 2 + 2 0 Addng 2nd man track

La and Barkan 37 Three requred basc unt costs are addng a new sdng, a new ntermedate sgnal, and a second man track. The default cost estmates are based on recent nformaton provded by ralroads and engneerng consultng companes. These values serve as the general average case consderng the need for new tracks, sgnals, and brdges, but do not nclude the cost of land acquston or envronment permttng. For a new 2,000-ft passng sdng, a cost of $4,870,000 for track work and cvl nfrastructure was assumed. For terrtory wth an exstng CTC sgnal system, the cost of sgnalzng a newly constructed sdng wthn ths terrtory would be $300,000 for each end of the sdng or $600,000 total. Therefore, the frst requred unt cost, addng a sgnalzed passng sdng, s $5,470,000. Wthn exstng CTC terrtory, the cost of a new ntermedate sgnal pont (.e., one sgnal n each drecton) s approxmately $00,000 (second requred unt cost). And the thrd requred unt cost, that of addng the second man track, s $2,250,000 per mle. Table 2 lsts the alternatves for the subdvson. Capacty planners would revew these alternatves durng the decson process and could remove nadequate alternatves or add addtonal ones accordng to ther experence and judgment. Both the enumeraton module and the cost and capacty evaluaton module can be combned and summarzed n the followng analytcal steps: Step. Obtan the followng nput data from exstng track condton or users: exstng number of sdngs and sgnals, lmt of sdng spacng (DL), and lmt of sgnal spacng (GL). Step 2: Use two loops to enumerate possble expanson alternatves and evaluate ther mpact: Loop (add addtonal sdngs from zero to DL) Loop 2 (add addtonal sgnals from zero to GL) Adjust CN parameters accordng to change(s) n sdngs and sgnals Develop the new delay volume curve for the expanson alternatve Compute the addtonal capacty and cost from the alternatve End of Loop 2 End of Loop Step 3. Create the expanson alternatves table (Table 2) Step 4. Overlap the delay volume curves for possble expanson alternatve (Fgure 3) Impact Analyss Module Based on Table 2, t s ntutve for capacty planners to select the alternatve provdng just enough capacty because ths opton requres the least expendture to meet the future demand f LOS s to reman the same. However, ths selecton may not be the best opton. Because capacty s defned by a partcular servce level, t s possble to run more trans per day f LOS s reduced. For example, n Fgure 4a, the sold exponental curve represents the general delay volume relatonshp for the exstng nfrastructure, whereas the dashed curve depcts the delay volume relatonshp wth upgraded nfrastructure. Wth the same LOS, the upgraded nfrastructure can provde more capacty than the exstng track. However, t s also possble to gan addtonal capacty by reducng the LOS (ncreasng delay) (Fgure 4b). Lne capacty s ncreased by ncreasng delay along the delay volume curve of the exstng nfrastructure. Consequently, an mpact analyss s essental to fnd the best opton to upgrade the nfrastructure. The mpact analyss module evaluates whether the captal nvestment s cost-effectve by comparng the delay cost to the captal nvestment. The delay cost depends on the mpact of addng addtonal demand to the exstng track layout wthout upgradng the nfrastructure. Accordng to the new demand for each lnk, the ncrease n delay can be determned usng the delay volume curve (Fgure 4b). The delay cost can then be computed as the product of total delay hours, and unt delay cost per hour. From an operatonal pont of vew, the unt delay cost can be calculated by summng four components: unproductve locomotve cost, dlng fuel cost, ral car and equpment cost, and crew cost. A recent estmate of delay cost for one Class ralroad s approxmately $26 per tran hour (9). Ths estmaton s conservatve because a more comprehensve delay calculaton would nclude downstream costs of mssed connectons, loss of future revenue, extra costs from mssng just-n-tme servces, and the lke. The captal nvestment of each alternatve s the output of the cost estmaton module. To compare delay cost and captal