Real-time arrival prediction models for light rail train systems EDOUARD NAYE

Transcription

1 DEGREE PROJECT IN TRANSPORT AND LOCATION ANALYSIS STOCKHOLM, SWEDEN 14 Real-time arrival preiction moels for light rail train systems EDOUARD NAYE KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ARCHITECTURE AND THE BUILT ENVIRONMENT

2 ROYAL INSTISTUTE OF TECHNOLOGY DEPARTMENT OF ENGINEERING Master Thesis in Vehicle Engineering Real-time arrival preiction moels for light rail train systems Author: Supervisor: Oe Cats Aviser: Oe Cats 3 th, January 14 Acaemic Year 1/13 ABSTRACT

3 Page of 9 One of the main objectives of public transport operators is to ahere to the planne timetable an to provie accurate information to passengers in orer to improve actual an perceive service reliability. The aim of this thesis is to aress the flowing question: how can the accuracy of a preiction system for light rail systems be measure an improve? The real-time preiction is an output of a telecommunication system, name Automatic Vehicle Location System, which computerizes the preictions. In orer to improve a system, it is first important to unerstan how it works. The mechanism of the preiction computation will be analyze an each part of the process will be stuie in orer to seek potential improvements. The first part of the preiction scheme evelopment consists in a statistical analysis of historical ata to provie the reference travel times an well times an their variations along a ay or along a week. Then, two moels (the esigne-spee moel an the spee/position moel will be stuie to estimate the remaining time to reach the ownstream stop. This estimation is mainly base on the current ata (vehicle position an spee. The propose preiction schemes were implemente an applie for a case stuy light rail line. Bybanen, a light rail train in Bergen was selecte as case stuy. Real-time information isplays are available at all platforms an refer to the waiting to the next two light rail trains. This stuy focuses on improving the accuracy of these waiting times preictions. In orer to establish an analyze the performance of the current preiction scheme, a moel for reproucing these computations was evelope. Then, the possible improvements have been implemente in the moel an the accuracy of the new preictions has been compare to the base case. The assessment an the comparison of preiction systems are not trivial tasks. Which preictions shoul be taken into account? How oes the moel ientify inconsistency in the ata? How coul the perception of passengers be taken into account? A set of measures has been use in orer to evaluate alternative preiction schemes. The comparison of the ifferent moels shows that it is possible to improve the accuracy of the short-term preictions, but it is more ifficult to improve the accuracy of long-term preictions because the incertitue of small changes has more impact in long-term preictions. This thesis shows that the reference travel times an well times shoul be assimilate to the most common value instea of the average which is too epenent on high values. Moreover, the well time variations are relate to the flow passengers. Finally, the most accurate an efficient moel is the esigne-spee moel. The spee/position moel is a bit less accurate except in the case of isturbances along the line but its moularity mae easier possible improvements. Finally, this paper highlights the time-epening variations of the well time in the case of a light rail train system. It coul be interesting to analyze the behavior of variations of two consequent well times an to implement a forgetting factor. Moreover, the spee-position moel shows really goo results an a better unerstaning of the rivers behaviors is a key to improve the moel. Finally, the ifferences between the ifferent moels will be probably larger for a mile-istance train system, which coul be an interesting application of this thesis. 3/1/14

4 Page 3 of 9 TABLE OF CONTENTS 1 INTRODUCTION... 7 LITERATURE REVIEW METHODOLOGY DATA SOURCES MODEL DEVELOPMENT Statistical analysis Deriving the time for arrival at the ownstream station with current ata Light rail train wells at a station Light rail train runs between two stations Combination of historical ata an current ata MODEL EVALUATION CASE STUDY SYSTEM DESCRIPTION TRAFFIC MANAGEMENT DATA COLLECTION PREDICTION SCHEME OF THE AVLS APPLICATION DWELL TIME ANALYSIS Data source Data filtering Analysis Moel improving Results TRAVEL TIME ANALYSIS Data source Data filtering Analysis Results DERIVING THE TIME FOR ARRIVAL AT THE DOWNSTREAM STATION WITH CURRENT DATA AVLS moel Designe-spee moel Spee-position moel MODEL COMPARISON OVERALL ASSESSMENT ANALYSIS OF THE SHORT-TERM PREDICTIONS ANALYSIS OF THE COMBINATION OF DIFFERENT MODELS ANALYSIS FOR DIFFERENT REGULAR TRAFFIC CONDITIONS ANALYSIS DURING AN ABNORMAL TRAFFIC SITUATION CONCLUSION ACKNOWLEDGMENT BIBLIOGRAPHY... 6 ANNEXE A: VBA CODE /1/14

5 Page 4 of 9 ANNEXE B: DETAILLED MODEL DESCRIPTION ANNEXE C: PERFORMANCE INDICATORS FOR DIFFERENT MODELS AT SPECIFIC PERIODS /1/14

6 Page 5 of 9 LIST OF FIGURES Figure.1: Example of spee-time curve [7]... 1 Figure 3.1: Automatic vehicle location system s structure Figure 3.: Evolution of the vehicle spee between two stations Figure 3.3: Evolution of the vehicle position between two stations Figure 3.4: Designe-spee of a light rail train between two stops in an ieal case Figure 3.5: Representation of the ifferent areas accoring to the current position an the current spee of the vehicle Figure 3.6: Distinction of the two parts of Case... Figure 3.7: Representation of the ifferent trajectories for Case... 1 Figure 3.8: Distinction of the two parts of Case Figure 3.9: Representation of the ifferent trajectories for the fourth area... 4 Figure 3.1: Illustration of ifferent skewness values [18]... 5 Figure 4.1: Overview of the Bybanen line between Byparken an Nesttun... 8 Figure 5.1: Occurrence of the well time at Sletten ingoing Figure 5.: Occurrence of the well time eviation Figure 5.3: Percentage of the eviation occurrence epening of the time Figure 5.4: Most common eviation of the well time by time slot Figure 5.5: Most common eviation of the well time by time slot uring weekays an weekens Figure 5.6: Occurrence of the well time eviation Figure 5.7: Occurrence of the travel time eviation... 4 Figure 5.8: Percentage of the eviation occurrence of the travel time epening of the time Figure 5.9: Most common eviation of the travel time by time slot Figure 5.1: Preiction accuracy of the current AVLS moel... 4 Figure 5.11: Comparison of the VBA moel with the current AVLS moel Figure 5.1: Estimation of the time to reach the next platform epening on the istance Figure 5.13: Deviation between the preicte arrival time an the actual arrival time for the next platform an for running vehicles Figure 5.14: Representation of the remaining travel time for the spee/position moel as function of the current vehicle position an spee Figure 5.15: Occurrence of the eviation between the preicte arrival time an the actual arrival time for the next platform an for running vehicles Figure 5.16: Representation of the occurrence of the eviation accoring to the area Figure 5.17: Representation of the occurrence of the eviation accoring to the area Figure 6.1: Occurrence of the eviation between the preicte arrival time an the actual arrival time for moel, moel A, moel 1 an moel Figure 6.: Occurrence of the eviation between the preicte arrival time an the actual arrival time for moel, moel 1 an moel for short-term preictions Figure 6.3: Occurrence of the eviation between the preicte arrival time an the actual arrival time for moel, moel 1A an moel A Figure 6.4: Occurrence of the eviation between the preicte arrival time an the actual arrival time for the night perio Figure 6.5: Occurrence of the eviation between the preicte arrival time an the actual arrival time for the weekens Figure 6.6: Occurrence of the eviation between the preicte arrival time an the actual arrival time for the rushhour Figure 6.7: Occurrence of the eviation between the preicte arrival time an the actual arrival time for the moel A Figure 6.8: Occurrence of the eviation between the preicte arrival time an the actual arrival time for the moel Figure 6.9: Occurrence of the eviation between the preicte arrival time an the actual arrival time for the moel Figure 6.1: Occurrence of the eviation between the preicte arrival time an the actual arrival time for moel, moel 1 an moel LIST OF TABLES 3/1/14

7 Page 6 of 9 Table 4.1: Implemente travel time in the AVLS... 3 Table 5.1: Average an stanar eviation of the well time at each platform... 3 Table 5.: Implemente well time at each platform Table 5.3: Implemente variable well time along a ay Table 5.4: Results of the ifferent well time moel Table 5.5: Average an stanar eviation of the travel time for each segment Table 5.6: Average an stanar eviation of the travel time for the complete line Table 5.7: Most common travel time for each portion Table 5.8: Results between the current moel an the esigne-spee moel Table 5.9: Comparison between the three moels Table 6.1: Performance inicators for moel, moel A, moel 1 an moel... 5 Table 6.: Performance inicators for moel, moel 1 an moel for short-term preictions Table 6.3: Performance inicators for moel, moel 1A an moel A Table 6.4: Performance inicators for moel, moel 1 an moel /1/14

