A comparative study of Macroscopic Fundamental Diagrams of arterial road networks governed by adaptive traffic signal systems

Using a stochastic cellular automaton model for urban traffic flow, we study and compare Macroscopic Fundamental Diagrams (MFDs) of arterial road networks governed by different types of adaptive traffic signal systems, under various boundary conditions. In particular, we simulate realistic signal systems that include signal linking and adaptive cycle times, and compare their performance against a highly adaptive system of self-organizing traffic signals which is designed to uniformly distribute the network density. We find that for networks with time-independent boundary conditions, well-defined stationary MFDs are observed, whose shape depends on the particular signal system used, and also on the level of heterogeneity in the system. We find that the spatial heterogeneity of both density and flow provide important indicators of network performance. We also study networks with time-dependent boundary conditions, containing morning and afternoon peaks. In this case, intricate hysteresis loops are observed in the MFDs which are strongly correlated with the density heterogeneity. Our results show that the MFD of the self-organizing traffic signals lies above the MFD for the realistic systems, suggesting that by adaptively homogenizing the network density, overall better performance and higher capacity can be achieved.     

A three-dimensional macroscopic fundamental diagram for mixed bi-modal urban networks

Recent research has studied the existence and the properties of a macroscopic fundamental diagram (MFD) for large urban networks. The MFD should not be universally expected as high scatter or hysteresis might appear for some type of networks, like heterogeneous networks or freeways. In this paper, we investigate if aggregated relationships can describe the performance of urban bi-modal networks with buses and cars sharing the same road infrastructure and identify how this performance is influenced by the interactions between modes and the effect of bus stops. Based on simulation data, we develop a three-dimensional vehicle MFD (3D-vMFD) relating the accumulation of cars and buses, and the total circulating vehicle flow in the network. This relation experiences low scatter and can be approximated by an exponential-family function. We also propose a parsimonious model to estimate a three-dimensional passenger MFD (3D-pMFD), which provides a different perspective of the flow characteristics in bi-modal networks, by considering that buses carry more passengers. We also show that a constant Bus–Car Unit (BCU) equivalent value cannot describe the influence of buses in the system as congestion develops. We then integrate a partitioning algorithm to cluster the network into a small number of regions with similar mode composition and level of congestion. Our results show that partitioning unveils important traffic properties of flow heterogeneity in the studied network. Interactions between buses and cars are different in the partitioned regions due to higher density of buses. Building on these results, various traffic management strategies in bi-modal multi-region urban networks can then be integrated, such as redistribution of urban space among different modes, perimeter signal control with preferential treatment of buses and bus priority.     

Cooperative traffic control of a mixed network with two urban regions and a freeway

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.     

Hierarchical perimeter control with guaranteed stability for dynamically coupled heterogeneous urban traffic

Perimeter control based on the Macroscopic Fundamental Diagram (MFD) is widely developed for alleviating or postponing congestion in a protected region. Recent studies reveal that traffic conditions might not be improved if the perimeter control strategies are applied to unstable systems where high demand generates heavy and heterogeneously distributed traffic congestion. Therefore, considering stability of the targeted traffic system is essential, for the sake of developing a feasible and then optimal control strategy. This paper sheds light on this direction. It integrates a stability characterization algorithm of MFD system equations into the Model Predictive Control (MPC) scheme, and features respectively an upper and a lower bound of the feasible control inputs, to guarantee system stability. Firstly, the dynamics of traffic heterogeneity and its effect on the MFD are analyzed, using real data from Guangzhou in China. Piecewise affine functions of average flow are proposed to capture traffic heterogeneity in both regional and subregional MFDs. Secondly, stability of a three-state two-region system is investigated via stable equilibrium and surface boundaries analysis. Finally, a three-layer hierarchical control strategy is introduced for the studied two-region heterogeneous urban networks. The first layer of the controller calculates the stable surface boundaries for the given traffic demands and then determines the bounds of control input (split rate). An MPC approach in the second layer is used to solve an optimization problem with two objectives of minimizing total network delay and maximizing network throughput. Heterogeneity among the subregions is minimized in the last layer by implementing simultaneously a subregional perimeter flow control and an internal flow control. The effectiveness and stability of the proposed control approach are verified by comparison with four existing perimeter control strategies.     

