A Study on Travel Time Value in Railway Transportation Corridors

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1 A Study o Travel Time Value i Railway Trasportatio Corridors HaiJu Li *, HogChag Zhou 2 School of Traffic ad Trasportatio, Lazhou Jiao-Tog Uiversity, Lazhou , Gasu Provice, Chia. * Correspodig Author lihaiju@mail.lzjtu.c. 2 School of Traffic ad Trasportatio, Lazhou Jiao-Tog Uiversity, Lazhou , Gasu Provice, Chia @qq.com Abstract The value of travel time is a impact idicator whe aalyzig ecoomic iterests of trasportatio projects. I order to make quatitate study of travel time, the work i this paper first calculated the weighted average of travel time, whose impact is very importat, usig the weight-sharig rate method. Cosiderig that the Baoji-Lazhou trasportatio corridor has ot bee operated yet, i order to get a more accurate calculatio of the value of travel time, based o the curret data, we made a i-depth aalysis o GDP ad the volume of travelers of the year 207 usig Grey predictio model ad Matlab. The research ad aalysis provides value for railway costructio departmet ad passeger travel. Keywords - value of travel time; weighted average travel time; Grey predictio model I. INTRODUCTION Durig the ivestmet process i railway ad road costructio, much of the whole computatioal efficiecy is expressed by the form of time savigs, ad igorig that its value will lead to improper decisio-makig, ad cause great ecoomic losses []. The time value begis to be explored i the early 60's abroad, ad our coutry just begis to study o the basis of foreig research i the early 70's, achievig some results. A lot of research has bee doe o the value of travel time, ad a lot of valuable results have bee obtaied. Amog them, such as usig gravity model aalyzes the social value produced by the travel time savigs of Beijig-Shaghai high-speed railway [2]. Igeiously usig utility fuctio, ad maximum likelihood estimatio method studies travel time value i a corridor from Najig to Beijig. However, the model has a strog depedece o iitial value, ad a improperly iitial value will lead to a poor reliability result [3]. Usig improved logit model aalyzes the value of travel time, but it is lack of cosiderig may factors from the differet regios ad differet modes of trasport affectig the time value greatly, which should be aalysed more comprehesively[4]. I this paper, o the foudatio of the existig literature, it uses the gray predictio model makig predictio o the city GDP, the residet populatio ad passegers flow of the mai statios from Baoji to Lazhou i 207. Based o aalysig share ratio uder a variety of trasport modes, usig weighted average travel time calculates the average travel savig time after the operatio of the Baoji-Lazhou high-speed railway. Thus it more accurately aalyses the travel time value of the mai city statios alog the corridor of Baoji-Lazhou. II. THE TRAVEL TIME VALUE Time is a kid of irreproducible resources, ad huma productio activities produce value through the cosumptio of time, so time is a valuable resource. For the travelers, choosig differet trasportatio modes will cost the travelers differet time cosumptio. So cosiderig from the perspective of opportuity cost, the value of travel time is geerated by the opportuity cost [5]. The time value refers to the travel time savigs that passegers trasfer trasport mode from a slower ruig speed oe to a faster oe. If this savig time used o productio activities will create value i a currecy form. I chia, the related data research shows that the effectiveess produced by time savigs from the road is accouted for 30% to 50%, which is a major factor i whether the project is feasible [6]. This shows that it is of great sigificace to study the value of travel time. The high speed of the high-speed railway has greatly shorteed the time passegers travellig. Oly this ca create great ecoomic beefits. I geeral, the passegers travel purpose ca be divided ito: busiess, tourism, visitig relatives ad frieds, shoppig, goig to school ad other purposes. The time cosumed i a variety of trasportatio ifrastructure is the cost this travel payig. Especially for busiess trip, the time cosumed i trasportatio caot produce value, but by chagig the mode of travel, the travel time is shorteed, thereby icreasig the productio time to DOI 0.503/ IJSSST.a ISSN: x olie, prit