8 Page 7 of 9 1 INTRODUCTION The accuracy of the real time information changes the feeling of passengers concerning the harship of the waiting time. It is hence relevant for public transport companies to evaluate alternative schemes to preict the waiting time by taking account of variables such as ay of the week, weather, an status of the previous trains. Inee, a lot of public transport systems haven t yet incorporate these kin of variables into their waiting time preiction schemes. This thesis reports the evelopment of a strategy esigne to increase the accuracy of the preiction by incorporating aitional variables. Given my current position in the company Thales, the Bergen Light Rail Train name Bybanen, will be the case stuy. The access to automatically collecte ata an the small scale of the infrastructure are avantageous in eveloping the methoology for this project. An analysis will be carrie out an ifferent moels will be compare in orer to obtain the best performing preiction scheme: an efficient moel with high accuracy level. Light rail trams are uner construction in ifferent cities (Paris, Liege an Bergen for example, because this transport moe is highly appreciate by passengers [] [3]. It is often consiere as a goo compromise between a bus network an a subway line [4]. Inee, the construction of light rail trains is more flexible than the construction of a subway line. There is no nee to buil unergroun platforms, which is cost efficient an time efficient. Moreover, the transit time is reuce when the platform is accessible irectly on the street [4]. Even if buses represent the most wiely use transit technology [5], travelling by bus is more time-consuming than travelling by light rail train. Inee most of the time, buses have neither eicate lanes nor signal priority at intersections. The buses capacity is also lower than the light rail train capacity [4] an the possibility of coupling two light rail train vehicles can allow operators to increase its capacity. For all these reasons, a light rail train line is a goo alternative to a bus network an to a subway line. A light rail train interacts with other transport moes incluing private car traffic, buses, cyclists an peestrian movements. These interactions coul be exercise along line segments as well as at intersections an therefore inuce sources of uncertainty to light rail train travel times on links an well times at stops. That s why the arrival time of a light rail train can be consiere stochastic in urban networks as it is the case for a bus network [6]. Most of the previous stuies which have been carrie out to evelop an accurate preiction scheme are ealing with bus networks ue to its higher uncertainty [7] [8]. The thesis aim is to evelop a preiction scheme for light rail trains. Preiction moels often use static ata concerning travel time components. Base on these parameters, the preiction system can calculate the neee time to reach ownstream platforms an inform passengers accoringly. In this thesis, a methoology will be escribe in orer to moify this part of the system an shoul answer the following question: how is it possible to improve the current preictions by mean of previous preictions an current vehicle position. Objectives of the thesis are: (1 To collect the ifferent ata (arrival time, eparture time an vehicle position using the on-boar mileage counter ( To evelop ifferent moels to preict the light rail train arrival times by combining historical ata an current ata (position an spee of the vehicle (3 To valiate an compare the moels by using fiel ata The stuy is limite to the evelopment of a preiction scheme using historical an mileage counter ata from light rail trains in the case of Bergen Light Rail Train. The preiction scheme will not consier abnormal situations (vehicle failure, accient but such cases are use for the valiation an the comparison of the preiction schemes. 3/1/14

9 Page 8 of 9 LITERATURE REVIEW Transit light rail train arrivals at platforms in urban networks are consiere as stochastic because well times at stops, travel times on links an elays at intersections fluctuate spatially an temporally [8] [9]. That s why it is really challenging to evelop an arrival time preiction scheme which can aapt to the time an spatial variations. There are three main streams of preiction schemes which have been evelope over the last ecaes: time series moels, artificial neural network moels [9] an support vector regression machine moels [7] [8]. The time series moels are base on the similarities between historical ata an real time ata. The statistics provie tools to choose the appropriate parameters to preict future events. The stuie process has to be stochastic an the scope of time series moels is really wie: aily volume of flows in a river or monthly eman for a prouct [1]. Time-series moels require analyzing empirical ata which shoul link the travel time an the well time to exogeous parameters. For example, the well time at a specific stop is relate to the number of passengers, to the time of the ay [4]. Moreover, some unexpecte events as bus lift operations or the vehicle esign (presence of bicycle rack or integration of fare box have also effects on the well time [4]. Concerning the travel time, it is more ifficult to link the possible elays with exogenous variables because almost each link is specific (length, spee limit, crossing. Some stuies have been carrie out to relate empirical travel time value with the status of the traffic via ifferent methos [6] [1], which have shown an possible improvement of preiction scheme by taking the traffic status into account. The artificial neural network moel is an approach for solving complex problems an has successfully been applie to transportation issues [9]. The moel is base of interconnecte functions, which means that its process is similar to those of a brain. These functions can be linear or nonlinear. In the case of artificial neural network moels, there is no explicit function connecting inputs an outputs. It has been shown that artificial neural network moels can accurately preict traffic conitions on street ways [1], where historical ata an the current vehicle position woul be the inputs an the estimation of the arrival time woul be the output as previously one by Kalaputapu an Demetsky [11]. Finally, the support vector machine regression moel is the most recent approach, still uner evelopment for various applications (forecasting of financial market [13], estimation of power consumption [14]. Its main avantage compare to the artificial neural network moel is its capability to obtain the global minima whereas the artificial neural networks moel only results in a local minimum [7]. Furthermore, the support vector machine moel can be aapte for complex problems an is robust in managing corrupte ata [7]. As a backgroun stuy, it is interesting to investigate the universal basis of real-time information to users. All preiction algorithms can be ivie into three steps: the tracker, the filter an the preictor [15]. The tracker consists in ata collection in orer to raw the vehicle trips. It is mae of a set of ata compose of position an time to track the vehicle along the line or insie the city. After collecting ata, the filter shoul be applie in orer to minimize the imperfection of the on-boar equipment. Different filters can be applie such as Grubbs test metho, which eletes abnormal ata from input ata [6]. Frank E. Grubbs presents ifferent methos to etect outliers in a series [16] an shows that the average an the stanar eviation are meaningful values in the research of outliers in a sample. Concerning the preictor, two ifferent approaches are commonly use: link-base moels an stop-base moels. Link-base moels, which are use to preict arrival times at any ownstream stops, sum the travel times on all traverse links between pair of stops [9] an consier there is no correlation between travel times along the run. In orer to avoi this oversimplification, ifferent techniques are use such as the forgetting factor, which takes into consieration the real-time status of the traffic [6]. If it takes longer than expecte to traverse a link for some vehicles, the preiction scheme will consequently elay the arrival time of the next 3/1/14

10 Page 9 of 9 vehicles. The improvement of the link-base moel shows that the preiction calculation must be time-varying. In the other han, the stop-base moels o not separately manage the ifferent links an o not ivie a travel time between two platforms into smaller sections. The possible errors of each sub-section can accumulate, which ecreases the accuracy of the moel, especially for long-term preictions [1] [6]. In the case of light rail trains, the scheule heaway is smaller than for buses, which means light rail train preictions can be consiere as short-term an the risk to accumulate errors is reuce. Therefore, the link base moel has been chosen for this thesis. Different stuies report that, as a vehicle approaches a target stop, the preiction becomes more an more precise [1]. In the case of bus system, the vehicle location is the only real-time input. That is why some moels approximate the vehicle spee by using the travel time an the istance run by the vehicle uring the two last inputs. The vehicle spee can be use to reflect the traffic conitions of links [1] or to reflect the particular conition of a single vehicle. The secon option has been chosen here because the vehicle position is usually upate at a high frequency in light rail train system, which gives a status of the current spee of the vehicle rather than an overview of the traffic status. Then, the current spee an the current position can be use to estimate the remaining time to reach the ownstream stop, which requires knowing the spee profile between two stations. Usually, the spee profile can be split in four phases in the case of a rail system: stop, accelerating, coasting an ecelerating [6] [7]. Inee, such spee profile can be use to calculate the neee power for the system in case of light rail train base on batteries [5]. More elaborate moels can be also use as escribe in Figure.1. It can be seen that the acceleration is consiere as constant for low spees an the acceleration becomes smaller at higher spees [6]. The coasting phase is not escribe by a constant spee. Different moels exist but all agree on the presence of the four phases. Finally, the spee profile of the vehicle is also epenent on the river behavior when approaching a crossing or a stop [8]. It has been shown that rivers response to safety signals can be slightly ifferent [8], so it is almost impossible to preict the exact remaining time to reach the ownstream platform ue to the uncertainty of the rivers behaviors. In the case of light rail train system, it is important to remin that the river s position at the leaing extremity of the vehicle well outsie of the wheelbase means that he experiences lateral acceleration several times greater than his passengers. Driver behaviors have been the subject of many stuies, which are mainly focuse on the safety point of view. 3/1/14

