Valuing travel time variability: Characteristics of the travel time distribution on an urban road

Fosgerau, Mogens and Fukuda, Daisuke (2010): Valuing travel time variability: Characteristics of the travel time distribution on an urban road.

Abstract

Fosgerau and Karlstrom [The value of reliability. Transportation Research Part B, Vol. 43 (8–9), pp. 813–820, 2010] presented a derivation of the value of travel time variability (VTTV) with a number of desirable properties. This definition of the VTTV depends on certain properties of the distribution of random travel times that require empirical verification. This paper therefore provides a detailed empirical investigation of the distribution of travel times on an urban road. Applying a range of nonparametric statistical techniques to data giving minute-by-minute travel times for a congested urban road over a period of five months, we show that the standardized travel time is roughly independent of the time of day as required by the theory. Except for the extreme right tail, a stable distribution seems to fit the data well. The travel time distributions on consecutive links seem to share a common stability parameter such that the travel time distribution for a sequence of links is also a stable distribution. The parameters of the travel time distribution for a sequence of links can then be derived analytically from the link level distributions.

• Item Type: MPRA Paper
• Language: English
• Keywords: value of travel time variability; travel time distribution; nonparametrics; stable distributions
• Subjects: R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R4 - Transportation Economics > R41 - Transportation: Demand, Supply, and Congestion ; Travel Time ; Safety and Accidents ; Transportation Noise

References

Bates, J., Polak, J., Jones, P., Cook, A., 2001. The valuation of reliability for personal travel. Transportation Research Part E: Logistics and Transportation Review 37 (2–3), 191–229.

Brownstone, D., Small, K., 2005. Valuing time and reliability: assessing the evidence from road pricing demonstrations. Transportation Research Part A: Policy and Practice 39 (4), 279–293.

Doornik, J. A., 2001. Ox: An Object-Oriented Matrix Language. London.

Fosgerau, M., 2010. On the relation between the mean and variance of delay in dynamic queues with random capacity and demand. Journal of Economic Dynamics and Control 34 (4), 598–603.

Fosgerau, M., Engelson, L., forthcoming. The value of travel time variance. Transportation Research Part B: Methodological.

Fosgerau, M., Karlstrom, A., 2010. The value of reliability. Transportation Research Part B: Methodological 43 (8–9), 813–820.

Gnedenko, B. V., Kolmogorov, A. N., 1954. Limit Distributions for Sums of Independent Random Variables. Addison-Wesley.

Hall, P., Racine, J., Li, Q., 2004. Cross-validation and the estimation of conditional probability densities. Journal of the American Statistical Association 99 (468), 1015–1027.

Härdle, W., 1990. Applied Nonparametric Regression. Econometric Society Monograph Series. Cambridge University Press.

Ichimura, T., Fukuda, D., 2010. A fast algorithm for computing least-squares cross-validations for nonparametric conditional kernel density functions. Computational Statistics & Data Analysis 54 (12), 3404–3410.

Lam, T. C., Small, K., 2001. The value of time and reliability: measurement from a value pricing experiment. Transportation Research Part E: Logistics and Transportation Review 37 (2-3), 231–251.

Li, Q., Racine, J., 2007. Nonparametric Econometrics: Theory and Practice. Princeton University Press.

Michael, J. R., 1983. The stabilized probability plot. Biometrika 70 (1), 11–17.

Nolan, J. P., 1997. Numerical calculation of stable densities and distribution functions. Stochastic Models 13 (4), 759–774.

Nolan, J. P., 2001. Maximum likelihood estimation of stable parameters. In: Barndorff-Nielsen, O. E., Mikosch, T., Resnick, S. I. (Eds.), Lévy Process: Theory and Applications. Birkhäuser, Boston, pp. 379–400.

Nolan, J. P., in press. Stable Distributions – Models for Heavy Tailed Data. Birkhäuser, Boston.

Noland, R. B., 1997. Commuter responses to travel time uncertainty under congested conditions: expected costs and the provision of information. Journal of Urban Economics 41 (3), 377–406.

Noland, R. B., Polak, J. W., 2002. Travel time variability: a review of theoretical and empirical issues. Transport Reviews 22 (1), 39–54.

Noland, R. B., Small, K. A., 1995. Travel-time uncertainty, departure time choice, and the cost of morning commutes. Transportation Research Record 1493, 150–158.

Noland, R. B., Small, K. A., Koskenoja, P. M., Chu, X., 1998. Simulating travel reliability. Regional Science and Urban Economics 28 (5), 535–564.

Pagan, A., Ullah, A., 1999. Nonparametric Econometrics. Cambridge University Press.

R Development Core Team, 2007. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.

Robust Analysis, Inc., 2006. User Manual for STABLE 4.0 S–Plus/R Version.

Scott, D. W., 1979. On optimal and data-based histograms. Biometrika 66 (3), 605–610.

Small, K. A., 1982. The scheduling of consumer activities: work trips. American Economic Review 72 (3), 467–479.

Small, K. A., Winston, C., Yan, J., 2005. Uncovering the distribution of motorists’ preferences for travel time and reliability. Econometrica 73 (4), 1367–1382.

Su, L., White, H., 2007. A consistent characteristic function-based test for conditional independence. Journal of Econometrics 141 (1), 807–834.

Vickrey, W. S., 1973. Pricing, metering, and efficiency using urban transportation facilities. Highway Research Record 476, 36–48.

Zolotarev, V., 1986. One-Dimensional Stable Distributions. American Mathematical Society.