2 produce value, amely so-called travel time value. Its formula is show as the formula R Q R W P ( t ) ( t ) O, D ( t ) Where R(t ) refers to the value of travel time, Q(t ) refers to the umber of passegers chagig the mode of trasportatio, R refers to the effective utilizatio coefficiet of passeger travel ; W ( O, D ) refers to the time savigs whe the passegers chage the travel mode from the origi to the destiatio; P(t ) refers to the uit time value. A. The uit time value The uit time value refers to the average value produced by a perso per hour i a area, which is affected by the gross domestic product ad the total umber of people i the area. The higher the uit time value, the greater the value of travel time, ad the coverse is also ture. Its formula is show i formula (2). G P( t ) T * M Where G refers to the GDP of the area; T refers to the aual workig hours; M refers to the area's resiet populatio. B. Passegers weighted average travel time The passegers weighted average travel time is the time measure from ay site to aother site i the corridor. The passegers average weighted travel time is smaller, idicatig that this site ad aother site are the more closely liked, amely, the accessibility is higher[9]. After the ew trasport tools are itroduced, various trasport modes are assiged a weight - sharig rate, which ca clearly idicate that passegers travel time is chaged after ew trasport tools are itroduced(amely, a compariso of average travel time betwee before ad after ew trasport tools are itroduced. The calculatio formula of the passegers weighted average travel time is show as the formula (3). W X M A, B j j j Where W ( A, B ) refers to the weighted average travel time betwee the city A to the city B. X j refers to the total travel time of the trasport mode J, M j refers to passeger sharig rate of the trasport mode J. (2) (3) C. The umber of passegers chagig the trasport mode After the high-speed railway operatig, the majority travelers will chage the origial travel modes cosiderig the time savig. So the local passeger market will establish a ew balace istead of the origial balace. See from the formula, predictig the umber of passegers chagig the trasport mode after the high-speed railway operatig is a importat parameter to calculate the travel time value of the corridor. Therefore establishig passeger flow forecastig model is the key of this paper. Cosiderig the special circumstaces of the trasport system: there are may factors affect the passegers flow trasport mode chage i the corridor, ad they caot be accurately aalyzed, therefore they ca ot be predicted by a exact mathematical model. Whe the trasportatio system is regarded as a grey system, the grey forecastig model has a uique advatage i passeger flow predictio. The model ca make a more accurate predictio of the system with less data. III. GREY PREDICTING MODEL Grey system theory uses the ways of makig a direct summatio of the raw data, ad movig average weighted summatio, to let the geerated sequece show a certai regularity, ad to use the typical curve to approximate the correspodig curve, ad settig the approximatio curve as the model predictes the system[7]. The differetial equatio model of the grey theory is called the GM model. Where GM (,) represets the differetial equatio of the first order sigle variable. A. Data preprocessig The geerated sequece is obtaied by makig a summatio of the origial sequece, as followig shows: x xi i xi xj (4) j The iverse of the summatio geeratio is called subtractio geeratio, which ca retur the summatio geeratio to o geeratio sequece. This method weakes the radomess ad istability of the origial sequece. Makig the test of the stage ratio ad the smooth ratio for x, X, respectively, whe the coditio is met, The GM (,) model is established for the X. B. Establishig grey forecastig model Settig X meets the first order differetial equatio, as show i the formula (5). DOI 0.503/ IJSSST.a ISSN: x olie, prit