nvestment n the same duraton base (year), the authors further defned an attrbute, annual net nvestment, as the total constructon cost of the alternatve (Table 2) dvded by the nfrastructure lfe ( 20 years). It s based on the lfe-cycle cost analyss method commonly used for multyear capacty plannng projects (0 4). Fnally, the alternatves were ranked on the bass of the beneft as defned by annual delay cost dvded by the annual net nvestment cost. Beneft s smlar to TABLE 2 Expanson Alternatves wth Constructon Cost and Capacty Increase Sgnals Capacty Cost/ Alternatve Sdngs Spacng (trans/day) Cost ($) Tran ($) +0 +0 +0 0 0 2 +0 + +3,000,000 333,000 3 +0 +2 +4 2,000,000 500,000 4 + +0 +3 5,470,000,823,000 5 + + +6 6,570,000,095,000 6 + +2 +7 7,670,000,096,000 7 +2 +0 +6 0,940,000,823,000 8 +2 + +9 2,40,000,349,000 9 +2 +2 +0 3,340,000,334,000 0 Addng 2nd man track +50 204,750,000 4,095,000

38 Transportaton Research Record 27 6 Alt 5 Alt 2 Alt 3 Alt 4 Delay (hours) 4 3 2 Alt 5 Alt 6 Alt 7 Alt 8 Alt 9 0 0 0 20 30 40 50 Volume (trans/day) FIGURE 3 Delay volume plot from RCET. the dea of return on nvestment, representng how much delay cost can be reduced per unt nvestment n the nfrastructure. A beneft value less than one means the nvestment s not cost-effectve because the return on nvestment s negatve. The output of the mpact analyss module s a table showng the constructon cost, delay cost, and beneft for each lnk subject to capacty expanson. Ths expanson beneft table can be provded to capacty planners for use n decson makng. Followng s a summary of the analytcal steps n the mpact analyss module: Step. Obtan captal nvestment and delay volume relatonshp for each alternatve from cost and capacty evaluaton module. Step 2. Based on the estmated future demand (number of trans), determne the average delay for each alternatve usng the delay volume relatonshp. Step 3. Compute the followng attrbutes for each alternatve: Total delay = the product of average delay and number of trans, Reduced delay = the dfference between ts total delay and the total delay of Alternatve (do-nothng scenaro), Delay (hours) Current LOS Volume (trans/day) (a) Delay (hours) Current LOS Volume (trans/day) (b) FIGURE 4 Increase n volume by (a) upgradng nfrastructure and (b) lowerng LOS. Annual delay savng = the product of reduced delay and 365 (days per year), Annual net nvestment = captal nvestment dvded by 20 (nfrastructure lfe), and Beneft = annual delay savng dvded by annual net nvestment. Step 4. Generate the mpact and beneft table by rankng alternatves by ther beneft. EMPIRICAL APPLICATION To demonstrate the potental use of the capacty evaluaton tool, the same subdvson descrbed above (00 m, nne sdngs, no ntermedate sgnals) was analyzed. The lst below summarzes the subdvson s key parameters computed based on ts track and traffc characterstcs: SL: 00 m, MPPPS: 20, MPPPU: 0.3, ISSR:, %DT: 0.04, TPF:.62, DPF: 0.344, SR:.44, AS: 30 mph, TO: 0, and TSO: 0. For ths applcaton, the subdvson s current capacty s about 30 trans per day, and the estmated future demand s 37 trans per day, so the queston s how to ncrease capacty by seven trans per day.

La and Barkan 39 Accordng to the nput data lsted above, RCET generates possble expanson alternatves by addng sdngs or ntermedate sgnals wth ther ncreases n capacty and constructon cost (Table 2). Wth the same LOS, Alternatve 6 s the best opton because t s able to accommodate seven more trans per day wth the least constructon cost. However, t s also possble to gan addtonal capacty by reducng the LOS (ncreasng delay) (Fgure 4b). To dentfy the true optmal soluton, an mpact analyss was conducted of possble alternatves (Alternatves 9). The double track opton (Alternatve 0) s gnored here because of the large dfference between demand and supply. Delay Volume Plot The frst output of RCET s the delay volume plot representng the mpact on capacty for each alternatve (Fgure 3). Snce each alternatve represents a specfc nfrastructure settng, t can be depcted by a unque delay volume relatonshp. The delay volume plot helps users determne the