11 Page 1 of 9 Figure.1: Example of spee-time curve [7] The travel-time estimations can be efine as: historical ata, current ata or both historical an current ata [3]. Better results happen when current ata (position an spee of the vehicle are combine with historical ata [17], which is the topic of this thesis. How to combine current ata receive from a vehicle (current position, current spee with historical ata to improve the preiction scheme? Many stuies have been carrie out to improve the accuracy of arrival-time preiction [6] [1]. The support vector machine moel souns the more promising moel even if it is still uner evelopment. Most of the previous stuies are ealing with a bus system where the uncertainty is higher. This thesis will evelop a moel to preict with accuracy the arrival-time for a light rail system. The chosen moel is close to a time series moel because of the use of empirical ata to estimate the future travel time on each link an the future well time at each stop. So, it is a link-base moel. Moreover, the current ata as the current position an the current spee of the vehicle are collecte to reflect the current status of the vehicle. Different moels will be evelope to estimate the arrival time at the ownstream stop through these values. The vehicle spee is not a irect input of the moel but will be estimate with the two last input positions [1]. This thesis principally aims to apply previous concepts use in bus system to a light rail train system to figure out if the same comparison an the same improvements can be rawn with a rail system which contains less uncertainty. 3/1/14

12 Page 11 of 9 3 METHODOLOGY A successful transport system is a system able to preict with efficiency an accuracy the arrival/eparture times at ownstream stops. Some systems, such as avance public transportation systems (APTS or avance traveler information system (ATIS, use the automatic vehicle location system (AVLS as a key element in their preiction scheme [9]. AVLS is a telecommunication system whose aim is to localize the vehicles along the line. With a precise location, it is possible to estimate the arrival time at ownstream stops. This thesis aims to improve the accuracy an the precision of the preiction scheme when the AVLS is the only available input for the moel. In some projects, the automatic passenger counter system (APCS can be available an coul be a further improvement of the moels etaile in this paragraph. AVLS structure is escribe in Figure 3.1. Timetable Vehicle association Vehicle position Inputs Automatic Vehicle Localization System System Vehicle elay/ahea Passengers waiting time Outputs Figure 3.1: Automatic vehicle location system s structure The vehicle position, the vehicle association an the timetable are the three main inputs of the AVLS. The vehicle position is the key element of the preiction scheme an can be use in ifferent ways. The vehicle association is the link between the official trips an the vehicles. It is manatory for operators to have a global vision of the ifferent vehicles over a ay or a week, but it oesn t affect the real-time preictions. Moreover, as the vehicle association is strongly relate to the stuy case, it will not be taken into consieration in orer to not reuce the number of possible applications. Finally, the timetable escribe the reference travel timest i between the station i an the stationi 1, an the reference well times Di at the station i. These parameters are the basis of the preiction scheme. The scope of this stuy will focus on a link-base approach, which means that, for a light rail train locate at the station p, the preiction timet pre at the station q is calculate as: q1 q1 T T D (3.1 pre i i p i i p1 Equation (3.1 shows the importance of the reference travel times T i an the reference well times D i. Different proceures can be use to efine these reference values: average values, forgetting factors A statistical analysis of the historical ata has been chosen to efine them. 3/1/14

13 Page 1 of 9 The methoology aopte for the present thesis can be split into three steps: extraction of ata, evelopment of new moels an moel evaluation. 3.1 Data sources As escribe in the previous paragraph, the historical ata an the current position of the vehicle are the two inputs of the preiction scheme. The current vehicle position is collecte an sen by the on-boar system, which usually consists in a GPS or a mileage counter. These evices might not properly work ue to some failures, which results in erroneous ata. Moreover, incomplete ata are also present in historical ata in case of suen changes or server shutowns. For these reasons, input ata will be filtere to elete corrupte ata. In case of incomplete ata, associate values are elete from the atabase. For example, if only the eparture time is present for a particular vehicle for a stop, then the arrival time will be elete from the baseline. Then, the moel verifies the ata consistency by analyzing the arrival times for each journey. To be consiere as consistent, a journey shoul be at least compose of three consequent arrival times. If a vehicle has a problem with its on-boar equipment or if a suen change appears in ata, the corresponing journey will not be taken in consieration. A journey is efine as a run from a terminus to the other terminus. Moreover, for the statistical analysis of the well times an the travel times, abnormal values are out of interest. A value can be qualifie of abnormal if the ifference between itself an the average value is bigger than three times the stanar eviation. 3. Moel evelopment The scope of this thesis is to improve the preiction scheme of a light rail train system. As the new preiction schemes shoul be applicable to other light rail train systems, it is important to remove all the specificities of our stuy case, which is escribe in 4. It explains why the ifferent preiction schemes have been evelope with Visual Basic for Applications (VBA, which is an implementation of Microsoft's programming language Visual Basic 6. The evelope moel in VBA only aims to calculate preictions an can be applie to other rail systems. As efine before, the travel time preictions can be characterize as both historical an current ata. Therefore the evelopment of new moels shoul be split into two istinct steps: a statistical analysis an the elaboration of a moel estimating the remaining time to reach the platform. The statistical analysis is base on historical ata whereas the secon part is mainly base on current ata. For a light rail train locate at the station p or between the station p an the station p 1, the preiction timet pre at the station q is the sum of the remaining timet remaining to reach the next station an of the ifferent reference travel timest i an well times D as expresse in Equation (3.. i Statistical analysis q1 q1 T t T D (3. pre remaining i i p1 i i p1 The first part of the preiction scheme evelopment consists in a statistical analysis of historical ata to provie the reference travel times an well times. The historical analysis aims to estimate a travel time or a well time which has not yet been starte an shoul not be mismatche with the remaining time t remaining to reach the next station. For the statistical 3/1/14

14 Page 13 of 9 analysis, only small eviations are consiere an the filters efine in 3.1 apply. These reference travel timest i an well times D i are the main components of the current timetable input. It is important to verify they reflect the real travel times an the real well times. If not, new reference travel timest * i for each link an new reference well times D * i for each stop shoul be efine. Then the variation of these values will be stuie along a ay or along a week. For example, if a well time is shorter uring the weeken than uring the weekays, a elta i(, h of the reference well times will be ae or retrieve in orer to fit with the reality. This variable allows the system to ajust the reference well times epening the fluctuation along a ay an along a week ue to exogenous variables. In the same way, it(, h represents the ajustment of the travel time between the stations i ani 1 ue to exogenous variables. With the new variables, for a light rail train locate at the station p or between the station p an the station p 1, the new preiction timet pre at the station q can be expresse as: T pre q1 * * tremaining ( T i it(, h ( D i i p1 q1 i p1 Deriving the time for arrival at the ownstream station with current ata (, h Equation (3.3 represents the first step of the preiction scheme improvement an is only base on historical ata. Current ata (vehicle position an spee are the basis of the preiction scheme an represent the main inputs for the estimation of the remaining timet remaining to reach the ownstream station. Two ifferent approaches will be analyze: the esigne-spee moel an the spee/position moel. Let us first efine several funamental values. As only the remaining time to reach the ownstream stop matters in this section, the entire line can be illustrate through concentrating on two stations. Consier a light rail train running from station A to station B which is D meters further ownstream. The esigne well time at station A is T D an the esigne travel time between stations A an B ist. These values are base on the historical analysis etaile in 3... The trajectory of a light rail train between the arrival at station A an the arrival at station B can be ivie in four phases as shown in Figure 3. an in Figure 3.3: the welling time (1, the acceleration phase (, the constant spee phase (3 an the eceleration phase (4. If the light rail train is running between stations A an B, the current istance between the light rail train an station A is given by the on-boar equipment an is enote by. If, the light rail train wells at a station. If D, the on-boar system hasn t correctly synchronise at station B an the system consiers the train has alreay arrive at station B. For preiction purposes, the istance between the vehicle an station A shoul be within the following range: i (3.3 D (3.4 3/1/14

15 Page 14 of v Spee (m/s T D Time (sec T D T Figure 3.: Evolution of the vehicle spee between two stations D Distance from the station A (m T D Time (sec T D T Figure 3.3: Evolution of the vehicle position between two stations In both moels, it is important to make a istinction epening on whether the light rail train stans at a station or if the train is running between two stations. Let s stuy first the case of a light rail train which is staning at a station. In both moels (esigne-spee an spee/position, the calculations are ientical for a train staning at a station. Light rail train wells at a station If the light rail train stans at station A, the moel keeps a recor of the arrival time to station A, which will be callet A. Let s call T B the preicte arrival time at station B an T now the time when the preiction is mae by the moel. If the actual welling time ( Tnow TA is shorter than the esigne well timet D, the system consiers that the vehicle is on time an the preicte arrival time to station B will be the sum of 3/1/14