3 d x d t ax u The formula (6) is obtaied by solvig the first order differetial equatio of the formula (5), as followig shows. x k u ak u x e a (6) a By usig the least square estimatio, we ca obtai the coefficiets u ada. By brigig the coefficiets back ito the origial equatio, the time respose equatio is obtaied. The by makig subtractio, we ca get the value of the reductio sequece. C. the precisio test residual The residual is calculated as followig: k x k x ˆk The ratio of posterior differece s (5) (7) C 2 (8) s Small deviatio probability P k S (9) If the ratio of posterior differece ad small deviatio probability of the data i the model are all meetig the accuracy grade demads i table, the model ca be used to forecast, otherwise, the date calculatio must be carried out after residual correctio. TABLE. THE MODEL ACCURACY GRADE DIVIDES Forecastig Accuracy P C Good >0.95 <0.35 Qualified >0.80 <0.50 Barely Qualified >0.70 <0.65 Uqualified <=0.70 >=0.65 IV. EXAMPLES ANALYSIS Takig the Baoji-Lazhou high speed railway as example i this paper, it studies the effect o travel time value i the corridor of Baoji-Lazhou after the Baoji-Lazhou high speed railway operatig. The Baoji-Lazhou high speed railway is east from Baoji West to Lazhou, ad its desiged speed is 250km/h. after the costructio completed, the ruig time from Baoji to Lazhou will be shorteed to 2.5 hours, ad it is expected to operate i 207. A. The share ratio Based o 875 sample data i the corridor of Baoji- Lazhou, the literature [8] used the logit fuctio ad Tras- CAD software to calculate the passeger share ratio of the mai city: Baoji, Tiashui, Digxi ad Lazhou alog the Baoji-Lazhou high speed railway after it operatig. Usig the same method, based o the existig trasportatio mode, this paper calculates the share ratio of each major trasportatio mode of the corridor, the specific values are show as the table 2. TABLE 2. THE PASSENGER MARKET SHARE RATIO OF EACH TRANSPORT MODES OF CORRIDOR FROM BAOJI TO LANZHOU WITHOUT HIGH SPEED RAILWAY Sectios Existig Super Civil Highway Rail Highway Aviatio Baoji--Tiashui Baoji--Digxi Baoji--Lazhou Tiashui--Digxi Tiashui--Lazhou Digxi--Lazhou B. The calculatio of weighted average travel time As the Baoji-Lazhou high speed rail way has ot yet bee operated, Now supposig that the Baoji-Lazhou high speed rail way travel at the speed of 250km / h, to speculate the travel time to each statio site. The travel time from oe statio site to other statio of other trasport modes is obtaied from the market survey. By takig the data ito the formula (2), the weighted average travel time, which is amog the mai statio sites i the baoji-lazhou corridor of havig high speed railway or ot, ca be calculated, after makig the differece of them, as the formula (0), the passeger average savig time ca be obtaied as show i table 3. W W W (0) O, D A, B( o) A, B( yes) TABLE 3. THE WEIGHTED AVERAGE TRAVEL TIME AMONG THE MAJOR STATIONS IN THE CORRIDOR OF BAOJI-LANZHOU The Weighted Average Travel Time Average Sectio Havig High Without High Savig Speed Railway Speed Railway Time (Mi) (Mi) (Mi) Baoji--Tiashui Baoji--Digxi Baoji--Lazhou Tiashui--Digxi Tiashui--Lazhou Digxi--Lazhou DOI 0.503/ IJSSST.a ISSN: x olie, prit

4 C. Predictig the umber of passegers chagig the traffic mode Accordig to the market survey, the total passeger traffic flow, amog each mai statio site by various traffic modes i the corridor of Baoji-Lazhou from the year of 202 to 205, ca be obtaied. I this paper, it establishes the GM (,) model by the grey forecastig method. Firstly, settig the passeger flow (84350, , , ) from Baoji to Tiashui durig the year of 202 to 205 as example to predict its passeger flow i the year of 207. By makig the sequece a summatio, X { 84350, 69850, , }, programmig by usig Matlab, the results are show as followig. The residual test ˆ a U u After calculatig the fitted value X~, ad the makig subtractio retur the sequece, the model calculated value ~ k X 0 ca be obtaied. The aalysig the deviatio, the result is show i Table 4. TABLE 4. THE SIMULATION RESULTS OF PASSENGERS FLOW GREY PREDICTION Actual Calculated Residual Relative Years Value Value Value Deviatio % % % Based o the relative data i Table 4, makig the fittig curves of the actual passeger flow value ad the passeger flow grey predictio value, which is show as figure. Fig. The fittig curves of grey predictio ad the actual value of Baoji- Lazhou. Combiig the figure ad the table 4, The fittig effect of grey predictio ad the actual value of Baoji-Lazhou is well, so the credibility by usig this method is high. The post differece test X S The mea of origial data: X K K The variace of origial data: S 2 ( X K X ) K The mea of residual: K K The variace of residual: ( K 40 2 ) K 2 The posterior differece ratio: S c 2 S 0.08 Small deviatio probability: p By checkig the table, the predictio accuracy is better. Therefore, usig this model to predict the passeger flow meets with the model requiremet of grey predictio theory. Therefore, usig the same method ca predict passeger flow amog the mai statio sites i the corridor of Baoji- Lazhou i the year of 207. The posterior differece ratio ad the small deviatio probability are show i the table 5. TABLE 5. THE MODEL ACCURACY Idicator C P Predictio Accuracy Baoji--Tiashui 0.08 Good Baoji--Digxi 0.09 Good Baoji--Lazhou Good Tiashui--Digxi 0.34 Good Tiashui--Lazhou 0.06 Good Digxi--Lazhou 0.3 Good. DOI 0.503/ IJSSST.a ISSN: x olie, prit

