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We examine adaptive strategies adopted by vehicles for route selection en-route in transportation networks. By studying a model of two-dimensional cellular automata, we model vehicles characterized by a parameter called path-greediness, which corresponds to the tendency for them to travel to their destinations via the shortest path. The path-greediness of each individual vehicle is updated based on the local traffic conditions, to either keep the vehicle travels via a shorter path in an un-congested region or to explore longer diverted paths in a congested region. We found that the optimal number of steps to trigger an update of path-greediness is dependent on the density of vehicles, and the magnitude of path-greediness increment affects the macroscopic traffic conditions of the system. To better coordinate vehicles in denser networks, the update on the tendency for vehicles to travel via the shorter paths should be gradual and less frequent.

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In this work, we study the effect of a traffic light system on the flow of a single lane road by proposing a traffic model based on a cellular automaton that also includes behavioral considerations. We focus on the macroscopic characterization of the system by studying the changes in vehicle density and the occurrence of jams. In this context, we observe and characterize a phase transition between the free flow and jammed states. This transition is induced by the instabilities originated by the vehicles stopping at the traffic lights. Moreover, we analyze the effect of these instabilities on the critical density of vehicles at which the transition occurs as a function of two parameters: (i) the in-flow of cars, (ii) the drivers’ behavior. For the latter we observe that the traffic light perturbations feedback on the drivers’ behavior can lead the system to different scenarios, which are also analyzed.

This paper is pedagogic in nature, meant to provide researchers a single reference for learning how to apply the emerging literature on differential variational inequalities to the study of dynamic traffic assignment problems that are Cournot-like noncooperative games. The paper is presented in a style that makes it accessible to the widest possible audience. In particular, we apply the theory of differential variational inequalities (DVIs) to the dynamic user equilibrium (DUE) problem. We first show that there is a variational inequality whose necessary conditions describe a DUE. We restate the flow conservation constraint associated with each origin-destination pair as a first-order two-point boundary value problem, thereby leading to a DVI representation of DUE; then we employ Pontryagin-type necessary conditions to show that any DVI solution is a DUE. We also show that the DVI formulation leads directly to a fixed-point algorithm. We explain the fixed-point algorithm by showing the calculations intrinsic to each of its steps when applied to simple examples.

Stochastic User Equilibrium (SUE) models allow the representation of the perceptual and preferential differences that exist when drivers compare alternative routes through a transportation network. However, as an effect of the used choice models, conventional applications of SUE are based on the assumption that all available routes have a positive probability of being chosen, however unattractive. In this paper, a novel choice model, the Bounded Choice Model (BCM), is presented along with network conditions for a corresponding Bounded SUE. The model integrates an exogenously-defined bound on the random utility of the set of paths that are used at equilibrium, within a Random Utility Theory (RUT) framework. The model predicts which routes are used and unused (the choice sets are equilibrated), while still ensuring that the distribution of flows on used routes accords to a Discrete Choice Model. Importantly, conditions to guarantee existence and uniqueness of the Bounded SUE are shown. Also, a corresponding solution algorithm is proposed and numerical results are reported by applying this to the Sioux Falls network.

Urban transportation with multiple roundabouts is facing significant challenges such as traffic congestion, gridlock and traffic accidents. In order to understand these behaviors, we propose a two-dimensional cellular automata (CA) model, where all streets are two-way, with one lane in each direction. To allow the turning movement, a roundabout is designed for each intersection where four roads meet. The distance between each pair of roundabouts is configured with the parameter K while the turning behavior of drivers is modeled by a parameter γ. To study the impact of these different parameters on the urban traffic, several traffic metrics are considered such as traffic flow, average velocity, accident probability and waiting time at the entrance of roundabout. Our simulation results show that the urban traffic is in free flow state when the vehicle’s density is low enough. However, when the density exceeds a critical density ρc, the urban traffic will be in gridlock state whenever γ is nonzero. In the case where γ=0, the urban traffic presents a phase transition between free flow and congested state. Furthermore, detailed analysis of the traffic metrics shows that the model parameters (γ, K) have a significant effects on urban traffic dynamics.