16 Page 15 of 9 the esigne travel time T between stations A an B an of the esigne well timet D at station A ae to the arrival timet at station A. It results in Equation (3.5. A T B T T T (3.5 A If the actual welling time ( Tnow TA is longer than the esigne well timet D, the system consiers the vehicle shoul leave in few secons an will not stay longer at station A. So, the vehicle is planne to reach the ownstream station after a time equal to the esigne travel time T between stations A an B as escribe in Equation (3.6. T B D T T (3.6 now These calculations are ientical for both moels an apply for a train staning at a station. If the train is running between two stations, two approaches will be consiere: the esignespee moel an spee/position moel. Light rail train runs between two stations Design-spee moel The esigne-spee moel is a moel which only consiers the vehicle position as an input for the system. From ata of the stuy case (vehicle acceleration, vehicle eceleration, link length an esigne travel times for each link, it is possible to calculate, for each link, the spee profile of a vehicle running in an ieal case. A vehicle is escribe as running in an ieal case if it respects the following phases: constant acceleration, constant spee an constant eceleration. These phases are escribe in Figure 3. an in Figure 3.3. Even if the real vehicle oesn t follow the ieal spee profile, the current spee of the vehicle is assume equal to the spee of a vehicle running in an ieal case for the vehicle position given by the on-boar system. It will be shown that only one spee profile can fit with following ata: acceleration, eceleration, link length an reference travel time. When leaving station A, the light train shoul accelerate with a constant acceleration a, then keep a constant spee an then finally ecelerate with a constant eceleration b in orer to reach the ownstream stop. The istance D between the two stations an the esigne travel timet between the two stations are two inputs of the preiction scheme. In the next paragraph, it will be shown that the vehicle can only reach a specific spee uring its constant phase if the acceleration, the eceleration, the travel time an the istance between two stations are given. Let us enote as follows: - 1: the istance run by the vehicle uring the acceleration phase, - t 1 : the travel time of the acceleration phase, - : the istance run by the vehicle uring the eceleration phase, - t : the travel time of the eceleration phase, Accoring to these efinitions, the train will run at a constant spee if an only if: 1 D or t 1 t T (3.7 The case 1 D an the case t 1 t T are irrelevant because unrealistic. If t 1 t T (or 1 D, the vehicle accelerates an then immeiately ecelerates after it reaches its maximum spee, which never happens because the travel times are long enough to avoi this situation. Now, it will be shown that only one solution is possible with these inputs ( a, b, T, D. First, we shoul calculate the istance run by the vehicle uring the ifferent phases. Accoring to the ifferent integrations of the acceleration (or eceleration, it results that the 3/1/14

17 Page 16 of 9 vehicle runs the istance 1 uring the acceleration phase an the istance uring the eceleration phase. These istances can be written as: 1 1 at 1 (3.8 1 bt (3.9 The sum of the istances run by the vehicle uring each phase (acceleration, constant spee an eceleration shoul be equal to D an the spee at the en of the acceleration phase an at the beginning of the eceleration phase shoul be equal an is calle v, which represents the maximal esigne-spee between two stations. In consequence: 1 1 (3.1 at1 bt v ( T ( t1 t D An therefore: v 1 a ( b a t b at 1 bt ( att1 D (3.1 Equation (3.1 is a quaratic equation where t 1 represents the unknown. In orer to solve it, the iscriminant has to be calculate. a at D( a b (3.13 b If the iscriminant is negative, the esigne travel timet has been chosen too short for the link. The vehicle can not run the istance D in T secons with acceleration a an a ecelerationb. This is not a feasible solution in the context of this application. If the iscriminant is equal to, the vehicle accelerates an then ecelerates immeiately after, without running at constant spee. It means that the esigne travel time is physically the smallest possible an this choice is not viable for a light rail train in operation. In this case, the acceleration phase lasts: bt t1 (3.14 a b So, the esigne travel timet between the stations A an B is consiere long enough to have a positive iscriminant. The esigne-spee profile is shown in Figure 3.4. With a positive iscriminant, it is possible to calculate the exact value for 1, t1,, t. By resolving Equation (3.1, it results: b a bt at ( a b D t a b ( b a 3/1/14

18 Page 17 of 9 v Designe spee (m/s D Travelle istance (m 1 D Figure 3.4: Designe-spee of a light rail train between two stops in an ieal case Two istinct solutions exist, but only one of them is physically possible. As in our stuy, the vehicle runs at constant spee uring a perio, the acceleration phase shoul be smaller than in the case of a iscriminant equal to zero efine in Equation (3.14. So, the smallest solution is the only acceptable solution. Finally, the ifferent values can be irectly calculate with Equations (3.8, (3.9 an ( bt b T ( D b a (3.16 t1 b a t 1 1 at a T ( D b a b a ( bt b T ( D 1 b a 1 a (3.18 b a 1 1 at a T ( D 1 b a b (3.19 b a v T ab 1 1 T ( D b a b a (3. 3/1/14

19 Page 18 of 9 Recall that the characteristic values 1, t1,, t, v are now consiere as inputs of the problem for every segment (sub-section of line between two consecutive stations. If the istance of a light rail train from station A is known, it is possible to estimate the time t remaining to reach station B as follows: - If, the remaining time is calculate as escribe in the If 1, t remaining T a D ( - If 1 D, tremaining t v ( D - If D D, t remaining b Spee-position moel The esigne-spee moel only consiers the vehicle position as an input. Inee, the esigne-spee moel oesn t epen on the current state of the light rail train, whereas the spee/position moel consiers the vehicle position an the vehicle spee as inputs to be more realistic. For example, if a train is stoppe before a crossing because it in t receive the priority signal, the esigne-spee moel consiers that the light rail train has a current spee equal to the esigne-spee for this position, which is not the case. The current vehicle spee is not irectly available in most of light rail train systems, but it is possible to erive an accurate estimation of the vehicle spee with the two inputs a an b at the respective times t a ant b, where the sub-scripts a an b refer to the two latest consecutive positions. Such an approximation is possible because the vehicle position is upate at high frequency in light rail train systems. v b a (3.1 tb ta In orer to estimate the remaining time t remaining to reach station B, the vehicle spee an the vehicle position are consiere as inputs in the spee/position moel. So the current state of the light rail train can be ientifie in Figure 3.5. After consieration of the esigne-spee profile escribe in an of the ifferent behaviors of rivers, the D graph can be ivie into four areas. In the moel-spee position, the river can accelerate with an acceleration a, keep a constant spee, ecelerate with a constant ecelerationb or let the vehicle roll, where the vehicle is assume to slightly ecelerate with a constant eceleration c, which is the consequence of the resultant of the inertia moment. In the following paragraph, the preiction is assume to be calculate at the timet. The light rail train is assume to have a current spee v an a current istance from station A. Let us examine an formulate the remaining time t remaining to reach station B for each case. 3/1/14

20 Page 19 of 9 1 v Designe spee (m/s 3 (, v 4 Travelle istance (m 1 D D Figure 3.5: Representation of the ifferent areas accoring to the current position an the current spee of the vehicle Case 1 Case 1 represents a light rail train approaching station B with a spee higher than the esigne-spee profile. A vehicle belongs to the first area if an only if: v ( D v (3. In Case 1, the river is assume to brake until the vehicle reaches station B with a constant ecelerationb new equal to: b new 1 v (3.3 D For Case 1, the vehicle reaches the ownstream station after a time equal to: v ( D tremaining (3.4 b v new Case Case represents a vehicle running faster than the maximal esigne-spee. In this case, the river is assume to first let the vehicle roll, which ecreases its spee until it reaches the blue line or the re line in Figure 3.5. Moreover, when the river lets the vehicle roll, the eceleration is assume to be constant an equal to c The light rail train will hence slowly ecrease its spee. If the vehicle is too close to station B, it will first reach the re line of Figure 3.5. In this case, the river will brake with a constant eceleration equal tob. If the vehicle is sufficiently far from station B, it will first reach the maximal esigne-spee v (blue line an will then run at a constant spee before the eceleration phase. The limit case is escribe in Equation (3.5 an Figure 3.6 represents the sub-cases for Case. 3/1/14

21 Page of 9 v v c( D (3.5 B A v Designe spee (m/s Travelle istance (m D D Figure 3.6: Distinction of the two parts of Case Let s calculate the time to reach station B for a vehicle in the part A of Case. The current ata, of the vehicle shoul satisfy: ( v v v ( D c( D v (3.6 The current spee of the vehicle is higher than expecte, so the river will ecelerate a bit until the light rail train approaches the platform an then the vehicle will strongly ecelerate. The river is assume to increase its eceleration when the following equation is satisfie (re line: v ( D v (3.7 Let s calculate the istance ' from station A, the spee v ' an the time t ' when the vehicle increases its eceleration from c tob. The spee an the istance run by the vehicle can be written: v ct (3.8 c v t vt (3.9 So the time can be expresse as a function of the spee in Equation (3.8 an be inserte into Equation (3.9. Therefore: 1 ( v v (3.3 c Equation (3.3 hols until the river increases the eceleration, escribe in Equation (3.7. These two equations represent a system of two equations with two unknowns (, v which results in the searche values (, v, t : ' ' 3/1/14

