A new schedule-based transit assignment model with travel strategies and supply uncertainties

This paper proposes a new scheduled-based transit assignment model. Unlike other schedule-based models in the literature, we consider supply uncertainties and assume that users adopt strategies to travel from their origins to their destinations. We present an analytical formulation to ensure that on-board passengers continuing to the next stop have priority and waiting passengers are loaded on a first-come-first-serve basis. We propose an analytical model that captures the stochastic nature of the transit schedules and in-vehicle travel times due to road conditions, incidents, or adverse weather. We adopt a mean variance approach that can consider the covariance of travel time between links in a space–time graph but still lead to a robust transit network loading procedure when optimal strategies are adopted. The proposed model is formulated as a user equilibrium problem and solved by an MSA-type algorithm. Numerical results are reported to show the effects of supply uncertainties on the travel strategies and departure times of passengers.

[1]  Shing Chung Josh Wong,et al.  A stochastic transit assignment model using a dynamic schedule-based network , 1999 .

[2]  Cristián E. Cortés,et al.  Stochastic transit equilibrium , 2013 .

[3]  W. Y. Szeto,et al.  A Cell‐Based Model for Multi‐class Doubly Stochastic Dynamic Traffic Assignment , 2011, Comput. Aided Civ. Infrastructure Eng..

[4]  Donald D. Eisenstein,et al.  A self-coördinating bus route to resist bus bunching , 2012 .

[5]  Shing Chung Josh Wong,et al.  A dynamic schedule-based model for congested transit networks , 2004 .

[6]  Liu Yang,et al.  Probit-Type Reliability-Based Transit Network Assignment , 2006 .

[7]  Henry X. Liu,et al.  Method of Successive Weighted Averages (MSWA) and Self-Regulated Averaging Schemes for Solving Stochastic User Equilibrium Problem , 2009 .

[8]  Otto Anker Nielsen,et al.  A Stochastic Traffic Assignment Model Considering Differences in Passengers Utility Functions , 2000 .

[9]  Nicolas Coulombel,et al.  The value of service reliability , 2013 .

[10]  E. Jenelius.  The value of travel time variability with trip chains, flexible scheduling and correlated travel times , 2012 .

[11]  W. Y. Szeto,et al.  Time-dependent transport network improvement and tolling strategies , 2008 .

[12]  Giulio Erberto Cantarella,et al.  Modelling sources of variation in transportation systems: theoretical foundations of day-to-day dynamic models , 2013 .

[13]  Fumitaka Kurauchi,et al.  Frequency-based transit assignment considering seat capacities , 2011 .

[14]  Nigel H. M. Wilson,et al.  Schedule-Based Dynamic Transit Modeling: Theory and Applications (Operations Research/Computer Science Interfaces, 28) , 2004 .

[15]  Umberto Crisalli,et al.  A schedule-based assignment model with explicit capacity constraints for congested transit networks , 2012 .

[16]  Hai Yang,et al.  A stochastic user equilibrium assignment model for congested transit networks , 1999 .

[17]  W. Y. Szeto,et al.  Distribution-free travel time reliability assessment with probability inequalities , 2011 .

[18]  Otto Anker Nielsen,et al.  Optimisation of timetable-based, stochastic transit assignment models based on MSA , 2006, Ann. Oper. Res..

[19]  Fumitaka Kurauchi,et al.  Capacity Constrained Transit Assignment with Common Lines , 2003, J. Math. Model. Algorithms.

[20]  Jia Hao Wu,et al.  Transit Equilibrium Assignment: A Model and Solution Algorithms , 1994, Transp. Sci..

[21]  Yu Jiang,et al.  Reliability-Based Transit Assignment for Congested Stochastic Transit Networks , 2011, Comput. Aided Civ. Infrastructure Eng..

[22]  Maria Börjesson,et al.  Valuations of travel time variability in scheduling versus mean-variance models , 2012 .

[23]  Michael Florian,et al.  Optimal strategies: A new assignment model for transit networks , 1989 .

[24]  W. Lam,et al.  Modeling Impact of Transit Operator Fleet Size under various Market Regimes with Uncertainty in Network , 2008 .

