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Journal ArticleDOI

The cell transmission model, part ii: network traffic

01 Apr 1995-Transportation Research Part B-methodological (Pergamon)-Vol. 29, Iss: 2, pp 79-93
TL;DR: This article shows how the evolution of multi-commodity traffic flows over complex networks can be predicted over time, based on a simple macroscopic computer representation of traffic flow that is consistent with the kinematic wave theory under all traffic conditions.
Abstract: This article shows how the evolution of multi-commodity traffic flows over complex networks can be predicted over time, based on a simple macroscopic computer representation of traffic flow that is consistent with the kinematic wave theory under all traffic conditions. The method does not use ad hoc procedures to treat special situations. After a brief review of the basic model for one link, the article describes how three-legged junctions can be modeled. It then introduces a numerical procedure for networks, assuming that a time-varying origin-destination (O-D) table is given and that the proportion of turns at every junction is known. These assumptions are reasonable for numerical analysis of disaster evacuation plans. The results are then extended to the case where, instead of the turning proportions, the best routes to each destination from every junction are known at all times. For technical reasons explained in the text, the procedure is more complicated in this case, requiring more computer memory and more time for execution. The effort is estimated to be about an order of magnitude greater than for the static traffic assignment problem on a network of the same size. The procedure is ideally suited for parallel computing. It is hoped that the results in the article will lead to more realistic models of freeway flow, disaster evacuations and dynamic traffic assignment for the evening commute.
Citations
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Journal ArticleDOI
TL;DR: This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic, including microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models.
Abstract: Since the subject of traffic dynamics has captured the interest of physicists, many surprising effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by ``phantom traffic jams'' even though drivers all like to drive fast? What are the mechanisms behind stop-and-go traffic? Why are there several different kinds of congestion, and how are they related? Why do most traffic jams occur considerably before the road capacity is reached? Can a temporary reduction in the volume of traffic cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize into lanes, while similar systems ``freeze by heating''? All of these questions have been answered by applying and extending methods from statistical physics and nonlinear dynamics to self-driven many-particle systems. This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic. These include microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models. Attention is also paid to the formulation of a micro-macro link, to aspects of universality, and to other unifying concepts, such as a general modeling framework for self-driven many-particle systems, including spin systems. While the primary focus is upon vehicle and pedestrian traffic, applications to biological or socio-economic systems such as bacterial colonies, flocks of birds, panics, and stock market dynamics are touched upon as well.

3,117 citations

Journal ArticleDOI
TL;DR: The literature is surveyed to identify potential research directions in disaster operations, discuss relevant issues, and provide a starting point for interested researchers.

1,431 citations


Cites background from "The cell transmission model, part i..."

  • ...Mitigation: Davidson et al. (2003), Dong et al. (1987), Jenkins (2000), Suzuki et al. (1984) Preparedness: Ambs et al. (2000), Belardo et al. (1984a,b), Hamalainen et al. (2000), Hernandez and Serrano (2001), Iakovou et al. (1996), Ishigami et al. (2004), Pidd et al. (1996), Viswanath and Peeta (2003) Response: Barbarosoglu and Arda (2004), Brown and Vassiliou (1993), de Silva and Eglese (2000), Psaraftis and Ziogas (1985), Shim et al. (2002), Srinivasa and Wilhelm (1997), Wilhelm and Srinivasa (1997) Recovery: Guthrie and Manivannan (1992), Song et al. (1996) of control which rarely exists in these situations....

    [...]

