# Multi-class AR model: comparison with microsimulation model for traffic flow variables at network level of interest and the two-dimensional formulation

04 Mar 2021-International Journal of Modelling and Simulation (Taylor & Francis)-Vol. 41, Iss: 2, pp 81-91

TL;DR: A two-dimensional formulation of a recently proposed multi-class, speed-area occupancy based, one-dimensional continuum model towards the measurement of network level traffic flow variables, namely, travel time and outflow is proposed.

Abstract: This paper discusses on the choice of a recently proposed multi-class, speed-area occupancy based, one-dimensional continuum model towards the measurement of network level traffic flow variables, n...

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TL;DR: In this paper, the authors proposed a continuum model based on a three-dimensional flow-concentration surface for multi-class traffic, which assumes that the flow of any vehicle class is a function of the class density as well as the fraction of road area occupied by other vehicle classes.

Abstract: This paper proposes a continuum model based on a three-dimensional flow-concentration surface for multi-class traffic. The model assumes that the flow of any vehicle class is a function of the class density as well as the fraction of road area occupied by other vehicle classes. By considering occupancy of road area instead of lane occupancy, the model effectively describes traffic flow that does not follow lane discipline. The propagation speed of small disturbance (PSSD), conventionally defined from the two-dimensional flow–density relationship, is reformulated for each class using a three-dimensional flow–concentration surface. Using the proposed PSSD and a speed–area occupancy (speed- A O ) relationship, a second-order continuum model for multi-class traffic is formulated. The speed– A O relationship captures class-specific congestion and replicates the gap-filling behaviour commonly observed in lane-indisciplined traffic. Properties of the proposed model are validated theoretically where possible, and through numerical simulation when theoretical derivations are cumbersome. Numerical simulation of the proposed multi-class traffic model replicates field-observed phenomena such as shockwaves and rarefaction waves, local cluster effect, and gap-filling behaviour. Finally, the model is calibrated using field traffic data collected on a road section with bottleneck, and is found to replicate class-wise vehicle flows and speeds, and stop-and-go phenomena.

4 citations

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10 Aug 2021TL;DR: In this paper, a simulation-based analytical design for aluminium recycling processing plant was carried out to ascertain the efficiency and reliability of the design before fabrication using finite element analysis (FEA) approach, which revealed a lesser maximum stress of 6.323 MPa for the furnace outer casing under the action of load with a displacement of 0.0795 mm.

Abstract: Indiscriminate disposal of beverage cans as waste poses a great threat to the environment, causing flooding, landfill, and blockage of drainages, leading to land pollution and sometimes accident. Hence, there is a need to design a system capable of converting these wastes into usable products. In this study, a simulation-based analytical design for aluminium recycling processing plant was carried out to ascertain the efficiency and reliability of the design before fabrication using finite element analysis (FEA) approach. The simulation results revealed a lesser maximum stress of 6.323 MPa for the furnace outer casing under the action of load with a displacement of 0.0795 mm. The stress of the machine components is less than the yield strength of the selected materials, making the machine fit and workable. The analytical results agree with the numerical analysis; hence the conceptual design is fit for fabrication based on the design analysis and evaluation. After the design analysis and simulation, the designed recycling process plant parts are found to be under negligible deflection and stress which is far below the yield strength of chosen materials.

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TL;DR: In this paper , a first-order two-dimensional Lighthill-Whitham-Richards (LWR) model is proposed for continuous macroscopic longitudinal and lateral dynamics of this type of traffic flow.

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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

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TL;DR: In this article, the theory of a distinctive type of wave motion, which arises in any one-dimensional flow problem when there is an approximate functional relation at each point between the flow q and concentration k (quantity passing a given point in unit time) and q remains constant on each kinematic wave.