22 Page 1 of 9 1 ( v v D c (3.31 c v ' v ' ' v ( D (3.3 ' 1 ' v t ( v (3.33 c After a time t ', the vehicle has the spee v ' an is at the istance ' from station A. It will then ecelerate with a constant ecelerationb until the arrival at station B. For the part A of Case, the vehicle reaches the ownstream station after a time equal to: ' ' v t remaining t (3.34 b The trajectory of the vehicle is shown in Figure 3.7. (, v ( ', v ' v Designe spee (m/s Travelle istance (m D D Figure 3.7: Representation of the ifferent trajectories for Case Let s calculate the time to reach station B for a vehicle in part B of Case. The vehicle will ecrease its spee an Equation (3.8 an Equation (3.9 hols untilv v. Let s calculate the istance ' from station A, the spee v ' an the time t ' when the vehicle reach the esigne spee: ' ' v v (3.35 ' 1 t ( v v c (3.36 c ' ' t vt (3.37 3/1/14

23 Page of 9 Then, the vehicle will run at constant spee until D an finally ecrease its spee with a constant ecelerationb until station B. By aing the estimate time for the three phases, the estimate time to reach station B for the part B of Case is equal to: ' ' D ( tremaining t t (3.38 v Case 3 Case 3 represents a vehicle far enough to station B to accelerate until reaching the maximal esigne-spee v. Then the vehicle will run at the constant maximal esigne-spee. A vehicle with the current ata, belongs to Case 3 if an only if: ( v v ( 1 D v v ( As for the part B of Case, the vehicle movement can be split into three phases: acceleration, constant spee an eceleration. During the acceleration phase, which applies until v v, the following equations hol. v at (3.4 a v t vt (3.41 Let s calculate the istance ' from station A, the spee v ' an the time t ' when the light rail train reaches the maximal esigne-spee v. ' v v (3.4 ' v v t a (3.43 ' a ' ' t vt (3.44 Then the vehicle will run at constant spee until D an finally ecrease its spee with a ecelerationb until station B. By aing the estimate time for the three phases, the estimate time to reach station B for Case 3 is equal to: ' ' D ( tremaining t t (3.45 v Case 4 Case 4 represents a vehicle running at normal (or low spee an approaching station B. The istance until the ownstream station is too small to reach the maximal esigne-spee v an the spee is lower than the spee profile for this istance. Case 4 shoul be split into two parts as shown in Figure /1/14

24 Page 3 of 9 v Designe spee (m/s A B D 1 3 Travelle istance (m D D Figure 3.8: Distinction of the two parts of Case 4 The part A represents a vehicle with a spee high enough for the river, which oesn t nee to accelerate to reach station B. In this case, the river is assume to let the vehicle roll as in Case. Then, when the vehicle reaches the blue line in Figure 3.8, the river will use the brake with a eceleration equal tob. The vehicle will en its run at station B. The part B represents a vehicle with a current spee too low to reach station B. So the river has to accelerate to increase its spee. The river is assume to accelerate with an acceleration a until the vehicle reaches the re line, an then ecrease its spee with a eceleration equal to c to stop at station B. As the vehicle is really close to the platform an running at low spee, the river is assume to brake smoother than usual. The limit case is represente by Equation (3.46. v c( D (3.46 Let s calculate the time to reach station B for a vehicle in part A of Case 4. A vehicle belongs to this area if an only if: v ( D v c( D (3.47 First, the river is assume to increase its eceleration when Equation (3.7 is satisfie (blue line. Let s calculate the istance ' from station A, the spee v ' an the time t ' when the vehicle moifies its eceleration from c tob, which is similar to calculation one for the part A of Case. So the istance ', the spee v ' an the time t ' are escribe in Equations (3.31, (3.3 an (3.33. After a time t ', the vehicle has a spee v ' an a istance ' from station A an will ecelerate with a ecelerationb until it reaches station B. So the estimate time to reach station B for the part A of Case 4 is equal to: ' ' v t remaining t (3.48 b The trajectory of the vehicle is escribe in Figure 3.9 for both parts of Case 4. 3/1/14

25 Page 4 of 9 v Designe spee (m/s ( ', v ' (, v 3 Travelle istance (m D D Figure 3.9: Representation of the ifferent trajectories for the fourth area Let s now calculate the time to reach station B for a vehicle in the part B of Case 4. As shown in Figure 3.9, the vehicle will increase its spee an Equations (3.4 an (3.41 hols until: v c( D (3.49 So the time can be expresse as a function of the spee in Equation (3.4 an be injecte in Equation (3.41. Therefore 1 ( v v (3.5 a So, Equations (3.49 an (3.5 represent a system of two equations with two unknowns (, v which gives us the searche istance ' from station A, the searche spee ' v an the searche time t ' when the vehicle changes its behavior from the acceleration phase to the eceleration phase: ' 1 v ( cd (3.51 a c v ' c( D (3.5 ' ' 1 ' t ( v v (3.53 a Now after a time t ', the vehicle is assume to ecrease its spee with a constant eceleration c until it reaches station B. So the estimate time to reach station B for the part B of Case 4 is equal to: ' ' v t remaining t (3.54 c Finally, the time to reach station B has been calculate for each case. More etaile calculation can be foun in Annex B. 3/1/14

26

27 Page 6 of 9 Other statistical inicators will be use such as the percentage of the eviation istribution which is within the following ranges: 1 sec; 1 sec, 3 sec;3 sec or 6 sec;6 sec. The last value is important for a passenger point of view, because some operators start to count elays after 6 secons [17]. Moreover, the 5%, 75% an 95% confience intervals will be measure. The peak value of the curve will be also given. The curve looks like a Gaussian curve, so only one peak value is present. As the istribution of the ifferences between preicte an actual arrival time follows a Gaussian curve, the with at half maximum is also a hint concerning the preiction quality. For example, if two curves have a really high peak value, the smaller the with at half maximum, the more scattere is the istribution, which shoul be avoie. In general, a high with at half maximum means that most of the value are close to the average value. Its avantage compare to the stanar eviation is to not be impacte by extreme ifferences between the preicte an actual arrival times. Passengers o not have the same feeling if a light rail train is earlier than expecte or elaye [19]. Therefore it is important to efine some inicators to estimate to what extent the moel unerestimates the remaining waiting time. The average of the negative values an the stanar eviation of the negative values are calculate an expresse in Equations (3.57 an (3.58. A negative value means that the preicte waiting time is shorter than the actual waiting time. This situation shoul be avoie as often as possible. x 1 n n x i i1, x n xi i1, x ( x (3.58 n 3/1/14

28 Page 7 of 9 4 CASE STUDY 4.1 System escription The Bergen Light Rail Train is a recent project which was launche in 8. The first stage of the Bergen Light Rail Train was finishe in June 1. It was mainly compose of 15 stations between Byparken (the city centre an Nesttun, which are istance of 9.8km. Figure 4.1 represents a schema of the line where the main proportions have been conserve. The line is compose of 5 crossings an 4 tunnels. The loa profile is also shown. Every ay aroun 31 passengers are travelling with Bybanen []. The secon phase concerns the extension of the line with five new stations. Finally, the last step shoul link the city centre to the airport. In the city centre, tracks are share with the bus network which represents the main component of the public transportation in Bergen. The main Bybanen objective was to reuce the roa congestion in the city centre cause by the population growth. Inee, Bergen is the secon biggest city in Norway (accoring to its number of inhabitants an the city is surroune by seven mountains which make access ifficult. A political agreement name the Bergen Program for Transport, Urban Development an the Environment has been signe for an investment of 5.3 millions NOK [1], mostly finance by the state an by the implementation of toll roas aroun the city centre. It aims to buil the new light rail train Bybanen, a new tunnel an to improve the cyclist roas an peestrians area. THALES is a sub-contractor of Bybanen Utbygging for the two first phases an was in charge of the telecommunication systems: Automatic Vehicle Location System (AVLS, Supervisory Control An Data Acquisition (SCADA, Intercom, Close-Circuit TeleVision (CCTV, Public Aress... One of the main issues was to test an valiate the new systems an software without isruptions of the operating system. 4. Traffic management The timetable is compose of 1 trips ivie into two perios of rush-hour uring the weekays: one in the morning (6h3-9h3 an one in the afternoon (13h-17h3. The scheule heaway is fifteen minutes uring the night, normally equal to 1 minutes an lowere to 5 minutes uring perios of rush-hour. Seventeen light rail trains are currently in operation an the number of rivers is aroun seventy. The management woul like to avoi elays. Therefore they ask rivers to leave the terminus on-time, which means the regulation is base on the applicable timetable. Drivers shoul respect some rules. First, they are not allowe to leave the terminus before the scheule eparture time. Then, the river shoul not take into consieration the elays of other light rail trains. They have to wait for the previous vehicles only if the signalization requires it. Moreover, the well time at a platform epens on the number of passengers an on the rivers. Basically, they precisely respect the timetable at the terminus but not in other stations. In consequence, the well time may be strongly epenent on exogenous variables. The passenger s information is mainly compose of the waiting time for the two next vehicles at each platform. The waiting time correspons to the ifference between the expecte arrival time at the station an the current time. As the regulation is only base on timetable at the terminus, the preiction of the eparture time at the terminus is not consiere. Only the arrival time in stations will be compute. Inee, the eparture time at the terminus is base on the trip chaining of the ifferent vehicles. As ata on trip chaining are not available in our case stuy, the moel assumes that a vehicle is in commercial operation as soon as it leaves one of the terminuses. 3/1/14

