Presentation of the practical exercise on traffic forecasting

Transcription

1 Presentation of the practical exercise on traffic forecasting During this session you are going to be assigned a task aimed at making you more familiar with traffic forecasting for High Speed Rail lines. Task A High Speed Line (HSL) is planned between two cities Azurcity (A) and reducing travel time by 60 minutes. Bluecity (B) You are in charge of assessing the viability of this project for AMRAIL, the company which is promoting it. A first step for the profitability assessment is the traffic forecast. This is what you are going to carry out now. You have to go through the following 5-stage process. The Excel worksheet corresponding to each stage is given between brackets. Stage 1: Understanding of the present position of conventional rail on the rail + air market ( Price-Time Model) For this purpose you need to find the appropriate distribution function for the time value of people travelling in the AB corridor. Stage 2: Understanding the present rail demand ( Gravity Model Calibration) This stage aims at estimating 2 parameters: rail travellers value of time and generalized cost elasticity Stage 3: Forecasting the new rail market share on the rail + air market ( Model Application) Price-Time Based on the distribution functionn found in stage 1, you will use the mathematical Price-Time model to forecast the new rail market share. Stage 4: Forecasting the modal shift from road and mobility increasee ( Forecast) Traffic At this stage you will have to plan how many trains per day and per direction you will run. Using the 2 parameters estimated in stage 2, you will use the mathematical Gravity Model to forecast the modal shift from road and mobility increase. 1

2 Stage 5: Maximization of AMRAIL s Profit ( Traffic Forecast and Cost Function) You will estimate the production costs in relationship with the number of trains selected in stage 4. At the end of this exercise you will be able to assess the economic interest of the project for AMRAIL. Stage 1: Understanding of the present position of conventional rail on the rail + air market ( Price-Time Model) For a given origin-destination (A-B), competition between rail and air is modelized by a price-time model. Value of time Log Normal density Rail Market Share Air Market Share 0 20 h First, you have to determine the without project). The indifference value of time is takes the train or the plane. indifference time value in the reference situation (situation the value for which the traveller doesn t care whether he/she 2

3 Mathematically, the indifference value of time is defined as the value which equates rail and air generalized costs. Rail and Air generalized costs are respectively defined by GC r = P r + h x GT r GC a = P a + h x GT a GT r and GT a are respectively rail and air generalized time (including access time). GT r is the sum of rail access time and rail best travel time. GT a is the sum of air access time and air best travel time. P r is the price of the rail ticket. P a is the price of the air ticket. The indifference value of time, h 0, is such as GT r = GT a To calculate this value you have to use the following formula h = 3

4 Once you have calculated the indifference value of time and the rail market share, you have to select the right distribution function curves corresponding to these values (seee Price-Time Model worksheet). 100% 90% 80% 70% 60% 50% Time Value Distribution Function 40% 30% 20% 10% 0% According to you which is the curve (yellow, green, blue or red) which most describes the present Rail + Air Market? appropriately Stage 2: Understanding the present rail demand ( Gravity Model Calibration) 9 Origin-Destinations pairs are considered in order to help to calibrate the gravity model. Inputs are origin and destinationn populations, average rail journey time, average price and number of trains per day and direction (frequencies). The gravity model is stated as follows: is a multiplicative constant, = P i and P j are respectively the origin and destination populations 4

5 GC is the generalized cost of the trip. It is the sum of the average ticket price and of the generalized travel time multiplied by the value of time: GC = P + h x GT Generalized travel time is the sum of the rail journey time and of the average between two frequencies. waiting time h is the average value of time. is the generalized cost elasticity (in absolute value). You have to test various values of and h in order to minimize the difference between estimated and actual traffic (see Gravity Model Calibration worksheet). Stage 3: Forecasting the new rail market share on the rail + air market ( Model Application) Price-Time When the High Speed Line is commissioned, it will cut the travel time by 60 minutes. You have to go to the Price-Time Model Application worksheet in order to project rail market share. calculate the First, you have to choose the appropriate price for the high speed rail trip and calculate the new indifference value of time for people making a trade-off between rail and air. Please, note that the new rail ticket price must not be less than the reference rail price and must not exceed the reference rail price by more than 10%. Then, go back to the Price-Timee mode worksheet. Using the curve selected in Stage 1, you have to calculate the new rail market share. Finally, put this project rail market share value into cell Rail Market Share on the Price- Time Model Application worksheet and calculate the diverted traffic from air to rail. The calculation of the traffic shift from air to rail is done automatically by filling the market share value in the right place of the calculation sheet. Stage 4: Forecasting the traffic shift from road and mobility increasee ( Forecast) Traffic In order to estimate the increase of rail traffic from the reference situation to the project situation, you have to re-calculate the rail generalized cost, by increasing the ticket price by less than the reduction of generalized travel time. This condition is satisfied in our exercise thanks to the 10% maximum increase of the rail price (see Stage 3). So, we can write: 5

6 = = We can divide by and obtain: oj GC Re f Re f T Pr = i,j T i,j (*) GC Pr oj γ With the optimal parameters calculated in Stage 2, you have to calculate (using the Traffic Forecast worksheet) the travel generalized cost ( GC Re f ) in the reference situation and the travel generalized cost ( GCPr oj ) in the project situation. In this perspective, you have to use the project rail ticket price already chosen for the Price-Time Model Application and to plan the number of trains per day and direction (at least equal to the corresponding number in the reference situation since you expect an increase of traffic). Once ( GCPr oj ) calculated, you have to apply the previous equation (*) to estimate the traffic coming from road and the mobility increase. Forecasting global project rail traffic At this stage, you only have to add the traffic shifting from air (assessed by the price-time model) to the traffic coming from road and mobility increase (assessed by the gravity model). You have to check that the annual average number of passengers by frequency does not exceed (capacity constraint). Project rail revenues are then obtained by multiplying project rail price and project rail traffic. Stage 5: Maximization of AMRAIL s Profit This stage consists in maximizing the difference between the previously estimated revenues and the operating costs (including capital costs) for the railway undertaking. Operating costs depend on the number of trains (frequencies). The cost function is given in Cost Function worksheet. You have to test the number of trains (not lower than in the reference situation) and the rail ticket price (to be kept between the reference ticket price and this value plus 10%) in order to maximize the company margin. 6

7 If you have reached this stage, you will be promoted CEO of AMRAIL since you know how to optimize the economic relevance of the Azurcity Bluecity project. 7