Brownian Motion Models for Toll Traffic Forecasting and Financing Strategies under Uncertainty

Growing policy challenges and return on investment concerns arising from uncertainty in toll road traffic and revenue forecasting prompt deeper investigation into natural risks associated with future forecasts. Brownian motion models are a class of financial time series methods with stochasticity that represent fluctuating trends and future market patterns of particularly volatile stock or commodity prices. This study extends their application into equally dynamic toll travel markets, and explores a canonical sub-class called Brownian motion mean reversion (BMMR) models following the Ornstein–Uhlenbeck process. This stochastic process combined with Monte Carlo simulation provides an auxiliary tool for toll transactions forecasting while simultaneously internalizing forecast randomness. The integrated framework is demonstrated using system-wide annual toll transactions along an existing toll facility. Toll transactions are modeled as evolving with time in a stochastic process governed by volatility resulting from market ‘shocks’ and forecast uncertainty. Unit-root hypothesis testing and Augmented Dickey-Fuller statistics reveal non-stationarity in data (not atypical of traffic patterns), while suggesting Brownian phenomena. Theoretically, BMMR model transactions ultimately gravitate towards a state of dynamic equilibrium after continued long years of operation due to travel demand saturation, supply-side capacity limitations, and level-of-service considerations. Empirical validation on observed data is performed for the BMMR model forecasts, and their baseline estimates and percentile ranges are presented. Model forecast risk-levels are found to increase with future planning horizon, especially in outer years 2030 and beyond. The study concludes with tools and recommendations for long-range toll T&R forecasting, and risk-aware financing of toll infrastructure assets.

  • Supplemental Notes:
    • This paper was sponsored by TRB committee ABE10 Standing Committee on Revenue and Finance.
  • Corporate Authors:

    Transportation Research Board

    500 Fifth Street, NW
    Washington, DC  United States  20001
  • Authors:
    • Shah, Rohan
    • Jammalamadaka, Phani
  • Conference:
  • Date: 2016


  • English

Media Info

  • Media Type: Digital/other
  • Features: Figures; References; Tables;
  • Pagination: 23p
  • Monograph Title: TRB 95th Annual Meeting Compendium of Papers

Subject/Index Terms

Filing Info

  • Accession Number: 01593842
  • Record Type: Publication
  • Report/Paper Numbers: 16-6708
  • Files: TRIS, TRB, ATRI
  • Created Date: Jan 12 2016 6:55PM