29 Page 8 of 9 Figure 4.1: Overview of the Bybanen line between Byparken an Nesttun 3/1/14

30 Page 9 of Data collection As part of the THALES team for the Bergen project, it was possible to have access to all available ata sen by the ifferent components of the light rail trains an along the tracks to the Automatic Vehicle Location System (AVLS. It is mainly compose of three kins of information: - Vehicle location from GPS, - Vehicle location from oometer - Activation of loops an track circuits. Thanks to ata, the AVLS, evelope by THALES Florence, is able to know the exact position of light rail trains along the line an isplays them on a screen. In consequence, it is assume that the light rail train position is consiere as an input of the problem. Moreover, Quality of Service (QOS ata storage keeps recor of all the previous travel times an well times from the last six months. This information is registere with the ate, the hour, the eviation from the scheule an the vehicle service. These ata can be use for the historical analysis, which represent the first part of the improvement. Accoring to ata collecte from Staler, the Bybanen rolling stock supplier, the following values are consiere as inputs of the stuy case for the ifferent moels: acceleration a 1.5m. s eceleration b.8m. s free roll eceleration c.66 m. s 1 The acceleration is equivalent to the highest possible acceleration for the light rail train, whereas the eceleration is lower than the highest eceleration, which is reserve for emergency situations. To conclue, the necessary inputs of the moel are the current position of the vehicle along the line, a atabase which contains the previous travel an well times over 6 months (February 13 July 13 an technical ata on vehicle (acceleration an eceleration. 4.4 Preiction scheme of the AVLS As the preiction scheme of the AVLS is link-base, for a light rail train locate at the station p or between the station p an the station p 1, the preiction timet pre at the station q is the sum of the remaining time to reach the next station t remaining an of the ifferent reference travel times an well times as expresse in Equation (4.1. q1 q1 T t T D (4.1 pre remaining i i p1 i i p1 In the AVLS system in operation, the well time is equal to secons for each platform an the travel time is either 4 secons or 1 secons for the links. Table 4.1 precisely provies implemente travel times for each link. 3/1/14

31 Page 3 of 9 Station BYP NOS BYS NYG FLO DAP KRO BRS WER SLE SLB FAN PAR HOP NES Expecte ingoing travel time (sec Expecte outgoing travel time (sec NA NA Table 4.1: Implemente travel time in the AVLS As escribe in 3., the calculation of the remaining time t remaining to reach the next station iffers if a train wells at a stop or runs between two stations. In the first case, calculations are similar to those which are escribe in Please refer to this paragraph for further etails. If the light rail train runs between stations A an B, let s call T B the preicte arrival time at station B, Tnow the time when the preiction is mae by the moel, the current position of the vehicle an D the istance between stations A an B. Therefore, the arrival time to reach the ownstream stop is estimate by the AVLS as: T B Tnow T (4. D The estimation is base on the Rule of Three, which means that if the istance between the vehicle an the next station is equal to xd, where x represents a percentage, the estimation of the time to reach the next platform will be xt. The time an the travelle istance are linearly epenent. The Rule of Three is not representative of the reality but it is the simplest way to approximate the remaining time to reach the next platform. 3/1/14

32 Page 31 of 9 5 APPLICATION In this chapter, the methoology escribe in 3 is applie to the stuy case escribe in 4. First a stuy of the well times at each stop will be one in orer to analyze theirs variations. A similar analysis will be carrie out for the travel time. Finally, the remaining time to reach the next platform will be estimate with both moels: esigne-spee moel an spee/position moel. 5.1 Dwell time analysis In public transports, the well time is efine as the time between the arrival an the eparture of a vehicle at a given station. In our case, rivers on t have a minimum well time to respect at each station. In consequence, it epens on the passengers flow, on the visibility or on the river switch. Light rail trains are more flexible than trains because train rivers have to wait for the official eparture time before leaving every station. On the other han, the eparture time of a bus is really epenent on traffic conitions an on passenger flow. In orer to have an overview of the possible well time variations along a ay or along a week, an analysis of the well time will be one. The methoology will consist in the following steps: ata collecting, ata filtering, analysis, moel improving an results. For the statistical analysis, only small eviations will be consiere. Inee, large eviations of the well time are relate to exceptional elays, which mean that the operators have aske rivers to wait at their respective position. It is important to remin that in our stuy case, rivers are suppose to leave the terminus on time accoring to the timetable. The well time on terminus will therefore not be analyze. So, we consier the well time for every station which is not a terminus. Thirteen stations fulfill this requirement. Each station is compose of two platforms: one for vehicles in irection of Byparken (ingoing an one for vehicles in irection of Nesttun (outgoing. It means that twenty six variations (, h of the well time will be introuce. i Data source To perform the stuy of the well time, a set of 6-month ata, which contains 4851 arrival times is available. Data are compose of telegrams which are receive from the on-boar system an contain the information of the arrival time an the eparture time for each light rail train for each station. The ifference between those values results in the well time at a station. Unfortunately, it wasn t possible to have access to the Skyss atabase, which is compose of the history of the number of passengers which have registere through the ticket machine insie the vehicle. It coul have been useful to fin a relation between the variation of the well time an the flow of passengers at the station. Data filtering As explaine in 3.., the on-boar system is reliable, but it can happen that ata are not collecte for a station. It is really important to have a clear atabase, so a filter is applie to elete incomplete ata or exceptionally long well time. In case of incomplete ata, associate ata are elete from the atabase. For example, if only the eparture time is given, then the arrival time is not important anymore for this stop. The secon scenario is more ifficult to analyse. A long well time can have ifferent origins: vehicle failure, inconsistent ata ue to a wrong OBS synchronisation, evacuation of a passenger, huge elays For the statistical analysis, we nee to calculate the most frequent 3/1/14

33 Page 3 of 9 well time at a platform. Or, a long well time represents an exceptional scenario an shoul not be taken into account in our statistical analysis. To etermine the highest acceptable well time for the statistical eviation analysis, the average an the stanar eviation are calculate for each platform an are summarize in Table 5.1. Station NOS BYS NYG FLO DAP KRO BRS WER SLE SLB FAN PAR HOP Ingoing average (sec Ingoing stanar eviation (sec Outgoing average (sec Outgoing stanar eviation (sec Table 5.1: Average an stanar eviation of the well time at each platform In Table 5.1, stanar eviations are between 5 an 51 secons. Accoring to the Transit Capacity an Quality of Service Manual [], usual stanar eviations for rail systems with an average well time inclue between an 3 secons are aroun 5 or 1 secons. Except for few stops, the Bergen light rail system is in phase with other similar rail systems even if the stanar eviation is slightly higher. A value can be qualifie of abnormal if the ifference between this value an the average value is bigger than 3 times the stanar eviation. In our case, the maximal average value is aroun 3 secons an the maximal stanar eviation is aroun 5 secons, so we assume that well times higher than 18 secons are consiere as abnormally long an will not be taken into account for the following calculations in this chapter. Analysis In the AVLS system, all the well times are equal to secons. However, it makes sense that well times may vary between two platforms an along the ay or the week. The average well time oesn t represent a trustful inicator to know the most common well time at a station. The following example will explain it. In Table 5.1, the average well time is 6.6 secons for the platform Sletten outgoing (number 1. However, accoring to Figure 5.1, the most common well time for this platform is 3 secons. In consequence, there is a ifference between the average well time an the most common well time at a platform which can be explaine. Inee, it often happens a light rail train remains longer than expecte at a station, but it is quite exceptional that the well time is shorter than 1 secons. So, the skewness of the slop is positive as shown in Figure /1/14

34 Page 33 of 9 Occurrence Dwell time (secons Figure 5.1: Occurrence of the well time at Sletten ingoing The eviation between the expecte well time an the most common well time is equal to 3 secons for this platform. In orer to improve the preictions calculation, the store value of the expecte well time in the system shoul be tune. Table 5. represents new ata which will be implemente in the moel. They represent the most common well times from each platform as shown for the platform Sletten ingoing in Figure 5.1. Station NOS BYS NYG FLO DAP KRS BRS WER SLE SLB FAN PAR HOP Expecte ingoing well time (sec Expecte outgoing well time (sec Table 5.: Implemente well time at each platform The ifference between the real well times an the most common value (moel with tuning is compare to the ifference between the real well time an the implemente well time ( secons for all stops in Figure 5.. Both curves have a positive skewness. However, the skewness of the moel with tuning is smaller an its peak value is higher, which means that the ifferences are usually closer to the value for the moel with tuning. Now, it is interesting to analyse the variations of the well time along a ay or along a week. Consiering the well time is highly relate to the passenger flow, it can be expecte than the well time is lower uring a night than uring a rush-hour. To stuy the epenency of the well time with the time, Figure 5.3 represents the percentage of occurrence of the ifference between the real well time an the most common well time for all platforms. The curve 8:: gathers all light rain trains with a eparture time from a station inclue in the time slot 8am-9am. As there is almost no traffic uring the night except on Friays an Saturays, a time slot 1am-6am has been create to collect enough information to perform a correct analysis. A shift of the peak for the ifferent curves can be seen. For a better unerstaning, the eviation relate to the peak values along the ay is represente in Figure /1/14

