Empirical evaluation of influential factors on bifurcation in macroscopic fundamental diagrams

doi:10.1016/j.trc.2019.03.005

Transportation Research Part C: Emerging Technologies

Volume 102, May 2019, Pages 509-520

https://doi.org/10.1016/j.trc.2019.03.005 Get rights and content

Highlights

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Large-scale trip data from passenger vehicles in an urban network were analyzed.
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Distinctive macroscopic fundamental diagrams were observed on weekends and weekdays.
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Consistent and reproducible bifurcation was observed across weekdays.
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Upper bifurcation branch was formed in weekday mornings.
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Detouring trips were a key factor for the occurrence of bifurcation.

Abstract

Observations from empirical data in the roadway network showed that the relation between averages of network flow versus density often exhibit hysteresis and bifurcation phenomena, which may obscure the reproducibility of a well-defined macroscopic fundamental diagram (MFD). In this paper, we analyzed large-scale trip data from passenger vehicles in an urban network of South Korea and evaluated the shapes of MFDs over many days. It was found that MFDs have two distinctive, reproducible forms: a well-defined, unique relation on weekends and a bifurcation in high-density regime on weekdays.

With regard to the bifurcation, we observed higher network flows in the morning and lower network flows in the evening for the same average network density. This implies that the same set of drivers in the network collectively formed two different trip patterns. Hence, we evaluated possible factors that may have effects on the bifurcation phenomenon. In view of this, four factors – heterogeneity, trip completion rate, detouring ratio and commute trips – were analyzed in this study. The findings showed that travelers’ detours could be a key factor for the occurrence of bifurcation because, by detouring travelers improve neither their own travel times nor network-wide travel times, and thereby degrade the network production.

Introduction

Many studies have suggested that a reproducible and unique relation exists between averages of flow and density across the links in a roadway network (Godfrey, 1969, Herman and Prigogine, 1979, Mahmassani et al., 1984, Daganzo, 2007, Daganzo and Geroliminis, 2008). However, empirical evidence for the existence of this so-called macroscopic fundamental diagram (MFD) was not provided until network-scale real data recently became available (Geroliminis and Daganzo, 2008, Buisson and Ladier, 2009, Cassidy et al., 2011). These studies showed that a well-defined MFD can be realized if traffic conditions of the links in the network are homogenously congested and if the trip characteristics are time-invariant. Nevertheless, it is still in question whether a well-defined MFD can be regularly observed for a certain network because occasions in which nearly all the links in the network are similarly congested are rare.

One factor that obscures the shape of the MFD is hysteresis phenomenon. Buisson and Ladier (2009) analyzed loop detector data along the freeway network of Toulouse, France and showed that uneven distribution of congestion due to a major disturbance can contribute to a hysteresis-like loop in the MFD. Other studies confirmed, based on both empirical data and simulation experiments, that the spatial homogeneity of density determines the shape and scatter of the MFD (Mazloumian et al., 2010, Ji et al., 2010, Gonzales et al., 2011, Geroliminis and Sun, 2011a, Knoop et al., 2013). Geroliminis and Sun (2011b) later investigated the hysteresis phenomenon in further detail using loop detector data of a large-scale Minnesota freeway network in the U.S. The relation between average flow and density of the network formed a hysteresis loop: for the same density, higher average flow was observed during the onset of congestion, while lower average flow was observed during the offset. Gayah and Daganzo (2011) used a two-bin model and simulation results, and explained that a hysteresis loop is diminished when drivers adaptively change routes in response to congestion. Saberi and Mahmassani, 2012, Saberi and Mahmassani, 2013 found a larger variation in network occupancy during offset of congestion, and that the size of hysteresis loop was determined by the level of heterogeneity in congestion distribution.

The other phenomenon that obscures the shape of the MFD is bifurcation. Bifurcation refers to a split of a high-density branch in the MFD and was empirically observed in previous studies (Geroliminis and Sun, 2011b, Saberi and Mahmassani, 2013, Ambühl et al., 2017). Separate hysteresis loops were plotted in different time periods; evolution of congestion followed separate hysteresis loops, meaning that the shape of the MFD is continuously-varying over time. This finding may challenge the reproducibility of realizing a MFD for a network as bifurcation indicates multivaluedness for the same level of density. On the other hand, this multivaluedness is intriguing because understanding of the bifurcation phenomenon would shed light on ways to increase network performance by operating the system at higher efficiency (i.e., at higher flows for the same density level). Some theoretical studies have suggested that bifurcation is a natural phenomenon resulting from instability in the network (Daganzo et al., 2011, Mahmassani et al., 2013). Recent theoretical evidence suggested that travel demand patterns such as origin-destination (OD) matrix and travel distance have significant effects on the shape of the MFD (Leclercq et al., 2015).

