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Traffic Congestion, Modeling Approaches to

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Encyclopedia of Complexity and Systems Science

Definition of the Subject

Understanding of vehicular traffic congestion is the key for effective traffic management, traffic control, organization, and other engineering applications, which should improve traffic safety and result in high‐quality mobility. In empirical observations, traffic congestion occurs as the result of a so‐called traffic breakdown: the vehicle speed decreases sharply and vehicle density increases in an initially free traffic flow. The subsequent development of congested traffic exhibits a very complex spatiotemporal behavior. To explain traffic breakdown and resulting traffic congested patterns a huge number of traffic theories and models have been developed. It is clear that if a traffic flow model cannot show empirical features of traffic breakdown, the model cannot also show and predict many other traffic phenomena observed in real congested traffic. Thus an assessment of modeling approaches to show and predict traffic breakdown in vehicle...

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Abbreviations

Free flow:

Free flow is usually observed, when the vehicle density in traffic is small enough. The flow rate increases in free flow with increase in vehicle density, whereas the average vehicle speed is a decreasing density function.

Traffic breakdown:

In empirical observations, when density in free flow increases and becomes great enough, the phenomenon of the onset of congestion is observed in this free flow: The average speed decreases sharply to a lower speed in congested traffic . This speed breakdown observed during the onset of congestion is called the breakdown phenomenon or traffic breakdown.

Congested traffic:

Congested traffic is defined as a state of traffic in which the average speed is lower than the minimum average speed that is possible in free flow.

Bottleneck:

Traffic breakdown occurs mostly at highway bottlenecks. Just as defects and impurities are important for phase transitions in complex spatially distributed systems of various nature, so are freeway bottlenecks in freeway traffic. The bottleneck can be a result of roadworks, on- and off‐ramps, a decrease in the number of freeway lanes, road curves and road gradients, etc.

Moving jams:

A moving jam is a localized structure of great vehicle density spatially limited by two jam fronts. Within the downstream jam front vehicles accelerate escaping from the jam; within the upstream jam front, vehicles slow down approaching the jam. The jam as a whole structure propagates upstream in traffic flow. Within the jam (between the jam fronts) vehicle density is great and speed is very low (sometimes as low as zero). A sequence of moving jams is often called “stop‐and‐go” traffic.

Traffic flow model:

A traffic flow model is devoted to the explanation and simulation of traffic flow phenomena, which are observed in measured data of real traffic flow, and to the prediction of new traffic flow phenomena that could be found in real traffic flow. First of all, a traffic flow model should explain and predict empirical (measured) features of traffic breakdown.

Fundamental diagram of traffic flow:

The fundamental diagram is a relationship between the flow rate and density in vehicle traffic. Because the flow rate is the product of the average speed and density, the fundamental diagram is associated with a relationship between these traffic variables. In accordance with an obvious result of traffic measurements, on average the speed decreases when the density increases. Thus in the flow‐density plane, the fundamental diagram should pass through the origin (when the density is zero so is the flow rate) and should have at least one maximum. The fundamental diagram gives also a connection between the average space gap (net distance) between vehicles and the average speed.

Steady states of traffic flow:

Steady states of traffic flow are hypothetical states of homogeneous (in time and space) traffic flow of identical vehicles (and identical drivers) in which all vehicles move with the same time‐independent speed and have the same space gaps.

Fundamental diagram approach to traffic flow theory and modeling:

The fundamental hypothesis of the fundamental diagram approach to traffic flow theory and modeling suggests that steady states of both free flow and congested traffic lie on a one‐dimension curve(s) (i. e., on a theoretical fundamental diagram of traffic flow) in the flow‐density plane. At each given time‐independent speed of the preceding vehicle, the theoretical fundamental diagram determines a single desired space gap at which a vehicle moves with this time‐independent speed while following the preceding vehicle. This model vehicle behavior is related to a steady state of traffic flow associated with a hypothetical noiseless and acceleration less (deceleration less) model limit.

Three‐phase traffic theory:

In the author's three-phase traffic theory , besides the free flow phase there are two phases in congested traffic, the synchronized flow and wide moving jam phases. The synchronized flow and wide moving jam phases in congested traffic are defined through empirical spatiotemporal criteria (definitions) [S] and [J]. In contrast with the fundamental diagram approach, the fundamental hypothesis of three-phase traffic theory suggests that in steady states of synchronized flow, at each given time‐independent speed of the preceding vehicle, there is an infinite number of space gaps at which the vehicle can move with this speed, while following the preceding vehicle. Thus hypothetical steady states of synchronized flow cover a two‐dimensional (2D) region in the flow‐density plane, i. e., there is no desired space gap in hypothetical steady states of synchronized flow in this theory.

Wide moving jam traffic phase:

In three-phase traffic theory, the following definition of the wide moving jam phase [J] in congested traffic based on measured traffic data is made. A wide moving jam is a moving jam that maintains the mean velocity of the downstream jam front, even when the jam propagates through any other traffic states or bottlenecks. This is the characteristic feature of the wide moving jam phase.