35 Page 34 of 9 Occurrence of the eviation With tuning Without tuning Dwell time eviation Figure 5.: Occurrence of the well time eviation Percentage of the eviation occurence Dwell time eivation :: 1:: 6:: 7:: 8:: 9:: 1:: 11:: 1:: 13:: 14:: 15:: 16:: 17:: 18:: 19:: :: 1:: :: 3:: Figure 5.3: Percentage of the eviation occurrence epening of the time. 3/1/14

36 Page 35 of Usual well time 6:: 9:: 1:: 15:: 18:: 1:: :: Time Figure 5.4: Most common eviation of the well time by time slot. Accoring to Figure 5.4, the well time is shorter uring the night (between pm an 7am than uring a rush-hour (between 14pm an 17pm. The rush-hour is quite early compare to other European cities because it is common to leave the office aroun 15pm in Norway. There is surprisingly no long well time uring the morning rush-hour (between 7am an 9 am. In Figure 5.3 an Figure 5.4, there is no istinction between the weekays an the ays of the week en. Passenger flow is smaller uring the weeken in the morning than uring the weekays. The istinction between the weekays an weekens is shown in Figure 5.5, where it is possible to observe a ifferent behaviour uring the weekens. This istinction has to be taken in consieration. 1 Usual well time 6:: 9:: 1:: 15:: 18:: 1:: :: Weekays Weeken -4-5 Time Figure 5.5: Most common eviation of the well time by time slot uring weekays an weekens 3/1/14

37 Page 36 of 9 Moel improving After having analyse the global behaviour of the well time along the line, two improvements have been foun. First, the expecte well time shoul be tune for each platform instea of establishing it equal to secons everywhere. The most common well time, which matches with the peak value of the occurrence of the well time, will be esigne as the expecte value as escribe in Table 5.. Then, the well time is highly relate to the passenger flow, which fluctuates along a ay an along a week. In orer to stuy this phenomenon, trens have been foun out along a ay an along a week. It has been shown that the weekays an the ays of the week en have two ifferent behaviours, so the fluctuation of the well time shoul be clearly separate. Finally, Table 5.3 shows the time-relate eviation of the well time i(, h. It applies for every station which is not a terminus. Time interval (week en (, h (secons i Time interval (weekays i(, h (secons 7:3 9: -1 7: 9: 9: 13:3 9: 18: 1 13:3 14:3 1 18: 1:3 14:3 18:3-1 1:3 :3-18:3 19:3 1 :3 7: -1 19:3 :3 :3 7:3 - Table 5.3: Implemente variable well time along a ay Results To compare the results of these moifications, Figure 5.6 represents the occurrence of the well time eviation. The peak value an the full with at half maximum are two goo inicators to estimate the accuracy of the moel. Accoring to Figure 5.6, some conclusions can be rawn. First, the tuning of the well time for each platform has improve the moel. Inee, the most common well time epens on the platform, because the passenger flow is ifferent for each platform. However, it is not really appropriate to use the average of the well time as a reference. Inee, it was shown that the average oesn t really fit with our statistical stuies. The peak value of the occurrence of the well time was preferre. Table 5.4 summarizes the ifferent results for the three moels. It can be seen that the moel with time-epenent well times has the highest peak value but its accuracy is comparable to the moel with tuning. There is a small shift between the two curves which correspon to the time-epenent well times. So, the moel with time-epenent well times improves a bit the accuracy, but this moel can not be applie for a light rail train uner construction because it requires historical ata. Finally, it has been shown that the variations of the well time epen on the ay (weekays or ay of week en an on the time (rush hour or night perio. In orer to take these parameters into account, a elta of the expecte well time was ae to the preiction as * escribe in Equation (5.1. The value D i represents the new implemente well time that can be foun in Table 5. an the value i(, h represents the variations of the well times, which epen on the stop, the ay an the time as escribe in Table /1/14

38 Page 37 of 9 T pre q1 tremaining Ti i p1 q1 * ( D i i, i p1 (, h (5.1 Moel Percentage of the well time eviation lower than 5s Percentage of the well time eviation lower than 1s Original 67.7% 87.9% Tune moel 7.3% 91% Moel with timeepenent well times 74% 89.6% Table 5.4: Results of the ifferent well time moel Occurrence of the eviation With tuning Without tuning With time epenent value Dwell time eviation Figure 5.6: Occurrence of the well time eviation 5. Travel time analysis In public transport systems, the travel time between two stations is efine as the ifference between the arrival time at the station N an the eparture time from the station N 1. Most public transport systems interact with other systems (roa traffic, peestrians. So, it makes harer to anticipate possible problems or elays. A rail light train has strong interactions with traffic ynamics at crossings an with peestrian area. These three components can cause elays, which can not be anticipate. Moreover, tunnels are also sensible areas because rivers have to ecrease their spee in tunnel if the lights are on, which happens when intrusion etectors are triggere. In this chapter, we will 3/1/14

39 Page 38 of 9 focus on the statistical analysis of travel times along the line in orer to improve preictions in the case of normal operation. The same methoology will be use than in 5.1: ata collecting, filtering, analysing, moel improving an comparing. For the statistical analysis, only the small eviations will be consiere. As efine in Equation (3., the preiction of the arrival time is compose of travel timest i between the stations i an i 1 an well times Di at the stationi. After the statistical analysis, Equation (3.3 gives the new preiction time where it(, h an i(, h respectively represent the variation of the well time an the variations of the travel time ue to exogenous parameters. In 5.1, the variation of the well time i(, h has been consiere. In this chapter, the variation of the travel time it(, h between two stations will be stuie. It is important to remin that the main line is compose of fifteen stations. All light rail trains are suppose to leave the terminus accoring to the timetable. Each station is compose of two platforms in opposing irections, which means the main line can be ivie into twenty eight sections. So, twenty eight travel times shoul be consiere. Data source To stuy the variation of the travel time, a set of 6-month ata which contains 4851 arrival times is available. As iscusse in 5.1.1, the eparture time an the arrival time for each train an for each platform can be extracte. Unfortunately, the AVLS oesn t manage the following signals: priority etection, tunnel signal. But it seems logical that the behaviour of the crossings an the behaviour of the signalisation at tunnel entrance are strongly relate to the travel time an can be at the origin of some elays. Data filtering As one in 5.1., a filter is applie to have an operational atabase. Incomplete ata an exceptionally long travel times ue to huge perturbations will not be taken into account. In orer to etect outliers, the average an the stanar eviation are calculate for each segment in Table 5.5: Average an stanar eviation of the travel time for each segmenttable 5.5. It can be seen than the stanar eviation is often inferior to 1 secons an the average value is aroun 6 secons. A value can be qualifie of abnormal if the ifference between this value an the average value is bigger than 3 times the stanar eviation. In our stuy, it was ecie to ignore all the travel times higher than 36 secons in orer to focus on a normal traffic situation. Segment BYP NOS BYS NYG FLO DAP KRO BRS WER SLE SLB FAN PAR HOP NES Ingoing average (sec Ingoing stanar eviation (sec Outgoing average (sec Outgoing stanar eviation (sec NA NA Table 5.5: Average an stanar eviation of the travel time for each segment NA NA 3/1/14