Properties of a well-defined macroscopic fundamental diagram for urban traffic

A field experiment in Yokohama (Japan) revealed that a macroscopic fundamental diagram (MFD) linking space-mean flow, density and speed exists on a large urban area. It was observed that when the highly scattered plots of flow vs. density from individual fixed detectors were aggregated the scatter nearly disappeared and points grouped along a well defined curve. Despite these and other recent findings for the existence of well-defined MFDs for urban areas, these MFDs should not be universally expected. In this paper we investigate what are the properties that a network should satisfy, so that an MFD with low scatter exists. We show that the spatial distribution of vehicle density in the network is one of the key components that affect the scatter of an MFD and its shape. We also propose an analytical derivation of the spatial distribution of congestion that considers correlation between adjacent links. We investigate the scatter of an MFD in terms of errors in the probability density function of spatial link occupancy and errors of individual links’ fundamental diagram (FD). Later, using real data from detectors for an urban arterial and a freeway network we validate the proposed derivations and we show that an MFD is not well defined in freeway networks as hysteresis effects are present. The datasets in this paper consist of flow and occupancy measures from 500 fixed sensors in the Yokohama downtown area in Japan and 600 loop detectors in the Twin Cities Metropolitan Area Freeway network in Minnesota, USA.     

Equilibrium analysis and route guidance in large-scale networks with MFD dynamics

Recent studies have demonstrated that Macroscopic Fundamental Diagram (MFD), which provides an aggregated model of urban traffic dynamics linking network production and density, offers a new generation of real-time traffic management strategies to improve the network performance. However, the effect of route choice behavior on MFD modeling in case of heterogeneous urban networks is still unexplored. The paper advances in this direction by firstly extending two MFD-based traffic models with different granularity of vehicle accumulation state and route choice behavior aggregation. This configuration enables us to address limited traffic state observability and to scrutinize implications of drivers’ route choice in MFD modeling. We consider a city that is partitioned in a small number of large-size regions (aggregated model) where each region consists of medium-size sub-regions (more detailed model) exhibiting a well-defined MFD. This paper proposes a route guidance advisory control system based on the aggregated model as a large-scale traffic management strategy that utilizes aggregated traffic states while sub-regional information is partially known. In addition, we investigate the effect of equilibrium conditions (i.e. user equilibrium and system optimum) on the overall network performance, in particular MFD functions.     

On the stability of traffic perimeter control in two-region urban cities

In this paper, stability analysis of traffic control for two-region urban cities is treated. It is known in control theory that optimality does not imply stability. If the optimal control is applied in a heavily congested system with high demand, traffic conditions might not change or the network might still lead to gridlock. A city partitioned in two regions with a Macroscopic Fundamental Diagram (MFD) for each of the regions is considered. Under the assumption of triangular MFDs, the two-region MFDs system is modeled as a piecewise second-order system. Necessary and sufficient conditions are derived for stable equilibrium accumulations in the undersaturated regimes for both MFDs. Moreover, the traffic perimeter control problem for the two-region MFDs system is formulated. Phase portraits and stability analysis are conducted, and a new algorithm is proposed to derive the boundaries of the stable and unstable regions. Based on these regions, a state-feedback control strategy is derived. Trapezoidal shape of MFDs are also addressed with numerical solutions.     

Perimeter and boundary flow control in multi-reservoir heterogeneous networks

In this paper, we macroscopically describe the traffic dynamics in heterogeneous transportation urban networks by utilizing the Macroscopic Fundamental Diagram (MFD), a widely observed relation between network-wide space-mean flow and density of vehicles. A generic mathematical model for multi-reservoir networks with well-defined MFDs for each reservoir is presented first. Then, two modeling variations lead to two alternative optimal control methodologies for the design of perimeter and boundary flow control strategies that aim at distributing the accumulation in each reservoir as homogeneously as possible, and maintaining the rate of vehicles that are allowed to enter each reservoir around a desired point, while the system’s throughput is maximized. Based on the two control methodologies, perimeter and boundary control actions may be computed in real-time through a linear multivariable feedback regulator or a linear multivariable integral feedback regulator. Perimeter control occurs at the periphery of the network while boundary control occurs at the inter-transfers between neighborhood reservoirs. To this end, the heterogeneous network of San Francisco is partitioned into three homogeneous reservoirs and the proposed feedback regulators are compared with a pre-timed signal plan and a single-reservoir perimeter control strategy. Finally, the impact of the perimeter and boundary control actions is demonstrated via simulation by the use of the corresponding MFDs and other performance measures. A key advantage of the proposed approach is that it does not require high computational effort and future demand data if the current state of each reservoir can be observed with loop detector data.     