Currently most optimization methods for urban transport networks (i) are suited for networks with simplified dynamics that are far from real-sized networks or (ii) apply decentralized control, which is not appropriate for heterogeneously loaded networks or (iii) investigate good-quality solutions through micro-simulation models and scenario analysis, which make the problem intractable in real time. In principle, traffic management decisions for different sub-systems of a transport network (urban, freeway) are controlled by operational rules that are network specific and independent from one traffic authority to another. In this paper, the macroscopic traffic modeling and control of a large-scale mixed transportation network consisting of a freeway and an urban network is tackled. The urban network is partitioned into two regions, each one with a well-defined Macroscopic Fundamental Diagram (MFD), i.e. a unimodal and low-scatter relationship between region density and outflow. The freeway is regarded as one alternative commuting route which has one on-ramp and one off-ramp within each urban region. The urban and freeway flow dynamics are formulated with the tool of MFD and asymmetric cell transmission model, respectively. Perimeter controllers on the border of the urban regions operating to manipulate the perimeter interflow between the two regions, and controllers at the on-ramps for ramp metering are considered to control the flow distribution in the mixed network. The optimal traffic control problem is solved by a Model Predictive Control (MPC) approach in order to minimize total delay in the entire network. Several control policies with different levels of urban-freeway control coordination are introduced and tested to scrutinize the characteristics of the proposed controllers. Numerical results demonstrate how different levels of coordination improve the performance once compared with independent control for freeway and urban network. The approach presented in this paper can be extended to implement efficient real-world control strategies for large-scale mixed traffic networks.

We introduce a stochastic discrete automaton model to freeway traffic. Monte-Carlo simulations of the model show a transition from laminar traffic flow to start-stop-waves with increasing vehicle density, as is observed in real freeway traffic. For special cases analytical results can be obtained.

Optimizing paths on networks is crucial for many applications, ranging from subway traffic to Internet communication. Because global path optimization that takes account of all path choices simultaneously is computationally hard, most existing routing algorithms optimize paths individually, thus providing suboptimal solutions. We use the physics of interacting polymers and disordered systems to analyze macroscopic properties of generic path optimization problems and derive a simple, principled, generic, and distributed routing algorithm capable of considering all individual path choices simultaneously. We demonstrate the efficacy of the algorithm by applying it to: (i) random graphs resembling Internet overlay networks, (ii) travel on the London Underground network based on Oyster card data, and (iii) the global airport network. Analytically derived macroscopic properties give rise to insightful new routing phenomena, including phase transitions and scaling laws, that facilitate better understanding of the appropriate operational regimes and their limitations, which are difficult to obtain otherwise.

We present a simple cellular automaton (CA) model for two-lane roads explaining the physics of traffic breakdown, highway capacity, and synchronized flow. The model consists of the rules "acceleration," "deceleration," "randomization," and "motion" of the Nagel-Schreckenberg CA model as well as "overacceleration through lane changing to the faster lane," "comparison of vehicle gap with the synchronization gap," and "speed adaptation within the synchronization gap" of Kerner's three-phase traffic theory. We show that these few rules of the CA model can appropriately simulate fundamental empirical features of traffic breakdown and highway capacity found in traffic data measured over years in different countries, like characteristics of synchronized flow, the existence of the spontaneous and induced breakdowns at the same bottleneck, and associated probabilistic features of traffic breakdown and highway capacity. Single-vehicle data derived in model simulations show that synchronized flow first occurs and then self-maintains due to a spatiotemporal competition between speed adaptation to a slower speed of the preceding vehicle and passing of this slower vehicle. We find that the application of simple dependences of randomization probability and synchronization gap on driving situation allows us to explain the physics of moving synchronized flow patterns and the pinch effect in synchronized flow as observed in real traffic data.

