01340275

Component

Travelers often reserve a buffer time for trips sensitive to arrival time, being frequently reminded of the uncertainties in a transportation system. This paper intends to model the effects of this risk-taking behavior of heterogeneous travelers. Travelers are assumed to choose routes to minimize the percentile travel time, i.e. the travel time budget that ensures the desired probability of on-time arrival; in doing so, they drive the system to a percentile user equilibrium (UE), which is an extension of the classic Wardrop equilibrium. The uncertainty in the supply of transportation is incorporated by modeling the capacity of each road segment as a random variable. The probability density functions of these random variables are specified exogenously with flow-dependent parameters. By directly convoluting the link travel time distributions, the distribution of route travel time is obtained. The percentile route time function derived from convolutions does not have a closed form and may not be monotone with respect to route flow in general. Numerical schemes are proposed to evaluate the percentile route travel time and to approximate its Jacobian through recursive convolutions. For two special cases analytical percentile UE solutions are obtained and verified by numerical experiments. The analyzes indicate that the travelers with higher on-time arrival probability always use the more reliable route, everything else equal. A route-based algorithm is proposed to solve a variational inequality formulation for the percentile UE problem. An important feature of the algorithm is the use of the diagonal elements in the Jacobian of percentile route travel to scale the flow shift, which mimics the Quasi-Newton method for the classic traffic assignment problem. The algorithm demonstrated satisfactory convergence performance and is able to achieve very precise equilibrium solutions in all reported tests.

The DVD lists the title of this paper as: Multiclass Percentile User Equilibrium Traffic Assignment Problem.

01329018

11-2458

English

29p

2011

Transportation Research Board 90th Annual Meeting

DVD

Figures (9) ; References; Tables (4)

Algorithms; Highway capacity; Random variables; Route choice; Time dependence; Traffic assignment; Travel time; Uncertainty

Arrival time; Buffer time; On-time arrival; User equilibrium; Wardrop model

Highways; Planning and Forecasting; Public Transportation; I72: Traffic and Transport Planning

Transportation Research Board Annual Meeting 2011 Paper #11-2458

TRIS, TRB

Feb 17 2011 6:10PM