Dynamics of heterogeneity in urban networks: aggregated traffic modeling and hierarchical control

Real traffic data and simulation analysis reveal that for some urban networks a well-defined Macroscopic Fundamental Diagram (MFD) exists, which provides a unimodal and low-scatter relationship between the network vehicle density and outflow. Recent studies demonstrate that link density heterogeneity plays a significant role in the shape and scatter level of MFD and can cause hysteresis loops that influence the network performance. Evidently, a more homogeneous network in terms of link density can result in higher network outflow, which implies a network performance improvement. In this article, we introduce two aggregated models, region- and subregion-based MFDs, to study the dynamics of heterogeneity and how they can affect the accuracy scatter and hysteresis of a multi-subregion MFD model. We also introduce a hierarchical perimeter flow control problem by integrating the MFD heterogeneous modeling. The perimeter flow controllers operate on the border between urban regions, and manipulate the percentages of flows that transfer between the regions such that the network delay is minimized and the distribution of congestion is more homogeneous. The first level of the hierarchical control problem can be solved by a model predictive control approach, where the prediction model is the aggregated parsimonious region-based MFD and the plant (reality) is formulated by the subregion-based MFDs, which is a more detailed model. At the lower level, a feedback controller of the hierarchical structure, tries to maximize the outflow of critical regions, by increasing their homogeneity. With inputs that can be observed with existing monitoring techniques and without the need for detailed traffic state information, the proposed framework succeeds to increase network flows and decrease the hysteresis loop of the MFD. Comparison with existing perimeter controllers without considering the more advanced heterogeneity modeling of MFD highlights the importance of such approach for traffic modeling and control.     

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.     

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.     

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.     

On the use of Lagrangian observations from public transport and probe vehicles to estimate car space-mean speeds in bi-modal urban networks

The Macroscopic Fundamental Diagram (MFD) has been recognized as a powerful framework to develop network-wide control strategies. Recently, the concept has been extended to the three-dimensional MFD, used to investigate traffic dynamics of multi-modal urban cities, where different transport modes compete for, and share the limited road infrastructure. In most cases, the macroscopic traffic variables are estimated using either loop detector data (LDD) or floating car data (FCD). Taking into account that none of these data sources might be available, in this study we propose novel estimation methods for the space-mean speed of cars based on: (i) the automatic vehicle location (AVL) data of public transport where no FCD is available; and (ii) the fused FCD and AVL data sources where both are available, but FCD is not complete. Both methods account for the network configuration layout and the configuration of the public transport system. The first method allows one to derive either uni-modal or bi-modal macroscopic fundamental relationships, even in the extreme cases where no LDD nor FCD exist. The second method does not require a priori knowledge about FCD penetration rates and can significantly improve the estimation accuracy of the macroscopic fundamental relationships. Using empirical data from the city of Zurich, we demonstrate the applicability and validate the accuracy of the proposed methods in real-life traffic scenarios, providing a cross-comparison with the existing estimation methods. Such empirical comparison is, to the best of our knowledge, the first of its kind. The findings show that the proposed AVL-based estimation method can provide a good approximation of the average speed of cars at the network level. On the other hand, by fusing the FCD and AVL data, especially in case of sparse FCD, it is possible to obtain a more representative outcome regarding the performance of multi-modal traffic.     

Modeling and optimization of multimodal urban networks with limited parking and dynamic pricing

Cruising-for-parking constraints mobility in urban networks. Car-users may have to cruise for on-street parking before reaching their destinations. The accessibility and the cost of parking significantly influence people's travel behavior (such as mode choice, or parking facility choice between on-street and garage). The cruising flow causes delays eventually to everyone, even users with destinations outside limited parking areas. It is therefore important to understand the impact of parking limitation on mobility, and to identify efficient parking policies for travel cost reduction. Most existing studies on parking fall short in reproducing the dynamic spatiotemporal features of traffic congestion in general, lack the treatment of dynamics of the cruising-for-parking phenomenon, or require detailed input data that are typically costly and difficult to collect. In this paper, we propose an aggregated and dynamic approach for modeling multimodal traffic with the treatment on parking, and utilize the approach to design dynamic parking pricing strategies. The proposed approach is based on the Macroscopic Fundamental Diagram (MFD), which can capture congestion dynamics at network-level for single-mode and bi-modal (car and bus) systems. A parsimonious parking model is integrated into the MFD-based multimodal modeling framework, where the dynamics of vehicular and passenger flows are considered with a change in the aggregated behavior (e.g. mode choice and parking facility choice) caused by cruising and congestion. Pricing strategies are developed with the objective of reducing congestion, as well as lowering the total travel cost of all users. A case study is carried out for a bi-modal city network with a congested downtown region. An elegant feedback dynamic parking pricing strategy can effectively reduce travel delay of cruising and the generic congestion. Remarkably, such strategy, which is applicable in real-time management with limited available data, is fairly as efficient as a dynamic pricing scheme obtained from system optimum conditions and a global optimization with full information about the future states of the system. Stackelberg equilibrium is also investigated in a competitive behavior between different parking facility operators. Policy indications on on-street storage capacity management and pricing are provided.     