Synchronized flow traffic phase:

In three-phase traffic theory, the following definition of the synchronized flow phase [S] in congested traffic based on measured traffic data is made. The downstream front of synchronized flow does not exhibit the above mentioned characteristic feature of wide moving jams; specifically, the latter front is often fixed at a bottleneck.

Microscopic criterion for traffic phases:

Within wide moving jams, there are regions in which traffic flow is interrupted: the inflow into the jam has no influence on the jam outflow. A sufficient condition for flow interruption determines the microscopic criterion for the wide moving jam phase. Based on this criterion both the synchronized flow and wide moving jam phases can be identified in congested traffic from single vehicle data measured even at one freeway location. This is because if in measured data congested traffic states associated with the wide moving jam phase have been identified, then with certainty all remaining congested states in the data set are related to the synchronized flow phase.

F → S transition:

In all known observations, traffic breakdown is a phase transition from the free flow phase to synchronized flow phase (F → S transition). Thus the terms traffic breakdown and an F → S transition are synonyms related to the same phenomenon of the onset of congestion in free flow.

Highway capacity of free flow at bottleneck:

Highway (freeway) capacity of free flow at a bottleneck (called also bottleneck capacity) is limited by traffic breakdown, i. e., F → S transition at the bottleneck, which occurs with probability (denoted by \( { P^\text{(B)}_\text{FS} } \)) during a given averaging time interval (denoted by \( { T_\text{av} } \)) for traffic variables. Highway capacity in free flow is equal to the flow rate downstream of the bottleneck at which free flow remains at the bottleneck during the time interval \( { T_\text{av} } \) with probability \( { P^\text{(B)}_\text{C}=1-P^\text{(B)}_\text{FS} } \), which is less than one; thus highway capacity has two attributes \( { P^\text{(B)}_\text{C} } \) and \( { T_\text{av} } \). At each given \( { T_\text{av} } \), there are infinite highway capacities in a limited range associated with different probabilities \( { P^\text{(B)}_\text{C} } \).

Spontaneous traffic breakdown (spontaneous F → S transition) at bottleneck:

If before traffic breakdown free flow has been at a bottleneck as well as upstream and downstream in a neighborhood of the bottleneck, the breakdown is caused by occurrence and subsequent growth of speed disturbances (fluctuations) within the free flow at the bottleneck. Such traffic breakdown is called a spontaneous traffic breakdown at the bottleneck. A speed disturbance begins to grow, i. e., the speed within the disturbance begins to decrease over time with the subsequent breakdown at the bottleneck, if within the disturbance the initial speed is equal to or lower than a critical speed for an F → S transition. Such a critical speed disturbance can be considered a nucleus for the breakdown at the bottleneck. There can be various sources for speed disturbances whose occurrence and subsequent growth lead to spontaneous traffic breakdown: unexpected vehicle braking and/or lane changing in free flow, fluctuations in flow rates upstream of the bottleneck, vehicle merging from other roads in the bottleneck neighborhood (e. g., at on‐ramp bottlenecks), etc.

Induced traffic breakdown (induced F → S transition) at Bottleneck:

In contrast with spontaneous traffic breakdown, which occurs when before the breakdown free flow is in a neighborhood of the bottleneck, an induced traffic breakdown at the bottleneck is caused by the propagation of a moving spatiotemporal congested traffic pattern, which has initially occurred at a different road location (e. g., at another bottleneck). When this congested pattern reaches the bottleneck, the pattern induces traffic breakdown at the bottleneck. The congested pattern whose propagation causes the breakdown at the bottleneck can be considered an external speed disturbance at the bottleneck.

Spontaneous wide moving jam emergence in synchronized flow:

Within synchronized flow, there can be speed disturbances (fluctuations) whose growth leads to wide moving jam emergence. Such wide moving jam emergence is called spontaneous wide moving jam emergence in synchronized flow (spontaneous S → J transition). A speed disturbance begins to grow, if within the disturbance the initial speed is equal to or lower than a critical speed for an S → J transition. Such a critical speed disturbance can be considered a nucleus for the S → J transition. The growing speed disturbance in synchronized flow propagates upstream; for this reason, in contrast with spontaneous traffic breakdown at a bottleneck, the S → J transition occurs usually upstream of the road location at which the critical speed disturbance has initially appeared. There can be various sources for speed disturbances whose occurrence and subsequent growth lead to spontaneous S → J transition: unexpected vehicle braking and/or lane changing within synchronized flow, fluctuations in upstream flow rates, vehicle merging from other roads, etc.

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Acknowledgments

I would like to thank Sergey Klenov, Andreas Hiller, Hubert Rehborn, Mario Aleksić, Ines Maiwald–Hiller and Olivia Brickley for help and useful suggestions.

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  1. GR/ETI, HPC: G021, Daimler AG, Sindelfingen, Germany

    Boris S. Kerner

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  1. Boris S. Kerner
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  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Kerner, B.S. (2009). Traffic Congestion, Modeling Approaches to. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_559

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