[25]  W. Y. Szeto,et al.  Reliability-based stochastic transit assignment with capacity constraints: Formulation and solution method , 2013 .

[26]  Patrice Marcotte,et al.  A Strategic Model for Dynamic Traffic Assignment , 2004 .

[27]  Federico Malucelli,et al.  A Modeling Framework for Passenger Assignment on a Transport Network with Timetables , 1998, Transp. Sci..

[28]  Enrique Fernández,et al.  Transit Assignment for Congested Public Transport Systems: An Equilibrium Model , 1993, Transp. Sci..

[29]  Siriphong Lawphongpanich,et al.  Schedule-based transit assignment model with travel strategies and capacity constraints , 2008 .

[30]  W. Y. Szeto,et al.  A turning restriction design problem in urban road networks , 2010, Eur. J. Oper. Res..

[31]  E. Cascetta,et al.  A MODIFIED LOGIT ROUTE CHOICE MODEL OVERCOMING PATH OVERLAPPING PROBLEMS. SPECIFICATION AND SOME CALIBRATION RESULTS FOR INTERURBAN NETWORKS , 1996 .

[32]  W. Y. Szeto,et al.  A bi-objective turning restriction design problem in urban road networks , 2014, Eur. J. Oper. Res..

[33]  Richard A. Davis,et al.  Time Series: Theory and Methods , 2013 .

[34]  Umberto Crisalli,et al.  A Doubly Dynamic Schedule-based Assignment Model for Transit Networks , 2001, Transp. Sci..

[35]  William H. K. Lam,et al.  A capacity restraint transit assignment with elastic line frequency , 2002 .

[36]  Agachai Sumalee,et al.  Dynamic stochastic transit assignment with explicit seat allocation model , 2009 .

[37]  W. Y. Szeto,et al.  Time-dependent transport network design under cost-recovery , 2009 .

[38]  A. Nagurney.  Network Economics: A Variational Inequality Approach , 1992 .

[39]  J. Jucker,et al.  An Empirical Study of Travel Time Variability and Travel Choice Behavior , 1982 .

[40]  Roberto Cominetti,et al.  A frequency-based assignment model for congested transit networks with strict capacity constraints: characterization and computation of equilibria , 2006 .

[41]  Giulio Erberto Cantarella,et al.  A General Fixed-Point Approach to Multimode Multi-User Equilibrium Assignment with Elastic Demand , 1997, Transp. Sci..

[42]  Hong Kam Lo,et al.  Modeling transfer and non-linear fare structure in multi-modal network , 2003 .

[43]  Yuqing Zhang,et al.  The multi-class schedule-based transit assignment model under network uncertainties , 2010, Public Transp..

[44]  Shing Chung Josh Wong,et al.  The Optimal Transit Fare Structure under Different Market Regimes with Uncertainty in the Network , 2009 .

[45]  W. Y. Szeto,et al.  Transit assignment: Approach-based formulation, extragradient method, and paradox , 2014 .

[46]  Patrice Marcotte,et al.  A Strategic Flow Model of Traffic Assignment in Static Capacitated Networks , 2004, Oper. Res..

[47]  Agachai Sumalee,et al.  Stochastic Multi-Modal Transport Network under Demand Uncertainties and Adverse Weather Condition , 2011 .

[48]  William H. K. Lam,et al.  A Reliability-Based Stochastic Traffic Assignment Model for Network with Multiple User Classes under Uncertainty in Demand , 2006 .

[49]  Ioannis Kaparias,et al.  Dynamic User Equilibrium in Public Transport Networks with Passenger Congestion and Hyperpaths , 2013 .

[50]  H. W. Ho,et al.  Schedule-based transit assignment model with vehicle capacity and seat availability , 2011 .

[51]  Atanu Biswas,et al.  Discrete-valued ARMA processes , 2009 .

[52]  W. Y. Szeto,et al.  A simultaneous bus route design and frequency setting problem for Tin Shui Wai, Hong Kong , 2011, Eur. J. Oper. Res..