Macroscopic modelling and robust control of bi-modal multi-region urban road networks

The paper concerns the integration of a bi-modal Macroscopic Fundamental Diagram (MFD) modelling for mixed traffic in a robust control framework for congested single- and multi-region urban networks. The bi-modal MFD relates the accumulation of cars and buses and the outflow (or circulating flow) in homogeneous (both in the spatial distribution of congestion and the spatial mode mixture) bi-modal traffic networks. We introduce the composition of traffic in the network as a parameter that affects the shape of the bi-modal MFD. A linear parameter varying model with uncertain parameter the vehicle composition approximates the original nonlinear system of aggregated dynamics when it is near the equilibrium point for single- and multi-region cities governed by bi-modal MFDs. This model aims at designing a robust perimeter and boundary flow controller for single- and multi-region networks that guarantees robust regulation and stability, and thus smooth and efficient operations, given that vehicle composition is a slow time-varying parameter. The control gain of the robust controller is calculated off-line using convex optimisation. To evaluate the proposed scheme, an extensive simulation-based study for single- and multi-region networks is carried out. To this end, the heterogeneous network of San Francisco where buses and cars share the same infrastructure is partitioned into two homogeneous regions with different modes of composition. The proposed robust control is compared with an optimised pre-timed signal plan and a single-region perimeter control strategy. Results show that the proposed robust control can significantly: (i) reduce the overall congestion in the network; (ii) improve the traffic performance of buses in terms of travel delays and schedule reliability, and; (iii) avoid queues and gridlocks on critical paths of the network

Cordon pricing consistent with the physics of overcrowding

This paper describes the modeling of recurring congestion in a network. It is shown that the standard economic models of marginal cost cannot describe precisely traffic congestion in networks during time-dependent conditions. Following a macroscopic traffic approach, we describe the equilibrium solution for a congested network in the no-toll case. A dynamic model of cordon-based congestion pricing (such as for the morning commute) for networks is developed consistent with the physics of traffic.Ê The paper combines VickreyÕs theory with a macroscopic traffic model, which is readily observable with existing monitoring technologies. The paper also examines some policy implications of the cordon-based pricing to treat equity and reliability issues, i.e. in what mobility level a city should choose to operate. An application of the model in a downtown area shows that these schemes can improve mobility and relieve congestion in cities.Cordon Pricing, Congestion Pricing, Road Pricing, Value Pricing, Social Equity

Investigation of the existence of city-scale three-dimensional macroscopic fundamental diagrams for bi-modal traffic

Recent research has demonstrated that the Macroscopic Fundamental Diagram (MFD) is reliable and practical tool for modeling traffic dynamics and network performance in single-mode (cars only) urban road networks. In this paper, we first extend the modeling of the single-mode MFD to a bi-modal (bus and cars) one. Based on simulated data, we develop a three-dimensional MFD (3D-MFD) relating the accumulation of cars and buses, and the total circulating flow in the network. We propose an exponential function to capture the shape of the 3D-MFD, which shows a good fit to the data. We also propose an elegant estimation for passenger car equivalent of buses (PCU), which has a physical meaning and depends on the bi-modal traffic in the network. Moreover, we analyze a 3D-MFD for passenger network flows and derive its analytical function. Finally, we investigate an MFD for networks with dedicated bus lanes and the relationship between the shape of the MFD and the operational characteristics of buses. The output of this paper is an extended 3D-MFD model that can be used to (i) monitor traffic performance and, (ii) develop various traffic management strategies in bi-modal urban road networks, such as redistribution of urban space among different modes, perimeter control, and bus priority strategies

The Spatial Variability of Vehicle Densities as Determinant of Urban Network Capacity

Due to the complexity of the traffic flow dynamics in urban road networks, most quantitative descriptions of city traffic so far are based on computer simulations. This contribution pursues a macroscopic (fluid-dynamic) simulation approach, which facilitates a simple simulation of congestion spreading in cities. First, we show that a quantization of the macroscopic turning flows into units of single vehicles is necessary to obtain realistic fluctuations in the traffic variables, and how this can be implemented in a fluid-dynamic model. Then, we propose a new method to simulate destination flows without the requirement of individual route assignments. Combining both methods allows us to study a variety of different simulation scenarios. These reveal fundamental relationships between the average flow, the average density, and the variability of the vehicle densities. Considering the inhomogeneity of traffic as an independent variable can eliminate the scattering of congested flow measurements. The variability also turns out to be a key variable of urban traffic performance. Our results can be explained through the number of full links of the road network, and approximated by a simple analytical formula

