Modelling and managing bus service regularity with influence of prevailing traffic

ABSTRACT This paper presents a multi-modal framework for modelling and analysing different headway control strategies for improving bus service regularity. The interaction between buses and their surrounding traffic is captured in a multi-modal system through a Hamilton–Jacobi formulation of kinematic wave model. This paper further presents a set of signal-based strategies which regulate bus headway through adjusting signal timing plans. The results reveal that the capability of regulating bus headway disturbances through utilising traffic signals is important for maximising bus service regularity and coordinating the bus dynamics with surrounding traffic. This study generates new insights on managing bus reliability and multi-modal traffic in busy urban networks.

[1]  Andy H.F. Chow,et al.  Dynamic system optimal traffic assignment – a state-dependent control theoretic approach , 2009 .

[2]  Monica Menendez,et al.  A Variational Formulation of Kinematic Waves: Bottleneck Properties and Examples , 2005 .

[3]  Andy H.F. Chow,et al.  Modeling and Data Fusion of Dynamic Highway Traffic , 2017 .

[4]  R B Potts,et al.  Maintaining a bus schedule , 1964 .

[5]  Ludovic Leclercq,et al.  Investigating the irregularity of bus routes: Highlighting how underlying assumptions of bus models impact the regularity results , 2015 .

[6]  Markos Papageorgiou,et al.  Store-and-forward based methods for the signal control problem in large-scale congested urban road networks , 2009 .

[7]  Roberto Horowitz,et al.  Behavior of the cell transmission model and effectiveness of ramp metering , 2008 .

[8]  Jiaqiu Wang,et al.  A Dynamic Spatial Weight Matrix and Localized Space–Time Autoregressive Integrated Moving Average for Network Modeling , 2014 .

[9]  C. Daganzo A variational formulation of kinematic waves: basic theory and complex boundary conditions , 2005 .

[10]  Monica Menendez,et al.  A Variational Formulation of Kinematic Waves , 2005 .

[11]  Yanfeng Ouyang,et al.  Mitigating Negative Impacts of Near-Side Bus Stops on Cars , 2013 .

[12]  W. Y. Szeto,et al.  Modelling urban traffic dynamics based upon the variational formulation of kinematic waves , 2015 .

[13]  Tao Cheng,et al.  Empirical assessment of urban traffic congestion , 2014 .

[14]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[15]  Ying Li,et al.  Robust Optimization of Dynamic Motorway Traffic via Ramp Metering , 2014, IEEE Transactions on Intelligent Transportation Systems.

[16]  P. I. Richards Shock Waves on the Highway , 1956 .

[17]  Carlos F. Daganzo,et al.  Reducing bunching with bus-to-bus cooperation , 2011 .

[18]  Mark A. Turnquist,et al.  Service frequency, schedule reliability and passenger wait times at transit stops , 1981 .

[19]  Pravin Varaiya,et al.  Aurora Road Network Modeler , 2009, CTS 2009.

[20]  Carlos F. Daganzo,et al.  Dynamic bus holding strategies for schedule reliability: Optimal linear control and performance analysis , 2011 .

[21]  Shing Chung Josh Wong,et al.  Derivatives of the performance index for the traffic model from TRANSYT , 1995 .

[22]  Andy H.F. Chow Properties of system optimal traffic assignment with departure time choice and its solution method , 2009 .

[23]  R. D. Bretherton,et al.  Optimizing networks of traffic signals in real time-the SCOOT method , 1991 .

[24]  Isaak Yperman,et al.  The Link Transmission Model for dynamic network loading , 2007 .

[25]  Shuai Li,et al.  Multi-objective optimal control formulations for bus service reliability with traffic signals , 2017 .

[26]  H. M. Zhang,et al.  Modelling network flow with and without link interactions: the cases of point queue, spatial queue and cell transmission model , 2013 .

[27]  W. Y. Szeto,et al.  A cell-based variational inequality formulation of the dynamic user optimal assignment problem , 2002 .

[28]  Yuwei Li,et al.  Models of Bus Queueing at Curbside Stops , 2015, Transp. Sci..

[29]  Roberto Horowitz,et al.  Computationally efficient model predictive control of freeway networks , 2015 .

[30]  G. F. Newell A simplified theory of kinematic waves in highway traffic, part I: General theory , 1993 .

[31]  Ying Li,et al.  Specifications of fundamental diagrams for dynamic traffic modeling , 2015 .

[32]  Benjamin G. Heydecker,et al.  Analysis of Dynamic Traffic Equilibrium with Departure Time Choice , 2005, Transp. Sci..

[33]  Carlos F. Daganzo,et al.  A headway-based approach to eliminate bus bunching: Systematic analysis and comparisons , 2009 .

[34]  H. Michael Zhang,et al.  A Polymorphic Dynamic Network Loading Model , 2008, Comput. Aided Civ. Infrastructure Eng..

[35]  C. Daganzo A variational formulation of kinematic waves: Solution methods , 2005 .

[36]  Carlos F. Daganzo,et al.  Dynamic control of complex transit systems , 2015 .

[37]  Jorge A. Laval,et al.  Hybrid models of traffic flow : impacts of bounded vehicle accelerations , 2004 .

[38]  M. Lighthill,et al.  On kinematic waves I. Flood movement in long rivers , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

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

[40]  Masao Kuwahara,et al.  Implementing kinematic wave theory to reconstruct vehicle trajectories from fixed and probe sensor data , 2011 .

[41]  Pravin Varaiya,et al.  Aurora RNM – A macroscopic tool for arterial traffic modelling and control , 2010 .

[42]  Wanjing Ma,et al.  Development and Evaluation of a Coordinated and Conditional Bus Priority Approach , 2010 .

[43]  Yunus Saatci,et al.  Data, modelling and inference in road traffic networks , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[44]  Ahmad H. Dehwah,et al.  Analytical and grid-free solutions to the Lighthill-Whitham-Richards traffic flow model , 2011 .

[45]  Hong Kam Lo,et al.  Adaptive traffic control system: control strategy, prediction, resolution and accuracy , 2002 .

[46]  Andy H.F. Chow,et al.  Optimisation of dynamic motorway traffic via a parsimonious and decentralised approach , 2015 .

[47]  Vikash V. Gayah,et al.  On the impacts of bus stops near signalized intersections: Models of car and bus delays , 2014 .

[48]  Hong Kam Lo,et al.  Sensitivity analysis of signal control with physical queuing: Delay derivatives and an application , 2007 .

[49]  Carlos F. Daganzo,et al.  Moving Bottlenecks: A Numerical Method that Converges in Flows , 2003 .

[50]  David Bernstein,et al.  The Holding Problem with Real - Time Information Available , 2001, Transp. Sci..

[51]  Gordon F. Newell,et al.  A SIMPLIFIED THEORY OF KINEMATIC WAVES , 1991 .

[52]  Gordon F. Newell,et al.  A moving bottleneck , 1998 .

[53]  S. Ilgin Guler,et al.  Analytical formulation and empirical evaluation of pre-signals for bus priority , 2014 .

[54]  Pravin Varaiya,et al.  Arterial travel time estimation based on vehicle re-identification using wireless magnetic sensors , 2009 .