addtonal capacty provded by each alternatve wth a specfc LOS (acceptable delay). It also demonstrates what the capacty wll be f the threshold for acceptable LOS s ncreased or decreased. For example, the capacty of Alternatve s 30 trans per day wth a 2-h average delay, 7 trans per day wth -h delay, and 38 trans per day wth 3-h average delay. Among the dfferent alternatves, the larger the dfference between two alternatves, the greater the dfference n capacty performance wll be. For nstance, there s a substantal dfference between Alternatve and the other alternatves, whereas the dfference n capacty between Alternatves 2 and 4 s neglgble. Impact and Beneft Table The second output of RCET s the mpact and beneft table (Table 3) created from the mpact analyss module. For each alternatve, average delay s obtaned accordng to ts delay volume relatonshp. Alternatve s the base case scenaro representng the current track layout; therefore, the reduced delay of each alternatve s computed as the dfference between ts total delay and that of Alternatve. The annual delay savngs s the product of reduced delay and number of days per year. Fnally, alternatves are ranked by ther beneft, whch s calculated by dvdng annual delay savngs by annual net nvestment. Table 3 provdes assstance to capacty planners n decson makng based on avalable budget. In ths example, Alternatve 2 provdes the greatest beneft because t offers substantal delay reducton wth relatvely lower expense compared wth the other alternatves. However, Alternatve 2 stll may not be acceptable because the average delay s 25% below the desred LOS. The dfferences n both beneft and average delay n Alternatves 5 and 6 are relatvely small, so the decson maker may choose Alternatve 5 to reduce captal expendtures. DISCUSSION OF NETWORK ANALYSIS An example of usng RCET to generate alternatves, compute cost and capacty, and analyze mpact of a studed subdvson s presented n ths paper. RCET can effcently process a subdvson wthn seconds, so ths applcaton can be expanded to the network level f necessary. For each subdvson n the studed network, the new capacty evaluaton tool wll produce a delay volume plot and an mpact and beneft table, whch capacty planners can use to evaluate possble alternatves and dentfy the best opton at the subdvson level. After completng ths process for all subdvsons, planners need to conduct traffc assgnment agan because the network traffc pattern (.e., route selectons of trans) after the capacty expanson may dffer from the orgnal plan. Routng the traffc wll assess the fludty of the proposed system. A possble routng technque would be a multcommodty flow network model (5) that can be formulated as follows: mnmze transportaton cost + mantenance of way cost, subject to capacty constrant for each subdvson and flow conservaton constrant for each node n the network. The objectve functon n the optmzaton model s to mnmze the expendtures requred to route traffc between varous orgns and destnatons. It s subject to lne capacty constrants such that the total traffc on a subdvson must be less than or equal to ts desgned capacty. The flow conservaton constrant guarantees that the fnal routng plan fulflls the estmated future demand. The goal of a multyear capacty plannng project should be to accommodate the estmated future demand whle mnmzng net present value of the captal expendture plus operatng costs due to transportaton, mantenance of way, and delay costs. Because ths procedure s a two-level process, t may take multple teratons to reach the system optmum. TABLE 3 Impact and Beneft Table from Upgradng Infrastructure Annual Net Average Delay Total Delay Reduced Delay Annual Delay Investment Alternatve (hours/tran/day) (hours/day) (hours/day) Savngs ($/year) ($/year) Beneft 2.8 04 0 0 0 N/A b 2 2.5 93,057,442 50,000 2. 3 2.3 85 9,762,403 00,000 7.6 5 2. 78 26 2,467,364 328,500 7.5 6 2 a 74 30 2,89,844 383,500 7.4 9.7 63 4 3,877,286 667,000 5.8 8.8 67 37 3,524,805 607,000 5.8 4 2.4 89 5,409,922 273,500 5.2 7 2. 78 26 2,467,364 547,000 4.5 a Current LOS = acceptable delay. b N/A = not applcable.