A stochastic version of the Biham-Middleton-Levine model with random update rule is studied. It is shown that under periodic boundary condition, the system exhibits a sharp transition from moving phase to jamming phase. Under open boundary condition, the coexistence of moving phase and jamming phase can be observed. We have presented a mean-field analysis for the moving phase, which successfully takes into account the correlation and produces good agreement with simulation results.

Traditional arterial coordination control models adopt aggregated demand from fixed detectors or manual counts as main input, which lack a self-feedback mechanism between the input and the optimization objective. With the population of connected vehicles and intelligent mobility, high-resolution trajectory data provide new possibilities for signal control evaluation and optimization. Therefore, the objective of this study is to propose a new arterial coordination control model for two-way arterial progression solely using sampled trajectories. Sampled trajectories are first used to extract prior arrival information and queuing states. Then, vehicle arrival time at the stop-line at each intersection is estimated as the function of signal timing parameters and prior arrival rates based on the shockwave theory, considering different sampled trajectory statuses. The delay of each sample vehicle is thus obtained as the difference between the actual arrival time and the projected arrival time. Sum of the delays of all the sampled trajectories ever travelling on the mainline of the arterial is selected to be the optimization objective, and the optimization problem is solved through a multi-sub-swarm Particle Swarm Optimization (PSO) algorithm. A simulation model is built to test the performance of the proposed model compared with the Synchro model and the MULTIBAND model under various demand scenarios. Results show that the performance of the proposed method is relatively satisfactory, which demonstrates that the optimization of fixed-time arterial coordination control solely using sample trajectories is feasible.

By introducing a simple model based on two-dimensional cellular automata, we reveal the relationship between the routing strategies of individual vehicles and the global behavior of transportation networks. Specifically, we characterize the routing strategies by a single parameter called path-greediness, which corresponds to the tendency for individuals to travel via a shortest path to the destination. Remarkably, we found that the effective dimension of the system is reduced when the congested states emerge. We also found that a high individual tendency to travel via the shortest path does not necessarily shorten the average journey time, as the system may benefit from less greedy routing strategies in congested situations. Finally, we show that adaptive routing strategies outperform controlled strategies in the free-flow state but not in the congested state, implying that controlled strategies may increase coordination among vehicles and are beneficial for suppressing traffic congestion.

This paper formulates the network-level traffic signal timing optimization problem as a Mixed-Integer Non-Linear Program (MINLP) and presents a customized methodology to solve it with a tight optimality gap. The MINLP is based on the Cell Transmission Model (CTM) network loading concept and captures the fundamental flow-density diagram of the CTM explicitly by considering closed-form constraints in the model and thus, eliminates the flow holding-back problem. The proposed solution algorithm is based on the Benders decomposition technique and decomposes the original MINLP to an equivalent Integer Program (IP) (Master problem), and a new MINLP (Primal problem). We will show that the new MINLP has only one optimal non-holding-back solution that can be found by a CTM simulation run. We will prove that the proposed solution technique guarantees convergence to optimal solutions with a finite number of iterations. Furthermore, we propose a dual estimation algorithm for the new MINLP (the Primal problem), which utilizes a simulation-based approach to generate Benders cuts instead of solving a complex optimization program. We applied the proposed solution technique to a simulated network of 20 intersections under various demand patterns and observed an optimality gap of at most 2% under all tested conditions. We compared the solutions of the proposed algorithm with two benchmark algorithms and found reductions in total travel time ranging from 7.0% to 35.7%.