  • ...Mitigation: Ariav et al. (1989), Artalejo and Gomez-Corral (1999), Atencia and Moreno (2004), Chao (1995), Duffuaa and Alnajjar (1995), Duffuaa and Khan (2002), Duffuaa and Nadeem (1994), Economou (2004), Economou and Fakinos (2003), Erkut and Ingolfsson (2000), Frohwein and Lambert (2000), Frohwein et al. (1999), Frohwein et al. (2000), Gillespie et al. (2004), Gottinger (1998), Haimes and Jiang (2001), Hartl et al. (1999), Jacobs and Vesilind (1992), Kent (2004), Lee (2001), Mehrez and Gafni (1990), Peizhuang et al. (1986), Perry and Stadje (2001), Peterson (2002), Sampson and Smith (1982), Semenova (2004), Shin (2004), Yi and Bier (1998) Preparedness: Daganzo (1995), Dudin and Nishimura (1999), Yamada (1996) Response: French (1996), Jianshe et al. (1994), Sarker et al. (1996) Recovery: Kim and Dshalalow (2002), Lambert and Patterson (2002), Manivannan and Guthrie (1994)...

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  • ...Mitigation: Psaraftis et al. (1986) Preparedness: Benini (1993), Takamura and Tone (2003) Response: Barbarosoglu et al. (2002) Recovery: no articles found...

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  • ...Mitigation: Coles and Pericchi (2003), Englehardt (2002), Hsieh (2004), Leung et al. (2003) Preparedness: Gregory and Midgley (2000), Reer (1994), Sherali et al. (1991), Wei et al. (2002), Wilhelm and Srinivasa (1996) Response: Mould (2001), Ozdamar et al. (2004), Sheffi et al. (1982), Swartz and Johnson (2004) Recovery: Boswell et al. (1999), Chang and Nojima (2001), Cret et al. (1993), Nikolopoulos and Tzanetis (2003)...

    [...]

  • ...Mitigation: Current and O Kelly (1992), Harrald et al. (1990) Preparedness: Gheorghe and Vamanu (1995), Obradovic and Kordic (1986), Simard and Eenigenburg (1990) Response: Belardo et al. (1984a,b), Hobeika et al. (1994), Kourniotis et al. (2001), Zografos et al. (1998) Recovery: no articles found...

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Journal ArticleDOI
TL;DR: In this paper, it is shown that any continuum model of traffic flow that smooths out all discontinuities in density will predict negative flows and negative speeds (i.e., "wrong way travel") under certain conditions.
Abstract: Although the “first order” continuum theory of highway traffic proposed by Lighthill and Whitham (1955) and Richards (1956)—the LWR model—can predict some things rather well, it is also known to have some deficiencies. In an attempt to correct some of these, “higher order” theories have been proposed starting in the early 70s. Unfortunately, the usefulness of these improvements can be questioned. This note describes the logical flaws in the arguments that have been advanced to derive higher order continuum models, and shows that the proposed high order modifications lead to a fundamentally flawed model structure. The modifications can actually make things worse. As an illustration of this, it is shown that any continuum model of traffic flow that smooths out all discontinuities in density will predict negative flows and negative speeds (i.e., “wrong way travel”) under certain conditions. Such unreasonable predictions are made by all existing models formulated as a quasilinear system of partial differential equations in speed, density, and (sometimes) other variables but not by the LWR model. The note discusses the available empirical evidence and ends with a (hopefully positive) commentary on what can be accomplished with first-order models.

827 citations

Journal ArticleDOI
01 Jun 2001
TL;DR: This paper presents a overview of some fifty years of modelling vehicular traffic flow, and a rich variety of modelling approaches developed so far and in use today will be discussed and compared.
Abstract: Nowadays traffic flow and congestion is one of the main societal and economical problems related to transportation in industrialized countries. In this respect, managing traffic in congeste...

674 citations

Journal ArticleDOI
TL;DR: The main objective of the paper is to demonstrate that the DTA problem can be modeled as an LP, which allows the vast existing literature on LP to be used to better understand and compute DTA.
Abstract: Recently, Daganzo introduced the cell transmission model--a simple approach for modeling highway traffic flow consistent with the hydrodynamic model. In this paper, we use the cell transmission model to formulate the single destination System Optimum Dynamic Traffic Assignment (SO DTA) problem as a Linear Program (LP). We demonstrate that the model can obtain insights into the DTA problem, and we address various related issues, such as the concept of marginal travel time in a dynamic network and system optimum necessary and sufficient conditions. The model is limited to one destination and, although it can account for traffic realities as they are captured by the cell transmission model, it is not presented as an operational model for actual applications. The main objective of the paper is to demonstrate that the DTA problem can be modeled as an LP, which allows the vast existing literature on LP to be used to better understand and compute DTA. A numerical example illustrates the simplicity and applicability of the proposed approach.