Multi-scale perimeter control approach in a connected-vehicle environment

This paper proposes a novel approach to integrate optimal control of perimeter intersections (i.e. to minimize local delay) into the perimeter control scheme (i.e. to optimize traffic performance at the network level). This is a complex control problem rarely explored in the literature. In particular, modeling the interaction between the network level control and the local level control has not been fully considered. Utilizing the Macroscopic Fundamental Diagram (MFD) as the traffic performance indicator, we formulate a dynamic system model, and design a Model Predictive Control (MPC) based controller coupling two competing control objectives and optimizing the performance at the local and the network level as a whole. To solve this highly non-linear optimization problem, we employ an approximation framework, enabling the optimal solution of this large-scale problem to be feasible and efficient. Numerical analysis shows that by applying the proposed controller, the protected network can operate around the desired state as expressed by the MFD, while the total delay at the perimeter is minimized as well. Moreover, the paper sheds light on the robustness of the proposed controller. This multi-scale hybrid controller is further extended to a stochastic MPC scheme, where connected vehicles (CV) serve as the only data source. Hence, low penetration rates of CVs lead to strong noises in the controller. This is a first attempt to develop a network-level traffic control methodology by using the emerging CV technology. We consider the stochasticity in traffic state estimation and the shape of the MFD. Simulation analysis demonstrates the robustness of the proposed stochastic controller, showing that efficient controllers can indeed be designed with this newly-spread vehicle technology even in the absence of other data collection schemes (e.g. loop detectors).     

Agent-based network transmission model using the properties of macroscopic fundamental diagram

The field of research that has recently come to the fore is the perimeter control, which aims to control traffic demand for a large urban area prior to controlling internal flow inside the area. Such control concept needs to be tested by simulations, hence, it is necessary to develop a model that can appropriately estimate the network-wide flow dynamics. In this paper, agent-based network transmission model (ANTM) is proposed for describing the aggregated flow dynamics over an urban area of multiple large-scale networks. The proposed model is the combination of the cell transmission model (CTM), macroscopic fundamental diagram (MFD), and agent concept. The CTM-based simulation is adopted for the simplicity considering the computation requirements for real-time feasibility. The MFD concept is applied for representing the network properties, and a new approach is taken particularly for estimating network outflow affected by both demand patterns and boundary capacity. The agent concept is applied for representing drivers’ travel behaviors. The model is compared with microscopic simulations and shows reasonable accuracy for large areas. In addition, various travel direction choice behaviors are applicable to this model. Various perimeter control policies are applicable as well, thus, the proposed model can be a useful tool for testing various control methods, in terms of reducing the congestion in urban areas.     

Traffic guidance–perimeter control coupled method for the congestion in a macro network

Macroscopic fundamental diagram (MFD) describes the macro relationship between a network vehicle density and a network space mean flow, without requiring the mastery of complex origin to destination data. Thus, MFD provides an opportunity for the macro control of urban road network. However, most of the existing MFD control methods ignore the active role of traffic guidance in solving congestion problems. This study presents a traffic guidance–perimeter control coupled (TGPCC) method to improve the performance of macroscopic traffic networks. The method considers the optimal cumulative volume of a network as the goal and establishes a programming function according to the network equilibrium rule of traffic flow amongst multiple MFD sub-regions, which regards the minimum delay of network, as the objective. The Logit model for the compliance rate of driver route guidance is established by the stated preference survey. Moreover, the perimeter control (PC) method is proposed for adjusting the phase split of intersections. Finally, three schemes, namely, the TGPCC, PC and the method without PC and guidance are tested on a network with four well-defined MFD sub-regions. Results show that the TGPCC addresses the issue of congestion and decreases the total delay accordingly.     