5 See the simulatio accuracy from the table 5, the passeger flow predictio of each sectio meets with the model requiremet of grey predictio theory, so the grey model ca predict the passeger flowig the year of 207. The specific predictio results are show i Table 6. TABLE 6. THE PASSENGER FLOW PREDICTION IN THE CORRIDOR OF BAOJI-LANZHOU IN THE YEAR OF 207 (TEN THOUSAND PEOPLE) D. sectios E. 207 Baoji--Tiashui F Baoji--Digxi G Baoji--Lazhou H Tiashui--Digxi I Tiashui--Lazhou J Digxi--Lazhou K D. Predictig the per time value i the corridor of Baoji- Lazhou I this paper, based o the major cities ecoomic data i the corridor of Baoji-Lazhou from the year of 202 to 205, it establishes the grey predictio model to estimate GDP ad residet populatio of Lazhou, Digxi, Tiashui ad Baoji by the year of 207. Accordig to the labor law: workig hours per week are 40 hours, i order to be coveiet to calculate, the year workig time is recorded as 50 weeks, amely, the aual workig hours are 2000 hours. Brigig it ito formula 3, the uit time value of each great cities, the specific results are show i table 7. TABLE 7. THE MAJOR CITIES ECONOMIC DATA IN THE CORRIDOR OF BAOJI-LANZHOU BY THE YEAR OF 207 Idictors Lazhou Digxi Tiashui Baoji Populatio (Te Thousad People) Gdp (Billio Yua) Uit Time Value (Yua) E. Travel time value of major cities i the corridor of Baoji- Lazhou. I this paper, it igores the time value produced by other travel purposes, ad maily cosiders the time value of busiess trip. Where R represets the passeger travel effective utilizatio coefficiet, ad geerally it is take as 50%. Accordig to Formula, the travel time value of major cities i the corridor of Baoji-Lazhou ca be obtaied, as show i table 8. TABLE 8. THE TRAVEL TIME VALUE OF MAJOR CITIES IN THE CORRIDOR OF BAOJI-LANZHOU Sectios Travel Time Value (Te Thousad Yua) Baoji Tiashui 4.2 Baoji Digxi Baoji Lazhou 86.0 Tiashui Digxi 7.64 Tiashui Lazhou Digxi Lazhou I Total V. CONCLUSIONS Travel time value is a importat idex to aalyze the ecoomic beefit i trasportatio project. The travel time value is a kid of opportuity cost, produced by beefits icreasig of time savigs. By aalyzig the travel time value, it has importat referece value for formulatig ticket price ad the choice of passeger travel way. I this paper, based o the grey predictio model, predictig the traffic flow, GDP ad the residet populatio i the corridor of Baoji-Lazhou by 207. Thus the travel time value, i the corridor of Baoji-Lazhou after operatio by 207, ca be calculated. From the above aalysis, oly time value ca geerate about 4 millio 780 thousad yua after the operatio of Baoji-Lazhou high-speed railway. With the study of the travel time value, from the macro aspect, the railway costructio decisio maker has a prelimiary judgmet o the feasibility of the railway costructio. From the micro aspect, it is better for the travelers to choose travel ways i their favour, to maximize their ow iterests. ACKNOWLEDGMENTS The authors thak the reviewers who gave a through ad careful readig to the origial mauscript. Their commets are greatly appreciated ad have help to improve the quality of this paper. This work is supported i part by the Research Plaig Fuds of Humaities ad social scieces for the Miistry of Educatio (4YJA790023); Natural Sciece Foudatio of Gasu Provice (48RJZA05); Higher Educatio Research Fuds for GasuProvice (204A05) ; Sciece ad Techology Support Ecoomic Society Developmet Educatio Fuds of Lazhou Jiao-tog Uiversity(ZC204005). REFERENCES [] L. D. Zou, B. H. Mao, A. Ji. Research o the model of highways travel time value i chia [J]. Highways & Trasportatio i Ier Mogolia. 996, 49 (4): DOI 0.503/ IJSSST.a ISSN: x olie, prit

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