A dynamic evacuation model for pedestrian–vehicle mixed-flow networks

In urban emergency evacuation, a potentially large number of evacuees may depend either on transit or other modes, or need to walk a long distance, to access their passenger cars. In the process of approaching the designated pick-up points or parking areas for evacuation, the massive number of pedestrians may cause tremendous burden to vehicles in the roadway network. Responsible agencies often need to contend with congestion incurred by massive vehicles emanating from parking garages, evacuation buses generated from bus stops, and the conflicts between evacuees and vehicles at intersections. Hence, an effective plan for such evacuation needs to concurrently address both the multi-modal traffic route assignment and the optimization of network signal controls for mixed traffic flows. This paper presents an integrated model to produce the optimal distribution of vehicle and pedestrian flows, and the responsive network signal plan for massive mixed pedestrian–vehicle flows within the evacuation zone. The proposed model features its effectiveness in accounting for multiple types of evacuation vehicles, the interdependent relations between pedestrian and vehicle flows via some conversion locations, and the inevitable conflicts between intersection turning vehicle and pedestrian flows. An illustrating example concerning an evacuation around the M&T stadium area has been presented, and the results indicate the promising properties of our proposed model, especially on reflecting the complex interactions between vehicle and pedestrian flows and the favorable use of high-occupancy vehicles for evacuation operations.     

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.     

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.     

A dynamic cordon pricing scheme combining the Macroscopic Fundamental Diagram and an agent-based traffic model

Pricing is considered an effective management policy to reduce traffic congestion in transportation networks. In this paper we combine a macroscopic model of traffic congestion in urban networks with an agent-based simulator to study congestion pricing schemes. The macroscopic model, which has been tested with real data in previous studies, represents an accurate and robust approach to model the dynamics of congestion. The agent-based simulator can reproduce the complexity of travel behavior in terms of travelers’ choices and heterogeneity. This integrated approach is superior to traditional pricing schemes. On one hand, traffic simulators (including car-following, lane-changing and route choice models) consider travel behavior, i.e. departure time choice, inelastic to the level of congestion. On the other hand, most congestion pricing models utilize supply models insensitive to demand fluctuations and non-stationary conditions. This is not consistent with the physics of traffic and the dynamics of congestion. Furthermore, works that integrate the above features in pricing models are assuming deterministic and homogeneous population characteristics. In this paper, we first demonstrate by case studies in Zurich urban road network, that the output of a agent-based simulator is consistent with the physics of traffic flow dynamics, as defined by a Macroscopic Fundamental Diagram (MFD). We then develop and apply a dynamic cordon-based congestion pricing scheme, in which tolls are controlled by an MFD. And we investigate the effectiveness of the proposed pricing scheme. Results show that by applying such a congestion pricing, (i) the savings of travel time at both aggregated and disaggregated level outweigh the costs of tolling, (ii) the congestion inside the cordon area is eased while no extra congestion is generated in the neighbor area outside the cordon, (iii) tolling has stronger impact on leisure-related activities than on work-related activities, as fewer agents who perform work-related activities changed their time plans. Future work can apply the same methodology to other network-based pricing schemes, such as area-based or distance-traveled-based pricing. Equity issues can be investigated more carefully, if provided with data such as income of agents. Value-of-time-dependent pricing schemes then can also be determined.     

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.     

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.     

Mitigation of disruptions in public transit by Bee Colony Optimization

Dispatchers in many public transit companies face the daily problem of assigning available buses to bus routes under conditions of bus shortages. In addition to this, weather conditions, crew absenteeism, traffic accidents, traffic congestion and other factors lead to disturbances of the planned schedule. We propose the Bee Colony Optimization (BCO) algorithm for mitigation of bus schedule disturbances. The developed model takes care of interests of the transit operator and passengers. The model reassigns available buses to bus routes and, if it is allowed, the model simultaneously changes the transportation network topology (it shortens some of the planned bus routes) and reassigns available buses to a new set of bus routes. The model is tested on the network of Rivera (Uruguay). Results obtained show that the proposed algorithm can significantly mitigate disruptions.     

Improving fuel consumption and CO2 emissions calculations in urban areas by coupling a dynamic micro traffic model with an instantaneous emissions model

Τhis study demonstrates the combination of a microscopic traffic simulator (AIMSUN) with an instantaneous emissions model (AVL CRUISE) to investigate the impact of traffic congestion on fuel consumption on an urban arterial road. The micro traffic model was enhanced by an improved car-following law according to Morello et al. (2014) and was calibrated to replicate measured driving patterns over an urban corridor in Turin, Italy, operating under adaptive urban traffic control (UTC). The method was implemented to study the impact of congestion on fuel consumption for the category of Euro 5 diesel <1.4 l passenger cars. Free flow and congested conditions led to respective consumption differences of −25.8% and 20.9% over normal traffic. COPERT 5 rather well predicted the impact of congestion but resulted to a much lower relative reduction in free flow conditions. Start and stop system was estimated to reduce consumption by 6% and 11.9% under normal and congested conditions, respectively. Using the same modelling approach, UTC was found to have a positive impact on CO₂ emissions of 8.1% and 4.5% for normal and congested conditions, respectively, considering the Turin vehicle fleet mix for the year 2013. Overall, the study demonstrates that the combination of detailed and validated micro traffic and emissions models offers a powerful combination to study traffic and powertrain impacts on greenhouse gas and fuel consumption of on road vehicles over a city network.     

