Incorporating within link dynamics in an agent-based computationally faster and scalable queue model

ABSTRACT

The growing pace of urbanization increases the need of simulation models to handle large-scale scenarios in reasonable time. The present study proposes a fast spatial queue model, which is anchored to an agent-based travel demand simulation framework. The existing queue model is extended to produce more realistic flow dynamics by introducing backward travelling holes to mixed traffic conditions. In this approach, the space freed by a leading vehicle is not immediately available to the following vehicle. The resulting dynamics resembles Newell's simplified kinematic wave model. The space freed corresponding to each leaving vehicle is named as ‘hole’ and, as following vehicles occupy the space freed by leading vehicles, the hole travels backward. This results in triangular fundamental diagrams for traffic flow. The robustness of the model is tested with flow density and average bike passing rate contours. Spatio-temporal trajectories are presented to differentiate the queuing patterns. Finally, a comparison of the computational performance of the different link and traffic dynamics of the queue model is made.

KEYWORDS:

• Queue model
• heterogeneous traffic
• backward travelling holes
• computational efficiency
• kinematic waves
• large-scale traffic simulation

Acknowledgements

Part of the material was presented in a preliminary form at the 11th Traffic Granular Flow (TGF)'15, Nootdorp. The authors also wish to thank H. Schwandt and N. Paschedag at the Department of Mathematics (Technische Universität Berlin), for maintaining our computing clusters. We are grateful to the anonymous reviewers for their constructive inputs on earlier drafts of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

A. Agarwal http://orcid.org/0000-0002-3352-0227

Notes

1. The queue model in MATSim can behave as PQ model by setting sufficiently high value of the link storage capacity. However, this is omitted in the present study due to its unrealistic nature.

2. Please note that the PCU value is not used to transform heterogeneous traffic into homogeneous traffic. The PCU of a vehicle class is required to observe the consumption of (out)flow and storage capacities of a link. Every vehicle with a PCU value is considered individually such that the vehicular interactions (e.g. passing, seepage) between different vehicles are possible.

3. At an intersection, if agents are queued to wait the downstream end of the link (more specifically in spill back situations), a hole traverses to upstream link from downstream link. There is no additional delay for, say, traversing the intersection; this could in principle be integrated into the length of the links. However, if no agents are waiting to enter the downstream link, the hole is closed.

4. As stated earlier, the assumption is that a link that is assumed to have a certain flow capacity in the assignment network needs to be physically able to process this flow; if this is not the case, the input data must be erroneous and thus be corrected in a plausible way. Maintaining the flow and increasing the storage seems the best way to do this in an assignment context.

5. In this study, irrespective of the number of vehicle classes in a simulation, the FDs are plotted for every vehicle class individually so that they are comparable with the FDs from the simulation of individual vehicle classes (homogeneous traffic conditions). The combined flow in the heterogeneous traffic conditions is additive in these contributions.

6. One should note that in this case, equal modal split (in PCU) of car and bike modes are simulated.

7. From Section 2.1, recall that the underlying queue model is simple which keeps track of agents at entry and exit. On the other hand, a link can have multiple lanes which is required to include the effect on the storage capacity. In general, the storage capacity of a link mainly depends on length of the link, number of lanes and size of the vehicle class.

8. One important consequence of the higher storage capacities is that at higher densities, the queue model with holes displays higher fluctuations.

9. These trajectories are derived in post-processing, therefore, minor rounding errors can be observed in the trajectories.

10. A few outliers are excluded which show very high simulation time for no reason. This is an artefact due to some unknown external job on the system.

11. MATSim can produce good results even with 1% sample size population if schedule-based transit assignment is not used (Nagel 2008, 2011).

Additional information

Funding

The support given by Deutscher Akademischer Austauschdienst (German Academic Exchange Service) to Amit Agarwal for his Ph.D. studies at Technische Universität Berlin is greatly acknowledged.