40 Transportaton Research Record 27 CONCLUSION AND FUTURE WORK Many ralroad lnes are approachng the lmts of ther practcal capacty; therefore, dentfyng optmal multyear capacty expanson plans have become a partcularly tmely and mportant objectve for ralroads. The CN parametrc model used n ths analyss accounts for the dynamc nature of capacty and provdes a systemwde measure of subdvsons n a ral network. However, a lmtaton of the current verson s that t s desgned for a sngle-track network. It does not take nto account multple-track scenaros (e.g., crossovers) or other dfferent operatonal practces (e.g., drectonal runnng). In addton to dentfyng areas of lmted or excess capacty, capacty tools serve as the baselne evaluaton nstrument for many other complcated optmzaton models, such as ralway schedulng optmzaton tools for solvng tran, crew, and locomotve schedulng problems. The better the user can assgn the rght capacty value, the better the optmal plan can be created from those tools. RCET can assst capacty planners n developng such plans. RCET accounts for network characterstcs, estmated future demand, and avalable budget, and automatcally generates expanson alternatves, computes ther lne capacty benefts and nvestment costs, and compares ther mpact. Ths decson support tool can be used to maxmze the capacty benefts that North Amercan ralroads wll derve from ther nvestment. Besdes use n the prvate sector, ths capacty evaluaton tool can also be useful to publc agences, helpng them set regonal or natonal transportaton prortes and nvestment plans. Therefore, the authors plan to develop a standard, comprehensve ralway parametrc capacty model. Such a model could assst publc and prvate fnancng of ral capacty nvestment by determnng the magntude, cost, and type of capacty mprovements needed for the desred servces. ACKNOWLEDGMENTS The authors are grateful to Harald Krueger at CN Ralway for hs assstance on ths project. A porton of the frst author s graduate study support has been from a CN Ralroad Engneerng Research Fellowshp at the Unversty of Illnos at Urbana Champagn. REFERENCES. Transportaton Invest n Our Future: Amerca s Freght Challenge. AASHTO, Washngton, D.C., 2007. 2. Conference Proceedngs on the Web 3: Research to Enhance Ral Network Performance. Transportaton Research Board of the Natonal Academes, Washngton, D.C., 2007. http://onlnepubs.trb.org/onlnepubs/ conf/cpw3.pdf. Accessed March 3, 2009. 3. Krueger, H. Parametrc Modelng n Ral Capacty Plannng. Proc., Wnter Smulaton Conference, Phoenx, Arz., 999. 4. Vantuono, W. C. Capacty Is Where You Fnd It: How BNSF Balances Infrastructure and Operatons. Ralway Age, February 2005. 5. Abrl, M., F. Barber, L. Ingolott, M. A. Saldo, P. Tormos, and A. Lova. An Assessment of Ralway Capacty. Transportaton Research Part E, Vol. 44, Issue 5, 2008, pp. 774 806. 6. Martland, C. D., and G. Hutt. Analyss of Potental Approaches to Interlne Capacty Flow Management. Ralnc, Cary, N.C., 2005 7. Prokopy, J. C., and R. B. Rubn. Parametrc Analyss of Ralway Lne Capacty. DOT-FR-504-2. FRA, U.S. Department of Transportaton, 975. 8. Natonal Ral Freght Infrastructure Capacty and Investment Study. Assocaton of Amercan Ralroads, Washngton, D.C., 2007. 9. La, Y.-C. Increasng Ralway Effcency and Capacty Through Improved Operatons, Control and Plannng. PhD dssertaton. Department of Cvl and Envronmental Engneerng, Unversty of Illnos at Urbana Champagn, 2008. 0. Zoeteman, A., and C. Esveld. Evaluatng Track Structures: Lfe Cycle Cost Analyss as a Structured Approach. Proc., World Congress on Ralway Research, Tokyo, 999.. Vet, P. Track Mantenance Based on Lfe-Cycle Cost Calculatons. Innovatons for a Cost Effectve Ralway Track, 2002, pp. 6 3. 2. Lee, D. B., Jr. Fundamentals of Lfe-Cycle Cost Analyss. In Transportaton Research Record: Journal of the Transportaton Research Board, No. 82, Transportaton Research Board of the Natonal Academes, Washngton, D.C., 2002, pp. 203 20. 3. Ozbay, K., D. Jawad, N. A. Parker, and S. Hussen. Lfe-Cycle Cost Analyss: State of the Practce Versus State of the Art. In Transportaton Research Record: Journal of the Transportaton Research Board, No. 864, Transportaton Research Board of the Natonal Academes, Washngton, D.C., 2004, pp. 62 70. 4. Lng, D. J., R. Roy, E. Shehab, J. Jaswal, and J. Stretch. Modellng the Cost of Ralway Asset Renewal Projects Usng Parwse Comparsons. Journal of Ral and Rapd Transt, Vol. 220, 2006, pp. 33 346. 5. Ahuja, R. K., T. L. Magnant, and J. B. Orln. Network Flows: Theory, Algorthms, and Applcatons. Prentce Hall, Upper Saddle Rver, N.J., 993. The Local and Regonal Ral Freght Transport Commttee sponsored publcaton of ths paper.