The macroscopic fundamental diagram (MFD) is developed to describe traffic operations aggregated over an area. The MFD is defined by network traffic states as a relationship between the accumulation of vehicles and flow or speed of vehicles. The concept of the MFD has been applied to model traffic dynamics and to design control strategies. For various applications (e.g., routing and departure time choices), the MFD is often assumed to be of a particular shape, consisting of two branches—a free-flow branch and a congestion branch. However, empirical observations show some inconsistencies between the theoretical and the empirical MFD. First, the empirical MFD only presents free-flow branch, i.e., the congestion branch is missing. Second, the MFD presents as hysteresis loop(s). This paper explores these differences, providing insights into urban network traffic dynamics. This work takes the travelers’ departure time choices and user equilibrium (UE) as starting points. We consider demand to be in UE in terms of departure time choices. Using this property of the demand profile, the paper proposes a closed-form expression for average density and outflow. Finally, we show some insights in the urban traffic dynamics: (i) an explanation of the hysteresis phenomenon solely from the perspective of departure time choices and UE and (ii) an explanation of why we hardly observe the MFD congestion branch in real life even in heavily congested networks. Our study shows that, for management purposes, the missing of congestion branch is a result of UE, rather than an indicator of congestion severity.

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In het Nederlandse wegverkeer is veel vertraging. Een vermindering van het verkeer zorgt ook voor een vermindering van die vertraging. Dit kan bereikt worden door maatregelen als beprijzing of spitsrechten. Het verkeerssysteem is één samenhangend systeem over grote afstanden. Om de effecten van deze maatregelen op netwerkschaal te beoordelen, moeten we daarom een netwerk beschouwen waarbinnen deze grote verplaatsingen geheel plaatsvinden. De vertraging en dynamiek in dat netwerk bepalen we op zone-niveau via het macroscopisch fundamenteel diagram (MFD); dit wordt ook wel een “badkuipmodel” genoemd. In dit artikel gaan we in op het modelleren op deze schaal: welke aanpak er mogelijk is, wat effecten van maatregelen zijn en welke mogelijkheden dat biedt. We laten ten eerste zien dat dat verkeerslichten sterk bijdragen aan effectief verkeersmanagement doordat de doorstroming in de zone beïnvloed wordt. Ten tweede presenteren we een vernieuwende manier om de vorm van het MFD te bepalen: we tonen aan dat dit – onafhankelijk van het netwerk - bepaald wordt door het vraagpatroon (hoeveel voertuigen vertrekken wanneer). Dit geeft aan dat vraag-beïnvloeding op twee manier doorwerkt: het bepaalt het aantal auto’s in het netwerk, maar het bepaalt ook (via het MFD) de uitstroom van het netwerk gegeven het aantal auto’s in het netwerk. Daardoor kan vraag-beïnvloeding een nog effectievere maatregel zijn dan al werd verondersteld. Ten derde laten we zien dat het mogelijk is om het MFD te gebruiken voor het simuleren van verkeer in grote netwerken (bijvoorbeeld een gebied als de hele Randstad). Ruimtelijk-economische kosten-batenberekeningen zijn met zo’n model te maken, waarbij het voordeel is dat het een dynamisch model is. Het tweede punt, een MFD dat onafhankelijk is van het netwerk, is een fundamenteel nieuw inzicht dat verdere studie behoeft: als het vraagpatroon het MFD bepaalt, hoe zit het met het vraagpatroon. Het derde punt, een zone-gebaseerd model, biedt belangrijke aanknopingspunten voor ruimtelijk-economische afwegingen gerelateerd aan mobiliteit. @en

With the renewed interest in the Macroscopic Fundamental Diagram (MFD) in the last decade, studies on network-level urban traffic control have increased in popularity. A popular urban traffic control approach is perimeter control, in which vehicle accumulation is kept below some critical accumulation value. An alternative control strategy is to optimize time series of departure rates as a means to limit inflows into the (sub)network. In this paper we test how these approaches compare in terms of minimizing total time spent (TTS), and whether network performance can be improved by combining these two approaches. To the best of the authors’ knowledge, answers to these two questions are still missing. Our findings indicate that—for a particular multi-region network under a specific demand profile—optimizing departure rates outperforms perimeter control. Particularly, we find that the combination of perimeter control and departure rates optimization may even have adverse effects on minimizing TTS, compared to optimizing departure rates only. We also show that properly over-saturating part of a network could result in less TTS than under the application of a perimeter control, which keeps the accumulation under the critical accumulation.@en

