TY - JOUR
T1 - Opposing Hysteresis Patterns in Flow and Outflow Macroscopic Fundamental Diagrams and Their Implications
AU - Xu, Guanhao
AU - Zhang, Pengxiang
AU - Gayah, Vikash V.
AU - Hu, Xianbiao
N1 - Funding Information:
This manuscript has been authored in part by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the U.S. Department of Energy (DOE). The U.S. government retains and the publisher, by accepting the work for publication, acknowledges that the U.S. government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the submitted manuscript version of this work, or allow others to do so, for U.S. government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan ( http://energy.gov/downloads/doe-public-access-plan ).
Funding Information:
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work is supported by NSF Grant CMMI-1749200.
Publisher Copyright:
© National Academy of Sciences: Transportation Research Board 2023.
PY - 2023/8
Y1 - 2023/8
N2 - Two key aggregated traffic models are the relationship between average network flow and density (known as the network or flow macroscopic fundamental diagram [flow-MFD]) and the relationship between trip completion and density (known as network exit function or the outflow-MFD [o-FMD]). The flow- and o-MFDs have been shown to be related by average network length and average trip distance under steady-state conditions. However, recent studies have demonstrated that these two relationships might have different patterns when traffic conditions are allowed to vary: the flow-MFD exhibits a clockwise hysteresis loop, while the o-MFD exhibits a counter-clockwise loop. One recent study attributes this behavior to the presence of bottlenecks within the network. The present paper demonstrates that this phenomenon may arise even without bottlenecks present and offers an alternative, but more general, explanation for these findings: a vehicle’s entire trip contributes to a network’s average flow, while only its end contributes to the trip completion rate. This lag can also be exaggerated by trips with different lengths, and it can lead to other patterns in the o-MFD such as figure-eight patterns. A simple arterial example is used to demonstrate this explanation and reveal the expected patterns, and they are also identified in real networks using empirical data. Then, simulations of a congestible ring network are used to unveil features that might increase or diminish the differences between the flow- and o-MFDs. Finally, more realistic simulations are used to confirm that these behaviors arise in real networks.
AB - Two key aggregated traffic models are the relationship between average network flow and density (known as the network or flow macroscopic fundamental diagram [flow-MFD]) and the relationship between trip completion and density (known as network exit function or the outflow-MFD [o-FMD]). The flow- and o-MFDs have been shown to be related by average network length and average trip distance under steady-state conditions. However, recent studies have demonstrated that these two relationships might have different patterns when traffic conditions are allowed to vary: the flow-MFD exhibits a clockwise hysteresis loop, while the o-MFD exhibits a counter-clockwise loop. One recent study attributes this behavior to the presence of bottlenecks within the network. The present paper demonstrates that this phenomenon may arise even without bottlenecks present and offers an alternative, but more general, explanation for these findings: a vehicle’s entire trip contributes to a network’s average flow, while only its end contributes to the trip completion rate. This lag can also be exaggerated by trips with different lengths, and it can lead to other patterns in the o-MFD such as figure-eight patterns. A simple arterial example is used to demonstrate this explanation and reveal the expected patterns, and they are also identified in real networks using empirical data. Then, simulations of a congestible ring network are used to unveil features that might increase or diminish the differences between the flow- and o-MFDs. Finally, more realistic simulations are used to confirm that these behaviors arise in real networks.
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U2 - 10.1177/03611981231155421
DO - 10.1177/03611981231155421
M3 - Article
AN - SCOPUS:85167354160
SN - 0361-1981
VL - 2677
SP - 100
EP - 117
JO - Transportation Research Record
JF - Transportation Research Record
IS - 8
ER -