In this study, an optimal traffic signal control framework is proposed for finding the signal control settings that minimize the total travel time in a road network with traffic lights. A novel aspect of this framework is its integration of the continuous-time double queue traffic flow model in a signal controlled traffic network to capture queue spillbacks in continuous-time. Furthermore, drivers’ long term responses to changes in traffic signal control settings are captured by their route choices following Wardrop’s first principle, which results in the dynamic user equilibrium state. Two signal control strategies, the fixed-timing control and the adaptive signal control, are considered. A continuous approximation method for the signal control is applied to eliminate integer variables and enhance the computational efficiency. A heuristic genetic algorithm based solution procedure is proposed to solve the proposed nonlinear programming problem with time-varying delay terms. Numerical tests are conducted in two testing networks and the results show that adaptive control with drivers taking into account signal timing on their route travel times performs best, and in some cases nearly as well as the benchmark performance derived from system optimal control without equilibrium constraints. The results also show that the advantage of adaptive over fixed-time signal control is more pronounced under UE than SO routing behavior.

A group-based adaptive traffic-control method for isolated signalized junctions is developed that includes a hierarchical structure comprising tactical and local levels of signal timing optimization. The control method optimizes the signal timings in adaptive traffic-control systems, and takes full advantage of flexible new technologies to incorporate the most up-to-date traffic information, as collected in real time. The definitions, combinations, and sequencing of the cycle structure stages are generated automatically using a procedure for optimizing the signal-timing plans in response to online data from traffic detectors. This new method provides a wider search space and improves the efficiency of the signal-control systems, thus improving the junction performance, minimizing delays, and maximizing capacity in real time. A multi-resolution strategy is proposed for updating the elements of the signal plans cycle-by-cycle and adjusting the current green signal timing second-by-second. The group-based variables and parameters for the proactive global-optimization method utilize lane-based predictive traffic-flow information, such as arrival and discharge rates, expressed as the slopes of polygonal delay formulas. Therefore, there is a high degree of flexibility in the tactical identification of the optimal signal plan in response to the real-time predicted traffic information, the objective function of the polygonal delay formula, and the direct differential equations for the adaptive group-based variables. The reactive local signal-control policy, which is formed based on the max-pressure strategy, is developed to locally adjust the current green signal time and to accommodate delicate demand fluctuations second-by-second at the fine-resolution level. The most appropriate cycle-structure for the tactical level of control is identified using a group-based global-optimization procedure that takes advantage of the latest available information. In part II of this study (Lee et al. 2017), the effectiveness of the proposed methods is validated based on the actualized mathematical frameworks, computer simulations, and a case study, using the appropriate computer programs.

In part I of this study (Lee et al., 2017), the formulation of a theoretical framework for a group-based adaptive traffic-control method for isolated signalized junctions is presented, which includes tactical and local levels of signal timing optimization. The global level control aims to determine the time-varying cycle structure, with a resolution of cycles, and the real-time adjustment of the green phase, with a resolution of seconds, based on longer-term traffic information observed by traffic detectors. Overall, the purpose of the study is to actualize a multi-resolution strategy for a group-based adaptive signal-control method and establish a microscopic simulation platform to implement the proposed methodology and test its effectiveness. To actualize the global proactive-optimization scheme, in this paper, a rolling-horizon approach to the temporal and spatial variables, signal structures for four-arm intersections, and discrete directional search methods is applied using the developed mathematical framework. The formulation of the group-based max-pressure policy is realized using the logical form of the local reactive-control policy at a typical directional three-lane, four-arm approach to an isolated intersection. The integrated group-based adaptive traffic-signal control is actualized using VISSIM, Fortran, and VBA based on the developed tactical and local levels of signal timing optimization. The results of the computer simulations and the case study presented in this paper show that the integrated group-based adaptive traffic-signal-control logic outperforms the other methods over a wide range of traffic conditions, from free-flowing traffic to extreme congestion. Moreover, the proposed models perform much better than the existing fixed-signal plan and the actuated signal-control in asymmetric traffic conditions.