Scarce urban space makes urban streets have to be partly shared by cars and cyclists. Traffic flow can be considerably influenced by cyclists, which are comparatively slower than cars. The fundamental diagram (FD) can change greatly, correlating to bike lane length and the cyclist flow. Models for the traffic dynamics on the space-shared streets are still lacking. This work fills the gap. This paper starts from proposing analytic formulas for the capacity, free-flow speed and critical density on a one-lane road, which together characterize the FD. The sensitivity of the FD to the bike lane length as well as the cyclist flow, using the analytical formulas, are presented. The given FD is satisfactory, compared with microscopic simulation results. Finally, we extend the research scope to a multi-lane road. It is expected that this work can benefit city designs and traffic operations.@en

Traffic flow downstream of the congestion is generally lower than the pre-queue capacity. This phenomenon is called the capacity drop. Recent empirical observations show a positive relationship between the speed in congestion and the queue discharge rate. Literature indicates that variations in driver behaviors can account for the capacity drop. However, to the best of authors' knowledge, there is no solid understanding of what and how this variation in driver behaviors lead to the capacity drop, especially without lane changing. Hence, this paper fills this gap. We incorporate the empirically observed desired acceleration stochasticity into a car-following model. The extended parsimonious car-following model shows different capacity drop magnitudes in different traffic situations, consistent with empirical observations. All results indicate that the stochasticity of desired accelerations is a significant reason for the capacity drop. The new insights can be used to develop and test new measures in traffic control.@en

The capacity drop indicates that the queue discharge rate is lower than the free-flow capacity. Studies show that the queue discharge rate varies under different traffic conditions. Empirical data show that the queue discharge rate increases as the speed in congestion increases. Insights into the underlying behavioral mechanisms that cause these variable queue discharge rates can help minimize traffic delays and eliminate congestion. However, to our knowledge, few efforts have been devoted to testing impacts of traffic behaviors on the queue discharge rate. This paper tries to fill this gap. We investigate to what extent the acceleration spread and reaction time can influence the queue discharge rate. It is found that the (interdriver) acceleration spread does not reduce the queue discharge rates as much as found empirically. Modeling reaction time might be more important than modeling acceleration for capacity drop in car-following models. A speed-dependent reaction time mechanism for giving variable queue discharge rates is proposed. That is, decreasing reaction time as the speed in congestion increases can give the same queue discharge rate as found empirically. This research suggests that motivating drivers to speed up earlier could increase the queue discharge rate and thereby minimize delays.

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On freeways, congestion always leads to capacity drop. This means the queue discharge rate is lower than the pre-queue capacity. Our recent research findings indicate that the queue discharge rate increases with the speed in congestion, that is the capacity drop is strongly correlated with the congestion state. Incorporating this varying capacity drop into a kinematic wave model is essential for assessing consequences of control strategies. However, to the best of authors’ knowledge, no such a model exists. This paper fills the research gap by presenting a Lagrangian kinematic wave model. “Lagrangian” denotes that the new model is solved in Lagrangian coordinates. The new model can give capacity drops accompanying both of stop-and-go waves (on homogeneous freeway section) and standing queues (at nodes) in a network. The new model can be applied in a network operation. In this Lagrangian kinematic wave model, the queue discharge rate (or the capacity drop) is a function of vehicular speed in traffic jams. Four case studies on links as well as at lane-drop and on-ramp nodes show that the Lagrangian kinematic wave model can give capacity drops well, consistent with empirical observations.@en

Traffic signals are not only useful facilities to ensure the safety at an intersection, but also an important traffic management tool to improve the urban traffic network performance. Many traffic signal strategies have been presented to increase the throughput of an urban network and reduce the total delay. The difficulty is that a successful local optimization does not mean a better global performance and that the high complexity makes centralized coordinated strategies usually not efficient for a large network. To overcome these drawbacks, some promising distributed strategies are presented, such as the back-pressure algorithm. Whereas the back-pressure algorithm overcomes the main fundamental problems, some practical issues are not considered. Firstly, the original back-pressure algorithm does not take the all red time into consideration. Secondly, the algorithm relies strongly on the loop detector, which decreases the robustness. Therefore, this paper shows a dynamic green time approach which overcomes these drawbacks of the back-pressure algorithm. In the approach, the green time length depends on two elements: The back-pressure at the intersection and the upstream queue length. Meanwhile the green time for each phase is restricted to durations between 15 seconds and 65 seconds to ensure the robustness. The method is tested in a simulation. This shows that optimal dynamic green time approach shows the best performance among other green time mechanisms, such as fixed green time approach. The green time approach not only makes the back-pressure more practical, but also keeps the good network performance of the original algorithm.