512 citations

References
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Journal ArticleDOI
TL;DR: In this article, a simple theory of traffic flow is developed by replacing individual vehicles with a continuous fluid density and applying an empirical relation between speed and density, which is a simple graph-shearing process for following the development of traffic waves.
Abstract: A simple theory of traffic flow is developed by replacing individual vehicles with a continuous “fluid” density and applying an empirical relation between speed and density. Characteristic features of the resulting theory are a simple “graph-shearing” process for following the development of traffic waves in time and the frequent appearance of shock waves. The effect of a traffic signal on traffic streams is studied and found to exhibit a threshold effect wherein the disturbances are minor for light traffic but suddenly build to large values when a critical density is exceeded.

3,475 citations

01 Jan 1971

1,071 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that a small amplitude disturbance propagates through a series of cars in the manner described by linear theories, except that the dependence of the wave velocity on the car velocity causes an accleration wave to spread as it propagates and a deceleration wave forming a stable shock.
Abstract: It is assumed that the velocity of a car at time t is some nonlinear function of the spacial headway at time t-Δ, so the equations of motion for a sequence of cars consists of a set of differential-difference equations. There is a special family of velocity-headway relations that agrees well with experimental data for steady flow, and that also gives differential equations which for Δ = 0 can be solved explicitly. Some exact solutions of these equations show that a small amplitude disturbance propagates through a series of cars in the manner described by linear theories except that the dependence of the wave velocity on the car velocity causes an accleration wave to spread as it propagates and a deceleration wave to form a stable shock. These conclusions are then shown to hold for quite general types of velocity-headway relations, and to yield a theory that in certain limiting cases gives all the results of the linear car-following theories and in other cases all the features of the nonlinear continuum theories, plus a detailed picture of the shock structure.

918 citations

Journal ArticleDOI
TL;DR: In this paper, it is shown how a formal solution for A ( x, t ) can be evaluated directly from boundary or initial conditions without evaluation at intermediate times and positions, and the correct solution, which is the lower envelope of all such formal solutions, will automatically have discontinuities in slope describing the passage of a shock.
Abstract: In the theory of “kinematic waves,” as described originally by Lighthill and Whitham in 1955, the evaluation of the shock path is typically rather tedious. Instead of using this theory to evaluate flows or densities, one can use it to evaluate the cumulative flow A ( x , t ) past any point x by time t . It is shown here how a formal solution for A ( x, t ) can be evaluated directly from boundary or initial conditions without evaluation at intermediate times and positions. If there are shocks, however, this solution will be multiple-valued. The correct solution, which is the lower envelope of all such formal solutions, will automatically have discontinuities in slope describing the passage of a shock. To evaluate A ( x, t ) at any particular location x , it is not necessary to follow the actual path of the shock. The solution can be evaluated directly in terms of the boundary data by either graphical or numerical techniques.

834 citations

Journal ArticleDOI
TL;DR: In this article, the authors proposed a method to relate the cumulative flow curve at any junction to the net cumulative entrance flow at this junction, and the cumulative curve for the freeway at the next upstream junction and/or the next downstream junction.
Abstract: For a freeway having various entrance and exit ramps, the methods described in Part I are used to relate the cumulative flow curve at any junction to the net cumulative entrance flow at this junction, and the cumulative flow curves for the freeway at the next upstream junction and/ or the next downstream junction. If the type of flow-density relations typical of freeway traffic are idealized by a triangular shaped curve with only two wave speeds, one for free-flowing traffic (positive) and the other for congested traffic (negative), then the relationship is easy to evaluate. The cumulative flow curve at the junction is simply the lower envelope of a translation of the cumulative curve from upstream and a different translation of the cumulative curve from downstream. This relationship is the basic building block for a freeway flow prediction model described in Part III.

547 citations