Dynamic and stochastic shortest path in transportation networks with two components of travel time uncertainty

Abstract The existing dynamic and stochastic shortest path problem (DSSPP) algorithms assume that the mean and variance of link travel time (or other specific random variable such as cost) are available. When they are used with observed data from previous time periods, this assumption is reasonable. However, when they are applied using forecast data for future time periods, which happens in the context of ATIS, the travel time uncertainty needs to be taken into account. There are two components of travel time uncertainty and these are the individual travel time variance and the mean travel time forecasting error. The objectives of this study are to examine the characteristics of two components of travel time uncertainty, to develop mathematical models for determining the mean and variance of the forecast individual travel time in future time periods in the context of ATIS, and to validate the proposed models. First, this study examines the characteristics of the two components of uncertainty of the individual travel time forecasts for future time periods and then develops mathematical models for estimating the mean and variance of individual route travel time forecasts for future time periods. The proposed models are then implemented and the results are evaluated using the travel time data from a test bed located in Houston, Texas. The results show that the proposed DSSPP algorithms can be applied for both travel time estimation and travel time forecasting.

[1]  Ronald Prescott Loui,et al.  Optimal paths in graphs with stochastic or multidimensional weights , 1983, Commun. ACM.

[2]  William L Eisele,et al.  Travel-Time Estimates Obtained from Intelligent Transportation Systems and Instrumented Test Vehicles: Statistical Comparison , 2002 .

[3]  Nagui M. Rouphail,et al.  TRAVEL TIME DATA FUSION IN ADVANCE , 1993 .

[4]  Bruce Hellinga.  COMPARATIVE ASSESSMENT OF AVI TAG MATCHING ALGORITHMS FOR ESTIMATING VEHICLE TRAVEL TIMES , 2001 .

[5]  S. M. Turner,et al.  Probe vehicle sample sizes for real-time information: the Houston experience , 1995, Pacific Rim TransTech Conference. 1995 Vehicle Navigation and Information Systems Conference Proceedings. 6th International VNIS. A Ride into the Future.

[6]  Bart van Arem,et al.  TRAVEL TIME ESTIMATION IN THE GERDIEN PROJECT , 1997 .

[7]  Dongjoo Park,et al.  Forecasting Multiple-Period Freeway Link Travel Times Using Modular Neural Networks , 1998 .

[8]  Randolph W. Hall,et al.  The Fastest Path through a Network with Random Time-Dependent Travel Times , 1986, Transp. Sci..

[9]  Laurence R. Rilett,et al.  Spectral Basis Neural Networks for Real-Time Travel Time Forecasting , 1999 .

[10]  Laurence R. Rilett,et al.  Incorporating Uncertainty and Multiple Objectives in Real-Time Route Selection , 2001 .

[11]  L. B. Fu,et al.  Expected Shortest Paths in Dynamic and Stochastic Traf c Networks , 1998 .

[12]  Elise Miller-Hooks,et al.  Least possible time paths in stochastic, time-varying networks , 1998, Comput. Oper. Res..

[13]  Dongjoo Park,et al.  Forecasting Freeway Link Travel Times with a Multilayer Feedforward Neural Network , 1999 .

[14]  Karthik K. Srinivasan,et al.  Determination of Number of Probe Vehicles Required for Reliable Travel Time Measurement in Urban Network , 1996 .

[15]  David E. Boyce,et al.  Estimation and measurement of link travel times in the ADVANCE project , 1993, Proceedings of VNIS '93 - Vehicle Navigation and Information Systems Conference.

[16]  Pitu B. Mirchandani,et al.  Shortest distance and reliability of probabilistic networks , 1976, Comput. Oper. Res..

[17]  Sumit Sarkar,et al.  A Relaxation-Based Pruning Technique for a Class of Stochastic Shortest Path Problems , 1996, Transp. Sci..

[18]  Piyushimita Thakuriah,et al.  FREQUENCY OF PROBE REPORTS AND VARIANCE OF TRAVEL TIME ESTIMATES , 1997 .

[19]  Hani S. Mahmassani,et al.  Least Expected Time Paths in Stochastic, Time-Varying Transportation Networks , 1999, Transp. Sci..