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Capacity drop indicates that the queue discharge rate is lower than the road capacity. Due to the capacity drop, traffic delays increase once queues form. Researchers find that queue discharge rates vary in different traffic conditions. Empirical data shows that the queue discharge rate increases as the speed in congestion increases. Understanding what and how driver behaviors result in such variable queue discharge rates can help minimize traffic delays and eliminate congestion. However, as far as authors know, few efforts have been devoted to testing impacts of traffic behaviors on the variable queue discharge rate. This paper tries to fill in the gap. The authors investigate to what extent acceleration variety and reaction time can influence the queue discharge rate. It is found that the acceleration variety cannot reduce the queue discharge rate considerably. Modelling reaction time might be more important than modeling acceleration when giving capacity drop in car-following models. A multi-phase reaction time mechanism for giving variable queue discharge rates is proposed. That is, decreasing reaction time as the speed in congestion increases can give the same variable queue discharge rate as empirical observations. The research might indicate that motivating drivers to speed up earlier could benefit increasing queue discharge rates and minimizing delays.@en

The capacity drop indicates that the queue discharge rate is lower than the free-flow capacity. Studies show that queue discharge rates vary under different traffic conditions. Empirical data show that the queue discharge rate increases as the speed in congestion increases. Insights into the underlying behavioral mechanisms that result in such variable queue discharge rates can help minimize traffic delays and eliminate congestion. However, to the best of the authors’ knowledge, few efforts have been devoted to testing impacts of traffic behaviors on the queue discharge rate. This paper tries to fill this gap. We investigate to what extent the acceleration spread and reaction time can influence the queue discharge rate. It is found that the (inter-driver) acceleration spread does not reduce the queue discharge rates as much as found empirically. Modelling reaction time might be more important than modeling acceleration for capacity drop in car-following models. A speed-dependent reaction time mechanism for giving variable queue discharge rates is proposed. That is, decreasing reaction time as the speed in congestion increases can give the same queue discharge rate as found empirically. This research suggests that motivating drivers to speed up earlier could increase the queue discharge rate and thereby minimize delays. @en

Earlier studies on the traffic flow on freeways reveal that queue discharge rate cannot reach as high as the free-flow capacity. This important phenomenon is called the “Capacity drop”, which indicates that the potential freeway capacity cannot be fully utilized when discharging traffic jams. Even though a majority of empirical and analytical research has already been conducted to understand the capacity drop, several relevant challenges still need to be addressed. Those challenges include (1) characterizing more empirical features of the capacity drop, (2) incorporating the capacity drop into macroscopic models, (3) revealing mechanism related to driver behaviors behind the capacity drop and incorporating the mechanism into microscopic models. This thesis fills the research gap. @en

It has been empirically observed for years that the queue discharge rate is lower than the pre-queue capacity. This is called the capacity drop. The magnitude of capacity drop varies over a wide range depending on the local traffic conditions. However, up to now it is unknown what determines the capacity drop value. In fact, there is still no thorough empirical analysis revealing a reliable relation between the congestion level and the capacity drop. This paper tries to fill in the gap by revealing the relation between the vehicle speed in congestion and the queue discharge rate through empirical analysis. The queue discharge rate is shown to increase considerably with increasing speed in the congestion. This finding indicates a promising speed-control scheme for increasing queue discharge rates.@en

It has been empirically observed for years that the queue discharge rate is lower than the prequeue capacity. This difference is called the capacity drop. The magnitude of capacity drop varies over a wide range, depending on the local traffic conditions. However, it is unknown what determines the capacity drop value. No thorough empirical analysis has yet revealed a reliable relationship between the capacity drop and the congestion level. This paper fills the gap by revealing, through empirical analysis, the relationship between vehicle speed in congestion and the queue discharge rate. The research studies congested states in which speed ranges from 6 to 60 km/h. The queue discharge rate is shown to increase considerably with increasing speed in the congestion. In contrast to previous research, this study bases the relationship on empirical data collected on freeways, and the data present a sufficiently large observation sample. A discussion about the influence of weather and study site characteristics on the discharge rate indicates that the relationship needs site-specific calibrations. This study provides a better prediction of capacity drop and a better theoretical understanding of the fluctuations in capacity drop.@en