TY - JOUR

T1 - Multi-class percentile user equilibrium with flow-dependent stochasticity

AU - Nie, Yu Marco

N1 - Funding Information:
Professor Hani Mahmassani at Northwestern University had provided many valuable comments. In particular, he convinced me that the service flow rate is a better term than “capacity” for the purpose of this study. At his suggestion, the current manuscript explicitly distinguishes the service flow rate, on which the calculation of travel time is supposed to be based, from capacity, which is typically defined as the maximum hourly volume that has a reasonable expectation of occurrence. Comments of an anonymous referee have helped to improve the analytical results presented in Section 5 . The research was supported by National Science Foundation under the Award Number CMMI-0928577 .

PY - 2011/12

Y1 - 2011/12

N2 - Travelers often reserve a buffer time for trips sensitive to arrival time in order to hedge against the uncertainties in a transportation system. To model the effects of such behavior, travelers are assumed to choose routes to minimize the percentile travel time, i.e. the travel time budget that ensures their preferred probability of on-time arrival; in doing so, they drive the system to a percentile user equilibrium (UE), which can be viewed as an extension of the classic Wardrop equilibrium. The stochasticity in the supply of transportation are incorporated by modeling the service flow rate of each road segment as a random variable. Such stochasticity is flow-dependent in the sense that the probability density functions of these random variables, from which the distribution of link travel time are constructed, are specified endogenously with flow-dependent parameters. The percentile route travel time, obtained by directly convolving the link travel time distributions in this paper, is not available in closed form in general and has to be numerically evaluated. To reveal their structural properties, percentile UE solutions are examined in special cases and verified with numerical results. For the general multi-class percentile UE traffic assignment problem, a variational inequality formulation is given and solved using a route-based algorithm. The algorithm makes use of the diagonal elements in the Jacobian of percentile route travel time, which is approximated through recursive convolution. Preliminary numerical experiments indicate that the algorithm is able to achieve highly precise equilibrium solutions.

AB - Travelers often reserve a buffer time for trips sensitive to arrival time in order to hedge against the uncertainties in a transportation system. To model the effects of such behavior, travelers are assumed to choose routes to minimize the percentile travel time, i.e. the travel time budget that ensures their preferred probability of on-time arrival; in doing so, they drive the system to a percentile user equilibrium (UE), which can be viewed as an extension of the classic Wardrop equilibrium. The stochasticity in the supply of transportation are incorporated by modeling the service flow rate of each road segment as a random variable. Such stochasticity is flow-dependent in the sense that the probability density functions of these random variables, from which the distribution of link travel time are constructed, are specified endogenously with flow-dependent parameters. The percentile route travel time, obtained by directly convolving the link travel time distributions in this paper, is not available in closed form in general and has to be numerically evaluated. To reveal their structural properties, percentile UE solutions are examined in special cases and verified with numerical results. For the general multi-class percentile UE traffic assignment problem, a variational inequality formulation is given and solved using a route-based algorithm. The algorithm makes use of the diagonal elements in the Jacobian of percentile route travel time, which is approximated through recursive convolution. Preliminary numerical experiments indicate that the algorithm is able to achieve highly precise equilibrium solutions.

KW - Convolution

KW - Flow-dependent stochasticity

KW - Percentile user equilibrium

KW - Traffic assignment

KW - Variational inequality

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U2 - 10.1016/j.trb.2011.06.001

DO - 10.1016/j.trb.2011.06.001

M3 - Article

AN - SCOPUS:80455164693

VL - 45

SP - 1641

EP - 1659

JO - Transportation Research, Series B: Methodological

JF - Transportation Research, Series B: Methodological

SN - 0191-2615

IS - 10

ER -