40 Page 39 of 9 Direction Byparken Nesttun (outgoing Nesttun Byparken (ingoing Average travel time (sec Stanar eviation of the travel time (sec Table 5.6: Average an stanar eviation of the travel time for the complete line Table 5.6 shows the averages an the stanar eviation of the travel time for both irections. It can be seen that the average travel time is almost equivalent to the sum of the average travel time for each section an of the well time for each stop in the associate irection. The interesting point is a really low stanar eviation. The first explanation is the non-linearity of the stanar eviation function. Then, it seems that rivers have the possibility to rive faster than usually or to make shorter well time if they are late. Finally, given the small size of the rail system in Bergen an the high scheule heaway, a elaye vehicle oesn t impact so much other vehicles. Moreover, a vehicle getting late in a section can run with a normal spee in the following sections. These ata confirm the choice of a link-base preiction scheme. The sections can be seen as inepenent from each other. Analysis At the beginning of the process, the same proceure is use than in Inee, the implemente travel times in the current AVLS are either 4 secons or 1 secons. These values shoul be tune in orer to improve the global behaviour of the system. The analysis of the most common travel time over the six last months are shown in the Table 5.7 for every section. Station BYP NOS BYS NYG FLO DAP KRO BRS WER SLE SLB FAN PAR HOP NES Expecte ingoing travel time (sec Expecte outgoing travel time (sec NA NA Table 5.7: Most common travel time for each portion With the current moel of preictions, the percentage of the occurrence of the travel time eviation is shown in Figure 5.7. The implemente travel time oesn t fit at all with the reality because no peak value can be observe for the pink curve. So the tuning of the implemente travel time improves the accuracy as shown by the blue curve in Figure 5.7. Results With the tuning, the average of the travel time eviations is aroun. The improvement is really huge between the two curves. We can now woner if the travel time is time-epenent. Figure 5.8 represents the occurrence of the travel time eviation for ifferent eparture times. Contrary to well times, travel times on t epen on the number of passengers. The external parameters which can have an influence are the following: roa traffic, crossing behaviour, peestrian areas or visibility ue to a low aylight. 3/1/14

41 Page 4 of 9 Occurence of the eviation With tuning Without tuning Travel time eviation Figure 5.7: Occurrence of the travel time eviation 15 Percentage of the eviation occurence Travel time eviation :: 1:: 6:: 7:: 8:: 9:: 1:: 11:: 1:: 13:: 14:: 15:: 16:: 17:: 18:: 19:: :: 1:: :: 3:: Figure 5.8: Percentage of the eviation occurrence of the travel time epening of the time. It is not possible to see some trens concerning the time-epenence in Figure 5.8. This is even more obvious in Figure 5.9. Concerning travel time, there is no time-epenency. So the only variation which will be implemente in the moel is the tuning of the efault travel time for every section. Table 5.7 summarizes the values for every section an Figure 5.7 shows the result of this analysis. This chapter has shown how ifficult it is to fin some variations for the next travel time, but it hasn t consiere the estimation of the remaining travel to reach the next platform when the light rail train is running, which can not be one with historical ata. The current position an current spee of the light rail train shoul be use as inputs to precisely estimate the arrival time to the next station, which is the matter of the next paragraph. 3/1/14

42 Page 41 of 9 1 6:: 9:: 1:: 15:: 18:: 1:: :: Usual eviation -4-5 Time -6 Figure 5.9: Most common eviation of the travel time by time slot. 5.3 Deriving the time for arrival at the ownstream station with current ata AVLS moel This section escribes the behaviour of the current AVLS moel, which is use as a benchmark. From the historical atabase, it is possible to extract the effective arrival times at stops. Moreover, some log files from the current AVLS system have been use. It is possible to extract from them preictions one by the AVLS. Collecte ata are train number, station name an platform name where the preiction applies, preicte arrival time one by the AVLS an the time when this information has been written in the log files. So a elta time can occur between the time when a preiction was calculate an the time when it has been written in the log file. With these log files an the historical atabase, it is possible to compare the preicte arrival time with the actual arrival time. The eviation between these two values has been calculate an its istribution is shown in Figure % of the preictions have a eviation smaller than one minute. 57% of them have a eviation smaller than 3 secons. These results are quite goo. Usually the preiction performance for a bus system is lower because traffic ynamics generate greater uncertainty [4]. However, this moel is only base on Rule of Three an coul probably be improve. 3/1/14

43 Page 4 of 9 8 percentage of occurrence (% Deviation between the preicte arrival time an the real arrival time (secons Figure 5.1: Preiction accuracy of the current AVLS moel. The coe of the AVLS is very complex because it shoul manage a lot of information an many interfaces (interface Web, signalisation, Passenger information isplays. Our stuy scope is limite to the preiction calculation. In orer to be more flexible with the moification of the coe, a moel in VBA has been evelope to replicate the behaviour of the AVLS for the preiction scheme. Only the core of the preiction calculation is present in the VBA coe. The evelope coe can be foun in Annexe A. The AVLS moel present in the VBA application is the benchmark of the stuy. First, the preiction one by the AVLS (available in log files an the preiction one by the VBA application shoul be compare. The preiction schemes of these two systems are similar. They shoul yiel similar preictions for the same scenario. Every time a preiction is written on a log file, the vehicle number, the stop, the preicte arrival time an the time when the line has been written are given. With these inications, the VBA application looks for the last known position of the vehicle in the historical atabase an calculates the arrival time for the eicate stop. A comparison between both results is one to assess its aequacy. The istribution of the ifference between the two implementations of the preiction scheme is shown in Figure /1/14

44 Page 43 of 9 1 Percentage of occurrence (% Deviation between the current AVLS moel an the simulate moel (secons Figure 5.11: Comparison of the VBA moel with the current AVLS moel. Figure 5.11 shows that the VBA moel is really close to the current AVLS moel. None of the ifferences excees 5 secons. We can see that it is no centre in zero. One of the reasons which coul explain this phenomenon is the reference time. Inee, the AVLS preiction (present on the log files was mae before the preiction was written on the log files. So, the VBA application an the AVLS o not exactly calculate the preiction with the same current timet Now, which can explain some ifferences between the two outputs. Designe-spee moel The esigne-spee moel has been implemente in the VBA application. So the inputs for the AVLS moel an the esigne-spee moel are the same. For each link, the esignespee profile has been calculate accoring to An example of the remaining time t remaining to reach ownstream stop is shown in Figure 5.1 as a function of the travelle istance. It has been calculate for the specific link Byparken Nonneseter with a esigne travel time of 59 secons. 3/1/14

45 Page 44 of time remaining (sec D 1 Distance (m Figure 5.1: Estimation of the time to reach the next platform epening on the istance In orer to compare both moels, only few estimations of the waiting time will be calculate. Inee, the two moels in the VBA application use the same moe of calculation when the train wells at the station. The preiction of the arrival platform of the vehicle will be ifferent only if a light rail train is running between two stations, which means. Only these preictions are calculate an compare in the following results. Figure 5.13 represents the eviation between the preicte arrival time an the actual arrival time only for the next platform an only if the vehicle is running between two stations. 35 Occurrence of the eviation (% Current moel Designe spee moel Deviation (sec Figure 5.13: Deviation between the preicte arrival time an the actual arrival time for the next platform an for running vehicles Figure 5.13 shows quite goo results, even if it oes not represent all the preictions but only a subset of it. The accuracy is very high because the average of the calculate waiting 3/1/14

46 Page 45 of 9 times is smaller than if all the preictions have been taken into account. The calculate waiting times are almost always inferior to secons, which leave few space to incertitue an explain the high accuracy. Table 5.8 shows some inicators for both moels. Current moel Designespee moel Peak value (% Average (sec Stanar eviation (sec Table 5.8: Results between the current moel an the esigne-spee moel It can be seen in Table 5.8 that the average of the current moel is smaller than the esigne-spee moel. Accoring to the esigne-spee moel, the eceleration phase takes longer than with the current moel. So, the expecte waiting time will be estimate higher than with the current moel. As escribe before, the passengers expect to arrive on time to their estination. If not, they will consier their travel unpleasant. That s why it is better to have a positive eviation than a negative eviation. So, even if the average of the esigne-spee moel is higher than those of the current moel, the esigne-spee moel improves the performance of the system, because it reuces the number of negatives eviation an the number of preictions which overestimate by more than 5 secons compare with the actual arrival time. Spee-position moel In orer to compare the three moels, preictions will be calculate an compare only if the light rail train is running between two stations (. In this case, the preictions of the arrival platform of the vehicle will be ifferent for each moel. An example of the remaining time t remaining to reach ownstream stop is shown in Figure 5.14 as a function of the travelle istance an the current vehicle spee. It has been calculate for the specific link Byparken Nonneseter with a esigne travel time of 59 secons. In Figure 5.14, the remaining time to reach the platform is lower if the current spee is higher which makes sense. The continuity of the remaining is assure except for the part B of Case 4. Inee, it can be seen that a small iscontinuity between it an Case 3. It represents a vehicle approaching station B an its river ecies either to accelerate to reach the maximal esigne spee (Case 3, either to accelerate enough to reach the station (part B of Case 4. Figure 5.15 represents the eviation between the preicte arrival time an the actual arrival time only for the next platform an only if the train is running between two stations for the three moels. 3/1/14

47 Page 46 of 9 Figure 5.14: Representation of the remaining travel time for the spee/position moel as function of the current vehicle position an spee 35 Occurrence of the eviation (% Current moel Designe spee moel Spee/position moel Deviation (sec Figure 5.15: Occurrence of the eviation between the preicte arrival time an the actual arrival time for the next platform an for running vehicles Figure 5.15 inicates that the spee/position moel has goo results, but not better than the esigne-spee moel. The spee/position moel has higher performances than the current 3/1/14