Abstract: In this paper and in part II, we give the theory of a distinctive type of wave motion, which arises in any one-dimensional flow problem when there is an approximate functional relation at each point between the flow q (quantity passing a given point in unit time) and concentration k (quantity per unit distance). The wave property then follows directly from the equation of continuity satisfied by q and k. In view of this, these waves are described as 'kinematic', as distinct from the classical wave motions, which depend also on Newton's second law of motion and are therefore called 'dynamic'. Kinematic waves travel with the velocity $\partial $q/$\partial $k, and the flow q remains constant on each kinematic wave. Since the velocity of propagation of each wave depends upon the value of q carried by it, successive waves may coalesce to form 'kinematic shock waves'. From the point of view of kinematic wave theory, there is a discontinuous increase in q at a shock, but in reality a shock wave is a relatively narrow region in which (owing to the rapid increase of q) terms neglected by the flow-concentration relation become important. The general properties of kinematic waves and shock waves are discussed in detail in section 1. One example included in section 1 is the interpretation of the group-velocity phenomenon in a dispersive medium as a particular case of the kinematic wave phenomenon. The remainder of part I is devoted to a detailed treatment of flood movement in long rivers, a problem in which kinematic waves play the leading role although dynamic waves (in this case, the long gravity waves) also appear. First (section 2), we consider the variety of factors which can influence the approximate flow-concentration relation, and survey the various formulae which have been used in attempts to describe it. Then follows a more mathematical section (section 3) in which the role of the dynamic waves is clarified. From the full equations of motion for an idealized problem it is shown that at the 'Froude numbers' appropriate to flood waves, the dynamic waves are rapidly attenuated and the main disturbance is carried downstream by the kinematic waves; some account is then given of the behaviour of the flow at higher Froude numbers. Also in section 3, the full equations of motion are used to investigate the structure of the kinematic shock; for this problem, the shock is the 'monoclinal flood wave' which is well known in the literature of this subject. The final sections (section section 4 and 5) contain the application of the theory of kinematic waves to the determination of flood movement. In section 4 it is shown how the waves (including shock waves) travelling downstream from an observation point may be deduced from a knowledge of the variation with time of the flow at the observation point; this section then concludes with a brief account of the effect on the waves of tributaries and run-off. In section 5, the modifications (similar to diffusion effects) which arise due to the slight dependence of the flow-concentration curve on the rate of change of flow or concentration, are described and methods for their inclusion in the theory are given.

1,336 citations

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TL;DR: A new "second order" model of traffic flow is introduced, which replaces the space derivative with a convective derivative and nicely predicts instabilities near the vacuum, i.e., for very light traffic.

Abstract: We introduce a new "second order" model of traffic flow. As noted in [C. Daganzo, Requiem for second-order fluid with approximation to traffic flow, Transportation Res. Part B, 29 (1995), pp. 277--286], the previous "second order" models, i.e., models with two equations (mass and "momentum"), lead to nonphysical effects, probably because they try to mimic the gas dynamics equations, with an unrealistic dependence on the acceleration with respect to the space derivative of the "pressure." We simply replace this space derivative with a convective derivative, and we show that this very simple repair completely resolves the inconsistencies of these models. Moreover, our model nicely predicts instabilities near the vacuum, i.e., for very light traffic.

1,158 citations

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TL;DR: In this article, the authors present a review of the existing literature on short-term traffic forecasting and offer suggestions for future work, focusing on 10 challenging, yet relatively under researched, directions.

Abstract: Since the early 1980s, short-term traffic forecasting has been an integral part of most Intelligent Transportation Systems (ITS) research and applications; most effort has gone into developing methodologies that can be used to model traffic characteristics and produce anticipated traffic conditions. Existing literature is voluminous, and has largely used single point data from motorways and has employed univariate mathematical models to predict traffic volumes or travel times. Recent developments in technology and the widespread use of powerful computers and mathematical models allow researchers an unprecedented opportunity to expand horizons and direct work in 10 challenging, yet relatively under researched, directions. It is these existing challenges that we review in this paper and offer suggestions for future work.

927 citations

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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