Clustering of heterogeneous networks with directional flows based on “Snake” similarities

Aggregated network level modeling and control of traffic in urban networks have recently gained a lot of interest due to unpredictability of travel behaviors and high complexity of physical modeling in microscopic level. Recent research has shown the existence of well-defined Macroscopic Fundamental Diagrams (MFDs) relating average flow and density in homogeneous networks. The concept of MFD allows to design real-time traffic control schemes specifically hierarchical perimeter control approaches to alleviate or postpone congestion. Considering the fact that congestion is spatially correlated in adjacent roads and it propagates spatiotemporaly with finite speed, describing the main pockets of congestion in a heterogeneous city with small number of clusters is conceivable. In this paper, we propose a three-step clustering algorithm to partition heterogeneous networks into connected homogeneous regions, which makes the application of perimeter control feasible. The advantages of the proposed method compared to the existing ones are the ability of finding directional congestion within a cluster, robustness with respect to parameters calibration, and its good performance for networks with low connectivity and missing data. Firstly, we start to find a connected homogeneous area around each road of the network in an iterative way (i.e. it forms a sequence of roads). Each sequence of roads, defined as ‘snake’, is built by starting from a single road and iteratively adding one adjacent road based on its similarity to join previously added roads in that sequence. Secondly, based on the obtained sequences from the first step, a similarity measure is defined between each pair of the roads in the network. The similarities are computed in a way that put more weight on neighboring roads and facilitate connectivity of the clusters. Finally, Symmetric Non-negative Matrix Factorization (SNMF) framework is utilized to assign roads to proper clusters with high intra-similarity and low inter-similarity. SNMF partitions the data by providing a lower rank approximation of the similarity matrix. The proposed clustering framework is applied in medium and large-size networks based on micro-simulation and empirical data from probe vehicles. In addition, the extension of the algorithm is proposed to deal with the networks with sparse measurements where information of some links is missing. The results show the effectiveness and robustness of the extended algorithm applied to simulated network under different penetration rates (percentage of links with data).     

Recent developments in traffic flow modeling using macroscopic fundamental diagram

ABSTRACT

This paper presents an overview of the recent developments in traffic flow modelling and analysis using macroscopic fundamental diagram (MFD) as well as their applications. In recent literature, various aggregated traffic models have been proposed and studied to analyse traffic flow while enhancing network efficiency. Many of these studies have focused on models based on MFD that describes the relationship between aggregated flow and aggregated density of transport networks. The analysis of MFD has been carried out based on experimental data collected from sensors and GPS, as well as simulation models. Several factors are found to influence the existence and shape of MFD, including traffic demand, network and signal settings, and route choices. As MFD can well express the traffic dynamics of large urban transport networks, it has been extensively applied to traffic studies, including the development of network-wide control strategies, network partitioning, performance evaluation, and road pricing. This work also presents future extensions and research directions for MFD-based traffic modelling and applications.     

Deriving macroscopic fundamental diagrams from probe data: Issues and proposed solutions

Well-defined relationships between flow and density averaged spatially across urban traffic networks, more commonly known as Macroscopic Fundamental Diagrams (MFDs), have been recently verified to exist in reality. Researchers have proposed using MFDs to monitor the status of urban traffic networks and to inform the design of network-wide traffic control strategies. However, it is also well known that empirical MFDs are not easy to estimate in practice due to difficulties in obtaining the requisite data needed to construct them. Recent works have devised ways to estimate a network’s MFD using limited trajectory data that can be obtained from GPS-equipped mobile probe vehicles. These methods assume that the market penetration level of mobile probe vehicles is uniform across the entire set of OD pairs in the network; however, in reality the probe vehicle market penetration rate varies regionally within a network. When this variation is combined with the imbalance of probe trip lengths and travel times, the compound effects will further complicate the estimation of the MFD.To overcome this deficit, we propose a method to estimate a network’s MFD using mobile probe data when the market penetration rates are not necessarily the same across an entire network. This method relies on the determination of appropriate average probe penetration rates, which are weighted harmonic means using individual probe vehicle travel times and distances as the weights. The accuracy of this method is tested using synthetic data generated in the INTEGRATION micro-simulation environment by comparing the estimated MFDs to the ground truth MFD obtained using a 100% market penetration of probe vehicles. The results show that the weighted harmonic mean probe penetration rates outperform simple (arithmetic) average probe penetration rates, as expected. This especially holds true as the imbalance of demand and penetration level increases. Furthermore, as the probe penetration rates are generally not known, an algorithm to estimate the probe penetration rates of regional OD pairs is proposed. This algorithm links count data from sporadic fixed detectors in the network to information from probe vehicles that pass the detectors. The simulation results indicate that the proposed algorithm is very effective. Since the data needed to apply this algorithm are readily available and easy to collect, the proposed algorithm is practically feasible and offers a better approach for the estimation of the MFD using mobile probe data, which are becoming increasingly available in urban environments.     