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

The Importance of Being Early

The assumption that the penalty for being early is less than that for being late was put forward by Vickrey (1963) who analyzed how commuters compare penalties in the form of schedule delay (due to peak hour congestion), against penalties in the form of reaching their destination (ahead or behind their desired time of arrival). This assumption has been tested by many researchers since then for various applications, especially in modeling congestion pricing (Arnott et al., 1990) where it is critical to understand the tradeoff between schedule delay and travel delay. Key findings are summarized in the second section of this paper. This research aims to test this hypothesis of earliness being less expensive than lateness using empirical data at different levels and across different regions. New methods to estimate the ratio of earliness to lateness for different types of datasets are developed, which could be used by agencies to implement control policies like congestion pricing or other schemes more accurately. Travel survey data from metropolitan areas provide individual travel patterns while loop detector data provide link level traffic flow data.Schedule Delay, Travel Time, Traffic, Travel Behavior.

Approximation methods for large-scale spatial queueing systems

Different than the conventional queueing systems, in spatial queueing systems (SQS) the service rate for each customer-server pairs differs and the server that intervenes for a specific customer is not known a priori, depending on the availability of servers at the moment a request was made. These features make the SQS computationally expensive (almost intractable for large scale) but at the same time more suitable for real-life problems with high reliability expectations. Emergency response and on-demand transportation systems are two similar systems that can be modeled with the SQS. In this research, we aim to solve facility location problems as SQS with stochastic demand and service time. The stochasticity concerned here is temporal and spatial, that emerges from the uncertainty in the demand and service time. In order to tackle this problem Larson (1974)'s 2n hypercube queueing model (HQM) is extended to 3n HQM. In this model, there are two different possible service types for each server: (i) service for locations in the proximity of a server (area of responsibility) and (ii) service for other locations where the first responsible server is busy during this event. In addition, to decrease the dimension of the problem, which is intractable due to their size, a new 3n aggregate hypercube queueing model (AHQM) is developed that treats group of servers (bins) in a similar manner by considering interactions among bins. An efficient graph partitioning algorithm is proposed to cluster servers in groups with an objective to minimize the interactions among groups. Both exact and approximate approaches are integrated inside two optimization methods (i.e. variable neighborhood search and simulated annealing) to find server locations that improve system performance. Computational experiments showed that both models are applicable to use inside optimization algorithms to find good server locations and to improve system performance measures of SQS

Modeling the morning commute for urban networks with cruising-for-parking: An MFD approach

This study focuses on the morning commute problem with explicit consideration of cruising-for-parking, and its adverse impacts on traffic congestion. The cruising-for-parking is modeled through a dynamic aggregated traffic model for networks: the Macroscopic Fundamental Diagram (MFD). Firstly, we formulate the commuting equilibrium in a congested downtown network where travelers have to cruise for curbside parking spaces. The cruising-for-parking would yield longer trip distance and smaller network outflow, and thus can induce severe congestion and lengthen the morning peak. We then develop a dynamic model of pricing for the network to reduce total social cost, which includes cruising time cost, moving time cost (moving or in-transit time, which is the duration during which vehicles move close to the destination but do not cruise for parking yet), and schedule delay cost. We show that under specific assumptions, at the system optimum, the downtown network should be operating at the maximum production of its MFD. However, the cruising effect is not fully eliminated. We also show that the time-dependent toll to support the system optimum has a different shape than the classical fine toll in Vickrey's bottleneck model. In the end, analytical results are illustrated and verified with numerical experiments

Network Fundamental Diagram (NFD) and traffic signal control: First empirical evidences from the city of Santander

According to recent literature, the aggregate traffic conditions of an urban road network may be measured by an asymmetric inverse-U shaped diagram, called Network or Macroscopic Fundamental Diagram (NFD or MFD). The research on NFD was finalizes for applications connected to congestion control by means of gating, pricing schemes, multi-modal network analysis, freight vehicle routing. The control of urban road networks by means of NFD is a promising research area, where new methods and models are proposed to reduce traffic congestion and delay. The general objective of the research is to investigate if and in which measure the NFD profile (estimated by means of observed traffic data) changes according to the control strategy adopted for junction signals in an urban area. The first empirical evidences presented in this paper are related to a portion of Santander urban area, where a specific zone has been identified according to traffic characteristics and land uses. Data from traffic loops are collected and correlated with the signal control plans during a working day at link (flow-density diagrams) and network levels (NFD). Some preliminary considerations are derived from the empirical results. The cycle length with a fixed regulation plan does not influence the main traffic variables (flow, density) at link and network level, but these results cannot be generalized