These previous studies indicate that MFDs often include divergence – hysteresis and bifurcation – in high-density range, and suggest that heterogeneity of network state or travel properties such as routing behavior; travel distance and OD matrix have significant effects on the shape of the MFD. However, empirical evidence for the divergence remains scarce due in part to limitations in travel data. This underscores the need for investigation with real network-wide travel data.

The objectives of this study are to estimate MFDs in an urban arterial network and to empirically investigate the effects of various factors on the shape of the MFD, especially in terms of bifurcation and trip characteristics. Section 2 below describes the large-scale travel data used in this paper. Section 3 estimates MFDs for a network across several days to examine the variations in the shape of MFDs. Section 4 investigates various factors that may have potential effects on the bifurcation phenomenon with the focus on the effect of trip characteristics on the shape of MFDs, and develop metrics for quantifying the relative impact of detouring behavior on MFD. Section 5 discusses the findings, concluding with implications and some future research needs.

Section snippets

Descriptions of study network and data

Daegu City is the third largest metropolitan area in South Korea, with over 2.5 million residents. Roadway networks in the city are about 2400 km long, and are concentrated near the center of the city, where a large portion of the city population resides. Recurrent congestion arises during weekday morning and evening peak hours near the city center. Accordingly, the focus of this study is on the central business district (CBD) surrounding the city hall. The CBD area, highlighted on the map in

MFD estimation

We apply Edie’s generalized definitions to estimate the average network flow and the density weighted by the penetration rate, $\hat{ρ}$ (Nagle and Gayah, 2014). In this study, we assume that the penetration rate is invariant at 0.21 over time and space. The average network flow and density for the tth time interval, are estimated: $\hat{q} (t) = \frac{\sum_{i} N_{i}^{p} (t)}{\hat{ρ}} \cdot \frac{{\bar{d}}_{p} (t)}{LT}$ $\hat{k} (t) = \frac{\sum_{i} N_{i}^{p} (t)}{\hat{ρ}} \cdot \frac{{\bar{t}}_{p} (t)}{LT}$ where ${\bar{d}}_{p} (t)$ and ${\bar{t}}_{p} (t)$ are the average travel distance and the average travel time of probe vehicles for the t^th time interval,

Network heterogeneity

Heterogeneity of network state is a well-known factor that affects the shape of MFD in a network by inducing hysteresis, scatter, multivaluedness, and bifurcation (Mazloumian et al., 2010, Gonzales et al., 2011, Geroliminis and Sun, 2011a, Geroliminis and Sun, 2011b, Saberi and Mahmassani, 2012, Saberi and Mahmassani, 2013). Therefore, we first examined the possible effect of network heterogeneity on the bifurcation in the MFD of Daegu CBD network with empirical analysis. The measure to

Discussion and conclusion

This study estimated MFDs for the roadway network in the city of Daegu, South Korea. For the estimation, in October 2015, large-scale traffic data were collected from passenger cars equipped with ETC transponders. The penetration rate is sufficiently high to represent the general traffic patterns in the network. MFDs were estimated for the network of the CBD over both weekdays and weekends. Reproducible patterns were distinctly observed in the MFDs for weekdays and weekends: a well-defined

Acknowledgement

This research was supported by a grant (19RDRP-B076268-06) from R&D Program funded by Ministry of Land, Infrastructure and Transport of Korean government. The work of one by the authors is partially supported by the Simon Lee Endowment and the National Science Foundation under Grant No. 1351647. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of Sponsors.

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Citation Excerpt :
The probe vehicle data's applicability depends on the penetration rate of probe vehicles in the traffic stream. When the information on traffic variables like flow and travel time is available for a few samples (like Wi-Fi/Bluetooth probes), then the penetration rate can be adopted as an approximation to estimate flow and density, assuming that the penetration rate is known (Nagle and Gayah, 2014; Du et al., 2015; Shim et al., 2019). Therefore, if probe vehicle data is available, traffic flow, density, and speed can be approximated by adopting a suitable value of penetration rate.
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Empirical evaluation of influential factors on bifurcation in macroscopic fundamental diagrams

Highlights

Abstract

Introduction

Section snippets

Descriptions of study network and data

MFD estimation

Network heterogeneity

Discussion and conclusion

Acknowledgement

Transp. Res. Part B: Methodol.

Transp. Res. Part B: Methodol.

Transp. Res. Part B: Methodol.

Transp. Res. Part B: Methodol.

Transp. Res. Part B: Methodol.

Transp. Res. Part B: Methodol.

Transp. Res. Part B: Methodol.

Transp. Res. Part A: Policy Pract.

Transp. Res. Part B: Methodol.

Transport. Res. Part B: Methodol.

Transp. Res. Part B: Methodol.

Transp. Res. Procedia

Transport. Res. Part B: Methodol.

Soc. Behav. Sci.

Transport. Res. Part B: Methodol.

Empirical macroscopic fundamental diagrams: New insights from loop detector and floating car data

Proceedings of the 96th Annual Meeting of the Transportation Research Board, Washington, DC