Data fusion algorithm for macroscopic fundamental diagram estimation

A promising framework that describes traffic conditions in urban networks is the macroscopic fundamental diagram (MFD), relating average flow and average density in a relatively homogeneous urban network. It has been shown that the MFD can be used, for example, for traffic access control. However, an implementation requires an accurate estimation of the MFD with the available data sources.Most scientific literature has considered the estimation of MFDs based on either loop detector data (LDD) or floating car data (FCD). In this paper, however, we propose a methodology for estimating the MFD based on both data sources simultaneously. To that end, we have defined a fusion algorithm that separates the urban network into two sub-networks, one with loop detectors and one without. The LDD and the FCD are then fused taking into account the accuracy and network coverage of each data type. Simulations of an abstract grid network and the network of the city of Zurich show that the fusion algorithm always reduces the estimation error significantly with respect to an estimation where only one data source is used. This holds true, even when we account for the fact that the probe penetration rate of FCD needs to be estimated with loop detectors, hence it might also include some errors depending on the number of loop detectors, especially when probe vehicles are not homogeneously distributed within the network.     

Nonlinear gating control for urban road traffic network using the network fundamental diagram

This work proposes a nonlinear model predictive controller for the urban gating problem. The system model is formalized based on a research on existing models of the network fundamental diagram and the perimeter control systems. For the existing models, modifications are suggested: additional state variables are allocated to describe the queue dynamics at the network gates. Using the extended model, a nonlinear model predictive controller is designed offering a ‘non‐greedy’ policy compared with previous, ‘greedy’ gating control designs. The greedy and non‐greedy nonlinear model predictive control (NMPC) controllers are compared with a greedy linear feedback proportional‐integral‐derivative (PID) controller in different traffic situations. The proposed non‐greedy NMPC controller outperforms the other two approaches in terms of travel distance performance and queue lengths. The performance results justify the consideration of queue lengths in dynamic modeling, and the use of NMPC approach for controller design. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust constrained control of uncertain macroscopic fundamental diagram networks

This paper considers modeling and control of uncertain Macroscopic Fundamental Diagram (MFD) systems for multiple-region networks. First, the nonlinear vehicle conservation equations based on MFD dynamics, presented in earlier publications, are transformed to linear equations with parameter uncertainties. The parameter uncertainties include the destination decomposition fractions, that are difficult to estimate in reality. Then, the uncertain linear model is utilized to design a robust feedback controller by an interpolation-based approach. This approach (i) guarantees robustness against all parameter uncertainties, (ii) handle control and state constraints, and (iii) present a computationally cheap solution. The main idea is to interpolate between (i) a stabilizing outer controller that respects the control and state constraints and (ii) an inner robustly stable controller designed by any method. The robust control is further challenged to deal with different relative locations of reference accumulation points on the MFD diagrams. Numerical results for a two-region system show that the uncertain linear model can replace the nonlinear model for modeling and control. Moreover, the robust control law is presented as implicit and explicit solutions, where in the implicit case one linear programming (LP) problem is solved at each time instant, while in the explicit case, the control law is shown as a piecewise affine function of state. Finally, a comparison between the interpolating controller and other controllers in the literature is carried out. The results demonstrate the performance advantages from applying the robust interpolating controller.     