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.     

Influence of vehicle type and road category on natural resource consumption in road transport

This study calculates the natural resource use of road transport for different road categories and for different vehicle types. Material inputs per service are determined as the life cycle wide consumption of materials by the road and vehicles, and set against person-kilometres and ton-kilometres transported. If the material input of the infrastructure is allocated to the users according to traffic volume, the material input per service values for abiotic resources and for water are much higher for cars than for bus traffic. The material inputs per service unit for air is significantly lower for buses than for cars. For bicycles, abiotic natural resource consumption is between that for cars and buses, while water consumption is in most instances the highest and air consumption the lowest for the modes studied. The material input per service values for the full trailer are significantly lower than for other goods vehicles. The material inputs per service value for air is significantly higher in the case of vans. If the allocation of road infrastructure use is done by gross vehicle weight, the material input per service values for abiotic resources and water of buses and heavy lorries rise.     

Scheduling lane conversions for bus use on city-wide scales and in time-varying congested traffic

The paper explores what can occur when select street lanes throughout a city are periodically reserved for buses. Simulations of an idealized city were performed to that end. The city’s time-varying travel demand was studied parametrically. In all cases, queues formed throughout the city during a rush, and dissipated during the off-peak period that followed. Bus lanes were activated all at once across the city, and were eventually deactivated in like fashion. Activation and deactivation schedules varied parametrically as well. Schedules that roughly balanced the trip-time savings to bus riders against the added delays to car travelers were thus identified.Findings reveal why activating conversions near the start of a rush can degrade travel, both by car and by bus. Balance was struck by instead activating lane conversions nearer the end of the rush, when vehicle accumulation in the city was at or near its maximum. Most of the time savings to bus riders accrued after the conversions had been left in place for only 30 min. Leaving them for longer durations often brought modest additional savings to bus travelers. Yet, the added delays to cars often grew large as a result.These findings held even when buses garnered high ridership shares. This was the case when lane conversions gradually induced new bus trips among residents who formerly did not travel. It was also true when high ridership was a pre-existing feature of the city. Activating conversions a bit earlier in a rush was found to make sense only if commuters shifted from cars to buses in very large numbers. Findings also unveiled how to fine-tune activation and deactivation schedules to suit a city’s congestion level. Guidelines for scheduling conversions in real settings are furnished. So is discussion on how these schedules might be adapted to daily variations in city-wide traffic states. Roles for technology are discussed as well.     

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.     

On the fundamental diagram and supply curves for congested urban networks

Macroscopic fundamental diagrams (MFD) of traffic for some networks have been shown to have similar shape to those for single links. They have erroneously been used to help estimate the level of travel in congested networks. We argue that supply curves, which track vehicles in their passage through congested networks, are needed for this purpose, and that they differ from the performance curves generated from MFD. We use a microsimulation model, DRACULA and two networks, one synthesizing the network for Cambridge, England, and one of the city of York, England, to explore the nature of performance curves and supply curves under differing patterns of demand.We show that supply curves differ from performance curves once the onset of congestion is reached, and that the incorrect use of performance curves to estimate demand can thus seriously underestimate traffic levels, the costs of congestion, and the value of congestion relief measures. We also show that network aggregated supply curves are sensitive to the temporal distribution of demand and, potentially, to the spatial distribution of demand. The shape of the supply curve also differs between origin–destination movements within a given network.We argue that supply curves for higher levels of demand cannot be observed in normal traffic conditions, and specify ways in which they can be determined from microsimulation and, potentially, by extrapolating observed data. We discuss the implications of these findings for conventional modelling of network management policies, and for these policies themselves.     

Merging bus routes in Hong Kong’s central business district: Analysis and models

A significant portion of the 200,000 people working in Hong Kong’s central business district (CBD) relies on buses as their primary means of transport. During peak hours, nearly a thousand double-decker buses pour into a tiny area of 150 ha. This causes traffic congestion and air pollution. Moreover, given that the flow is uni-directional (into the CBD in the morning and out of the CBD in the afternoon), the occupancy of buses in the CBD is actually low.In this paper, we propose to reduce traffic congestion and to increase bus occupancy by merging bus routes. We describe the peculiar situation of the CBD in Hong Kong and explain the necessary conditions for the possible success of merging routes. Our analysis shows that merging will lead to an overall benefit for all parties, including government, bus operators, and passengers. The actual merging decisions, which routes to merge and at what frequencies buses should run, are determined by a mathematical model. The model also shows quantitatively the benefits of merging routes and the impacts of other factors. The procedure that we follow and the model that we adopt can be applied to other CBD.