Introducing Buses into First-Order Macroscopic Traffic Flow Models
Abstract
The aim of this paper is to provide a simple model of the interaction between buses and the surrounding traffic flow. Traffic flow is assumed to be described by a first-order macroscopic model of the Lighthill-Whitman-Richards type. As a consequence of their kinematics, which in large measure can be considered to be independent of the flow of other vehicles, buses should be considered as a moving capacity restriction from the point of view of other drivers. This simple interaction model is analyzed, mainly by considering the moving frame associated with the bus in order to derive analytical computation rules for derivation of the effects of the presence of the bus in the traffic flow. After deriving traffic equations in the moving frame associated with a bus, the usual basic concepts of first-order models, including those of relative traffic supply and demand, are generalized to the moving frame. A simple model for the bus-traffic interaction, assuming that the dimension of the bus can be neglected, can be derived from analytical calculations in the moving frame. Finally, some tentative results for the inclusion of buses into first-order traffic flow models, discretized according to Godunov’s scheme, are given.
Get full access to this article
View all access and purchase options for this article.
References
1. Van Aerde M. Integration: A Model for Simulating IVHS on Integrated Traffic Networks. User’s Guide for Model Version 1.5 e. Transportation Systems Research Group and M. Van Aerde and Associates, Kingston, Ontario, Canada, 1994.
2. Cameron G. D. B., and Duncan G. I. D. Paramics—Parallel Microscopic Simulation of Road Traffic. Journal of Supercomputing, Vol. 10, No. 1, 1996.
3. Jayakrishnan R., Mahmassani H. S., and Hu T. Y. An Evaluation Tool for Advanced Traffic Information and Management Systems in Urban Networks. Transportation Research, Part C, Vol. 2, No. 3, 1994, pp. 129–148.
4. Daganzo C. F. The Cell Transmission Model 1: A Dynamic Representation of Highway Traffic Consistent with the Hydrodynamic Theory. Transportation Research, Part B, Vol. 8, No. 4, 1994, pp. 269–287.
5. Daganzo C. F. The Cell Transmission Model 2: Network Traffic Simulation. Transportation Research, Part B, Vol. 29, No. 2, 1995, pp. 79–93.
6. Elloumi E., Hadjsalem H., and Papageorgiou M. Metacor, a Macroscopic Modelling Tool for Urban Corridors. TRISTAN II International Conference, Capri, 1994.
7. Harris S., Rabone A. J., Randall D., and Stevens A. Rogus—a Simulation of Dynamic Route Guidance Systems. Traffic Engineering and Control, Vol. 33, No. 5, 1992.
8. Buisson C., Lebacque J. P., Lesort J. B., and Mongeot H. The Strada Model for Dynamic Assignment. Proc., ITS Conference, Orlando, 1996.
9. Lebacque J. P., and Buisson C. Le Modèle de Trafic Strada. Modélisation du Trafic, Actes du Groupe de Travail 1995, Actes INRETS 1997 (in press).
10. Correge M., Gabard J. F., Henry J. J., and Tuffal J. Programme de Simulation Microscopique de Trafic Urbain. Journée AFCET Simulation dans les Transports, Paris, France, 1977.
11. Lighthill M. H., and Whitham G. B. On Kinematic Waves II: A Theory of Traffic Flow on Long Crowded Roads. Proc., Royal Society of London Series A, Vol. 229, 1955, pp. 317–345.
12. Richards P. I. Shock-Waves on the Highway. Opns. Research, Vol. 4, 1956, pp. 42–51.
13. Lebacque J. P. The Godunov Scheme and What It Means for First Order Traffic Flow Models. Proc., ISTTT (Lesort J. B., ed.), 1996.
14. Worrall R. D, and Lieberman E. B. Network Flow Simulation for Urban Traffic Control System—Phase II, Vols. 1 to 5. FHWA Reports 73-83 to 73-86, Washington, D.C., 1974.