Macroscopic relations of urban traffic variables: Bifurcations, multivaluedness and instability

Recent experimental work has shown that the average flow and average density within certain urban networks are related by a unique, reproducible curve known as the Macroscopic Fundamental Diagram (MFD). For networks consisting of a single route this MFD can be predicted analytically; but when the networks consist of multiple overlapping routes experience shows that the flows observed in congestion for a given density are less than those one would predict if the routes were homogeneously congested and did not overlap. These types of networks also tend to jam at densities that are only a fraction of their routes’ average jam density.This paper provides an explanation for these phenomena. It shows that, even for perfectly homogeneous networks with spatially uniform travel patterns, symmetric equilibrium patterns with equal flows and densities across all links are unstable if the average network density is sufficiently high. Instead, the stable equilibrium patterns are asymmetric. For this reason the networks jam at lower densities and exhibit lower flows than one would predict if traffic was evenly distributed.Analysis of small idealized networks that can be treated as simple dynamical systems shows that these networks undergo a bifurcation at a network-specific critical density such that for lower densities the MFDs have predictably high flows and are univalued, and for higher densities the order breaks down. Microsimulations show that this bifurcation also manifests itself in large symmetric networks. In this case though, the bifurcation is more pernicious: once the network density exceeds the critical value, the stable state is one of complete gridlock with zero flow. It is therefore important to ensure in real-world applications that a network’s density never be allowed to approach this critical value.Fortunately, analysis shows that the bifurcation’s critical density increases considerably if some of the drivers choose their routes adaptively in response to traffic conditions. So far, for networks with adaptive drivers, bifurcations have only been observed in simulations, but not (yet) in real life. This could be because real drivers are more adaptive than simulated drivers and/or because the observed real networks were not sufficiently congested.     

Hysteresis phenomena of a Macroscopic Fundamental Diagram in freeway networks

Observations of traffic pairs of flow vs. density or occupancy for individual locations in freeways or arterials are usually scattered about an underlying curve. Recent observations from empirical data in arterial networks showed that in some cases by aggregating the highly scattered plots of flow vs. density from individual loop detectors, the scatter almost disappears and well-defined macroscopic relations exist between space-mean network flow and network density. Despite these findings for the existence of well-defined relations with low scatter, these curves should not be universal. In this paper we investigate if well-defined macroscopic relations exist for freeway network systems, by analyzing real data from Minnesota’s freeways. We show that freeway network systems not only have curves with high scatter, but they also exhibit hysteresis phenomena, where higher network flows are observed for the same average network density in the onset and lower in the offset of congestion. The mechanisms of traffic hysteresis phenomena at the network level are analyzed in this paper and they have dissimilarities to the causes of the hysteresis phenomena at the micro/meso level. The explanation of the phenomenon is dual. The first reason is that there are different spatial and temporal distributions of congestion for the same level of average density. Another reason is the synchronized occurrence of transitions from individual detectors during the offset of the peak period, with points remain beneath the equilibrium curve. Both the hysteresis phenomenon and its causes are consistently observed for different spatial aggregations of the network.     

Model based urban traffic control,part I: Local model and local model predictive controllers

This paper is the first in a series of reports presenting a framework for the hierarchical design of feedback controllers for traffic lights in urban networks. The goal of the research is to develop an easy to understand methodology for designing model based feedback controllers that use the current state estimate in order to select the next switching times of traffic lights. In this paper we introduce an extension of the cell transmission model that describes with sufficient accuracy the major causes of delay for urban traffic. We show that this model is computationally fast enough such that it can be used in a model predictive controller that decides for each intersection, taking into account the vehicle density as estimated along all links connected to the intersection, what switching time minimizes the local delay for all vehicles over a prediction horizon of a few minutes. The implementation of this local MPC only requires local online measurements and local model information (unlike the coordinated MPC, to be introduced in the next paper in this series, that takes into account interactions between neighbouring intersections). We study the performance of the proposed local MPC via simulation on a simple 4 by 4 Manhattan grid, comparing its delay with an efficiently tuned pretimed control for the traffic lights, and with traffic lights controlled according to the max pressure rule. These simulations show that the proposed local MPC controller achieves a significant reduction in delay for various traffic conditions.