This paper studies phase diagrams of traffic states induced by the bottleneck of an unsignalized intersection which consists of two perpendicular one-lane roads. Parallel updates rules are employed for both roads. At the crossing point, in order to avoid colliding, the consideration of yield dynamics may be suitable herein. Different from previous studies, the deterministic Nagel and Schreckenberg model is adopted in this work. Based on theoretical analysis and computer simulations, the phase diagrams of traffic flow have been presented and the flow formulas in all regions have been derived in the phase diagram. The results of theoretical analysis are in good agreement with computer simulation ones. One finds an interesting phenomenon: there exist bistable states in some regions of the phase diagrams.

In this work, we propose an alternative stochastic model for the fundamental
diagram of traffic flow with minimal number of parameters. Our approach is
based on a mesoscopic viewpoint of the traffic system in terms of the dynamics
of vehicle velocity transitions. A key feature of the present approach lies in
its stochastic nature which makes it possible to describe not only the
flow-concentration relation, the so-called fundamental diagram in traffic
engineering, but also its variance -- an important ingredient in the observed
data of traffic flow. It is shown that the model can be seen as a derivative of
the Boltzmann equation when assuming a discrete velocity spectrum. The latter
assumption significantly simplifies the mathematics and therefore, facilitates
the study of its physical content through the analytic solutions. The model
parameters are then adjusted to reproduce the observed traffic flow on the "23
de maio" highway in the Brazilian city of Sao Paulo, where both the fundamental
diagram and its variance are reasonable reproduced. Despite its simplicity, we
argue that the current model provides an alternative description for the
fundamental diagram in the study of traffic flow.

The characteristics of the deterministic Nagel-Schreckenberg model with traffic-light boundary conditions are investigated and elucidated in a mostly theoretically way. First, precise analytical results of the outflow are obtained for cases in which the duration of the red phase is longer than one step. Then, some results are found and studied for cases in which the red phase equals one step. The main findings include the following. The maximum outflow is "road-length related" if the inflow is saturated; otherwise, if the inbound cars are generated stochastically, multiple theoretical outflow volumes may exist. The findings indicate that although the traffic-light boundary can be implemented in a simple and deterministic manner, the deterministic Nagel-Schreckenberg model with such a boundary has some unique and interesting behaviors.

Most existing works on transportation dynamics focus on networks of a fixed
structure, but networks whose nodes are mobile have become widespread, such as
cell-phone networks. We introduce a model to explore the basic physics of
transportation on mobile networks. Of particular interest are the dependence of
the throughput on the speed of agent movement and communication range. Our
computations reveal a hierarchical dependence for the former while, for the
latter, we find an algebraic power law between the throughput and the
communication range with an exponent determined by the speed. We develop a
physical theory based on the Fokker-Planck equation to explain these phenomena.
Our findings provide insights into complex transportation dynamics arising
commonly in natural and engineering systems.

In this paper, we give an elaborate and understandable review of traffic cellular automata (TCA) models, which are a class of computationally efficient microscopic traffic flow models. TCA models arise from the physics discipline of statistical mechanics, having the goal of reproducing the correct macroscopic behaviour based on a minimal description of microscopic interactions. After giving an overview of cellular automata (CA) models, their background and physical setup, we introduce the mathematical notations, show how to perform measurements on a TCA model's lattice of cells, as well as how to convert these quantities into real-world units and vice versa. The majority of this paper then relays an extensive account of the behavioural aspects of several TCA models encountered in literature. Already, several reviews of TCA models exist, but none of them consider all the models exclusively from the behavioural point of view. In this respect, our overview fills this void, as it focusses on the behaviour of the TCA models, by means of time-space and phase-space diagrams, and histograms showing the distributions of vehicles' speeds, space, and time gaps. In the report, we subsequently give a concise overview of TCA models that are employed in a multi-lane setting, and some of the TCA models used to describe city traffic as a two-dimensional grid of cells, or as a road network with explicitly modelled intersections. The final part of the paper illustrates some of the more common analytical approximations to single-cell TCA models.