15. Peirce J. R., and Wood K. Bus Transyt—A User’s Guide. TRRL Supplementary Report 266, Crowthorne, U.K. 1977.
16. Leonard R., Tough J. B., and Baguley P. C. Contram: A Traffic Assignment Model for Predicting Flows and Queue During Peak Periods. TRRL Report LR841, Crowthorne, U.K. 1978.
17. Newell G. F. A Moving Bottleneck. Research Report UCB-ITS-RR-93-3, Institute of Transportation Studies, University of California at Berkeley, March 1993.
18. Lebacque J. P. Note sur le Calcul du Modèle LWR avec Condition Initiale K>Kmax. Rapport CERMICS 97-102, ENPC, 1997.
19. Godlewski E., and Raviart P. A. Hyperbolic Systems of Conservation Laws. SMAI, Ellipses, 1991.
20. Mongeot H. Modelling of Urban Traffic Flow Dynamics in Incident Conditions Using the First Order Macroscopic Approach. UTSG 29 Annual Conference, Bournemouth, 1997 (in press).
21. Lebacque J. P., Lesort J. B., and Giorgi F. On a Simple Model of the Interaction Between Bus and Traffic Flow. Rapport CERMICS, LICIT, 1998.
22. Daganzo C. F. A Finite Difference Approximation of the Kinematic Wave Model. Transportation Research, Part B, Vol. 29, No. 4, 1995, pp. 261–276.
23. Lebacque J. P. Semimacroscopic Simulation of Urban Traffic. International 84 Minneapolis Summer Conference, AMSE, 1984.
24. Michalopoulos P. G., Beskos D. E., and Lin J. K. Analysis of Interrupted Traffic Flow by Finite Difference Methods. Transportation Research, Part B, Vol. 18, No. 4/5, 1984, pp. 409–421.
25. Michalopoulos P. G. LIN J. K. A Freeway Simulation Program for Microcomputers. Proc., 1st National Conference on Microcomputers in Urban Transportation, ASCE, California, 1985, pp. 330–341.
26. Bui N. N., Nelson P., and Narasimhan S. L. Computational Realizations of the Entropy Condition in Modelling Congested Traffic Flow. Report 1232-7, Texas Transportation Institute, 1992.
27. Leo C. J., and Pretty R. L. Numerical Simulation of Macroscopic Continuum Traffic Models. Transportation Research, Part B, Vol. 26, No. 3, 1992, pp. 207–220.
Cite article
Cite article
Cite article
OR
Download to reference manager
If you have citation software installed, you can download article citation data to the citation manager of your choice
Information, rights and permissions
Information
Published In
Article first published: January 1998
Issue published: January 1998
Authors
Metrics and citations
Metrics
Journals metrics
This article was published in Transportation Research Record: Journal of the Transportation Research Board.
VIEW ALL JOURNAL METRICSArticle usage*
Total views and downloads: 23
*Article usage tracking started in December 2016
Altmetric
See the impact this article is making through the number of times it’s been read, and the Altmetric Score.
Learn more about the Altmetric Scores
Articles citing this one
Receive email alerts when this article is cited
Web of Science: 0
Crossref: 66
- Mixed Traffic Modelling
- Control of multi-agent systems: Results, open problems, and applicatio...
- Interacting moving bottlenecks in traffic flow
- Macroscopic traffic flow modelling: from kinematic waves to autonomous...
- Learning Micro-Macro Models for Traffic Control Using Microscopic Data
- Centralized Traffic Control via Small Fleets of Connected and Automate...
- Mathematical modeling of mixed-traffic in urban areas
- Multi-Modal Traffic Signal Control in Shared Space Street
- Variable speed limits in the link transmission model using an informat...
- A macroscopic flow model for mixed bicycle–car traffic
- Optimal Railway Disruption Bridging Using Heterogeneous Bus Fleets
- A Macroscopic Traffic Flow Model Accounting for Bounded Acceleration
- Identifying the Impact of Low-Speed Vehicles on Freeway Capacity by Tr...
