Risk Analysis Model for High-Speed Rail Ridership and Revenue Forecasts

In the forecasting process, there is inherent uncertainty at every stage, from the underlying data used for estimation and calibration, to the estimated variables within the models, to the input assumptions with regard to the forecast year. To capture the uncertainty related to the process, a risk analysis model can be developed to provide a quick, systematic methodology for producing a range of forecasts. While common for assessing traffic and revenue forecasts, risk analysis models are less common for transit forecasting, so the development of the risk analysis process marks an innovative step forward in travel demand forecasting.


Develop a risk analysis model for producing a probabilistic range of high-speed rail (HSR) ridership and revenue forecasts.

Project Overview

Cambridge Systematics’ approach to forecasting ridership and revenue for the high-speed rail project was to build the best behavioral state-of-the-practice model possible, while recognizing and quantifying sources of uncertainty in the model estimation, as well as in the underlying assumptions about future conditions in society.  To achieve this, Cambridge Systematics (CS) followed a five-step process to develop and run the risk analysis model:

  1. Identify Risk Factors – Select which factors are most likely to have the greatest effect on ridership. The final factors included:
    • Total population, households, and employment.
    • Spatial distribution of population and employment.
    • Auto operating cost.
    • Airline fares.
    • High-speed rail main mode choice constants (HSR constants).
    • Trip frequency model constants.
  2. Develop Range of Risk Factors – Risk factors were quantified so each could be treated as a continuous independent variable within a regression model. For each risk factor, we developed a low, middle, and high value for each forecast year, and then developed a probabilistic distribution around these values based on available research and analysis.
  3. Run Ridership and Revenue Model – Once the risk factors and their distributions were defined, the full ridership and revenue model was run 48 times using different combinations of risk factor values to develop the input data for the estimation of the risk analysis regression equations.
  4. Estimate Regression Models – CS used the ridership and revenue forecasts from the full ridership and revenue model runs to estimate the relationship between levels of the risk factor inputs and the resulting ridership and revenue forecasts.
  5. Run Monte Carlo Simulation –

    The Monte Carlo method makes it feasible to estimate the probability distribution of possible outcomes by using a limited number of full model runs using a deterministic equation, which is the regression model in this case.

    The Monte Carlo simulation software constructed 5,000 unique scenarios and produced 5,000 forecasts of revenue and ridership for each analysis scenario, as shown in the figure below.

    The Result of the Process was 5,000 Forecasts of Ridership and Revenue for Each Analysis Scenario.

    risk analysis


This approach recognizes that even state-of-the-practice travel demand models that have been fully calibrated and validated are subject to uncertainty regarding the estimated variables within the models, the underlying data used for estimation, and the observed data collected for calibration of the existing model. In addition, future conditions cannot be known with certainty. The forecasts used for planning purposes need to recognize the uncertainties in the exogenous variables used as input to the model and present a reasonable range. The risk analysis model estimates a probabilistic range of HSR ridership and revenue forecasts, rather than a point-forecast that fails to recognize that uncertainty that accompanies these predicted outcomes.