A link queue model of network traffic flow

Jin, Wen-Long

doi:10.48550/arxiv.1209.2361

Cited by 11 publications

(15 citation statements)

References 61 publications

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“…We use Λ to represent a part of the function Λ, and Λ takes dynamic link flow as input and outputs the link travel time {t i } i . Precisely, Λ represents the dynamic link models [63,20].…”

Section: A Computational Graph For Mcdodementioning

confidence: 99%

“…In the backward iteration described in section 2.6, we need to compute the derivatives of link travel time ∂ Λ({xi}i) ∂xi . The function Λ represents the link flow models which include, but is not limited to, point queue, spatial queue, cell transmission model, link transmission model and link queue model [20,63]. There is no closed-form for link flow models, hence the derivatives of function Λ can be challenging to evaluate analytically.…”

Section: Derivatives Of Link Travel Timementioning

confidence: 99%

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Estimating multi-class dynamic origin-destination demand through a forward-backward algorithm on computational graphs

Qian

2019

Preprint

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Transportation networks are unprecedentedly complex with heterogeneous vehicular flow. Conventionally, vehicle classes are considered by vehicle classifications (such as standard passenger cars and trucks). However, vehicle flow heterogeneity stems from many other aspects in general, e.g., ride-sourcing vehicles versus personal vehicles, human driven vehicles versus connected and automated vehicles. Provided with some observations of vehicular flow for each class in a large-scale transportation network, how to estimate the multi-class spatio-temporal vehicular flow, in terms of time-varying Origin-Destination (OD) demand and path/link flow, remains a big challenge. This paper presents a solution framework for multi-class dynamic OD demand estimation (MCDODE) in large-scale networks. The proposed framework is built on a computational graph with tensor representations of spatio-temporal flow and all intermediate features involved in the MCDODE formulation. A forward-backward algorithm is proposed to efficiently solve the MCDODE formulation on computational graphs. In addition, we propose a novel concept of tree-based cumulative curves to estimate the gradient of OD demand. A Growing Tree algorithm is developed to construct tree-based cumulative curves. The proposed framework is examined on a small network as well as a real-world large-scale network. The experiment results indicate that the proposed framework is compelling, satisfactory and computationally plausible.

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Section: A Computational Graph For Mcdodementioning

confidence: 99%

Section: Derivatives Of Link Travel Timementioning

confidence: 99%

Estimating multi-class dynamic origin-destination demand through a forward-backward algorithm on computational graphs

Qian

2019

Preprint

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“…According to the link queue model (LQM) (Jin, 2012), vehicles in a link are treated as always being in a queue, and therefore, each link has only one state variable, the average link density. The left and the right rings in Figure 1(b) are denoted as rings 1 and 2 with average densities k 1 (t) and k 2 (t), respectively.…”

Section: A Link Queue Representationmentioning

confidence: 99%

“…In the signalized double-ring network, traffic statics and dynamics are easier to solve because we only need to keep track of traffic states on the two rings. Furthermore, instead of using the kinematic wave model in (Jin et al, 2013), we use a simplified approximation called the link queue model in (Jin, 2012) to formulate the traffic dynamics in the signalized double-ring network. With the assumption of a triangular traffic flow fundamental diagram (Haberman, 1977), the signalized double-ring network is studied as a switched affine system.…”

Section: Introductionmentioning

confidence: 99%

“…The rest of this paper is organized as follows. In Section 2, we formulate the traffic dynamics in a signalized double-ring network as a switched affine system when the link queue model (Jin, 2012) and a triangular traffic flow fundamental diagram (Haberman, 1977) are used. In Section 3, we derive the Poincaré maps from the density evolution orbits in the switched affine system.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of Traffic Statics and Dynamics in Signalized Networks: A Poincaré Map Approach

Gan

Jin

Gayah

2017

Transportation Science

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Understanding traffic statics and dynamics in urban networks is critical to develop effective control and management strategies. In this paper, we provide a novel approach to study the traffic statics and dynamics in a signalized double-ring network, which can provide insights into the operation of more general signalized traffic networks. Under the framework of the link queue model (LQM) and the assumption of a triangular traffic flow fundamental diagram, the signalized double-ring network is studied as a switched affine system. Due to periodic signal regulations, periodic density evolution orbits are formed and defined as stationary states. A Poincaré map approach is introduced to analyze the properties of such stationary states. With short cycle lengths, closed-form Poincaré maps are derived. Stationary states and their stability properties are obtained by finding and analyzing the fixed points on the Poincaré maps. It is found that a stationary state can be asymptotically stable, Lyapunov stable, or unstable. The impacts of retaining ratios and initial densities on the macroscopic fundamental diagrams (MFDs) and the gridlock times are analyzed. Multivaluedness and gridlock phenomena as well as the unstable branch with non-zero average network flow-rates are observed on the MFDs. With long cycle lengths, fixed points on the Poincaré maps are solved numerically, and the obtained stationary states and the MFDs are very similar to those with short cycle lengths.Compared with earlier studies, this paper provides an analytical framework that can be used to provide complete and closed-form solutions to the statics and dynamics of doublering networks. This can lead to a better understanding of how the combination of signalized intersections and turning maneuvers is expected to impact network properties, like the MFD.

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Continuous formulations and analytical properties of the link transmission model

Jin

2015

Transportation Research Part B: Methodological

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The link transmission model (LTM) has great potential for simulating traffic flow in large-scale networks since it is much more efficient and accurate than the Cell Transmission Model (CTM). However, there lack general continuous formulations of LTM, and there has been no systematic study on its analytical properties such as stationary states and stability of network traffic flow. In this study we attempt to fill the gaps. First we apply the Hopf-Lax formula to derive Newell's simplified kinematic wave model with given boundary cumulative flows and the triangular fundamental diagram. We then apply the Hopf-Lax formula to define link demand and supply functions, as well as link queue and vacancy functions, and present two continuous formulations of LTM, by incorporating boundary demands and supplies as well as invariant macroscopic junction models. With continuous LTM, we define and solve the stationary states in a road network. We also apply LTM to directly derive a Poincaré map to analyze the stability of stationary states in a diverge-merge network. Finally we present an example to show that LTM is not well-defined with non-invariant junction models. We can see that Newell's model and LTM complement each other and provide an alternative formulation of the network kinematic wave model. This study paves the way for further extensions, analyses, and applications of LTM in the future.

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A link queue model of network traffic flow

Cited by 11 publications

References 61 publications

Estimating multi-class dynamic origin-destination demand through a forward-backward algorithm on computational graphs

Estimating multi-class dynamic origin-destination demand through a forward-backward algorithm on computational graphs

Analysis of Traffic Statics and Dynamics in Signalized Networks: A Poincaré Map Approach

Continuous formulations and analytical properties of the link transmission model

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