- Prediction of moving bottleneck through the use of probe vehicles: a s...
- A multiscale model for traffic regulation via autonomous vehicles
- A Macroscopic Model for Platooning in Highway Traffic
- Autonomous vehicles: From vehicular control to traffic contro
- Macroscopic analysis of moving bottlenecks
- Width-Based Cell Transmission Model for Heterogeneous and Undiscipline...
- Traffic regulation via individually controlled automated vehicles: a c...
- Application of wireless sensor networks to environmental monitoring fo...
- First-Order Macroscopic Traffic Models
- A coupled PDE-ODE model for bounded acceleration in macroscopic traffi...
- Two algorithms for a fully coupled and consistently macroscopic PDE-OD...
- A fast simulation algorithm for multiple moving bottlenecks and applic...
- Modeling heterogeneous traffic flow: A pragmatic approach
- Introduction—The Reason for Paradigm Shift in Transportation Science
- Achievements of Empirical Studies of Traffic Breakdown at Highway Bott...
- Failure of Generally Accepted Classical Traffic Flow Theories
- Analysis of moving bottlenecks considering a triangular fundamental di...
- A numerical scheme for moving bottlenecks in traffic flow
- Failure of classical traffic flow theories: Stochastic highway capacit...
- Swarm intelligence algorithms for macroscopic traffic flow model valid...
- A cell-based multiple vehicle type dynamic user equilibrium model with...
- The physics of empirical nuclei for spontaneous traffic breakdown in f...
- Feedback-Coordinated Ramp Control of Consecutive On-Ramps Using Distri...
- Integrating the Bus Vehicle Class Into the Cell Transmission Model
- Modelling urban traffic dynamics based upon the variational formulatio...
- Modeling the Car-Truck Interaction in a System-Optimal Dynamic Traffic...
- Impact of underlying steady-state fundamental diagram on moving bottle...
- Comprehensive Framework for Estimating Traffic Stream Flow Rates past ...
- Criticism of generally accepted fundamentals and methodologies of traf...
- Traffic Delay of Vehicles Based on Traffic Flow Wave Theory Caused by ...
- Modeling space–time inhomogeneities with the kinematic wave theory
- Study on security features of freeway traffic flow with cellular autom...
- A multiple-vehicle type reactive dynamic user equilibrium model and al...
- Vehicular Traffic Flow Dynamics on a Bus Route
- Traffic Delay of Vehicles Caused by Curb-Lane Bus Stop
- Modeling and Control of Traffic Flow
- Capacity drops at merges: An endogenous model
- Cell transmission model and numerical schemes for mixed traffic
- Capacity Drops at Merges: an endogenous model
- Empirical Study on Relationship among the Lane-Changing, Speed and Tra...
- Topological-based bottleneck analysis and improvement strategies for t...
- Bounded acceleration close to fixed and moving bottlenecks
- Lane-changing in traffic streams
- A First-order Macroscopic Traffic Flow Model for Mixed Traffic Includi...
- On the numerical treatment of moving bottlenecks
- Moving Bottlenecks in Lighthill-Whitham-Richards Model: A Unified Theo...
- Macroscopic Model and Its Numerical Solution for Two-Flow Mixed Traffi...
- A traffic Flow Model for Urban Traffic Analysis: Extensions of the LWR...
- Some Recent Developments in Continuum Vehicular Traffic Flow Theory ...
- Review of Basic Research in Bicycle Traffic Science, Traffic Operation...
- First Order Macroscopic Traffic Flow Models for Networks in the Contex...
- Various Scales for Traffic Flow Representation: Some Reflections
- Introducing the Effects of Slow Vehicles in a LWR Two-Flow Traffic Mod...
Figures and tables
Figures & Media
Tables
View Options
Get access
Access options
If you have access to journal content via a personal subscription, university, library, employer or society, select from the options below:
loading institutional access options
Alternatively, view purchase options below:
Purchase 24 hour online access to view and download content.
Access journal content via a DeepDyve subscription or find out more about this option.
