Continuous formulations and analytical properties of the link transmission model

The link transmission model (LTM) has great potential for simulating traffic flow in large-scale networks since it is much more efficient and accurate than the Cell Transmission Model (CTM). However, there lack general continuous formulations of LTM, and there has been no systematic study on its analytical properties such as stationary states and stability of network traffic flow. In this study we attempt to fill the gaps. First we apply the Hopf–Lax formula to derive Newell’s simplified kinematic wave model with given boundary cumulative flows and the triangular fundamental diagram. We then apply the Hopf–Lax formula to define link demand and supply functions, as well as link queue and vacancy functions, and present two continuous formulations of LTM, by incorporating boundary demands and supplies as well as invariant macroscopic junction models. With continuous LTM, we define and solve the stationary states in a road network. We also apply LTM to directly derive a Poincaré map to analyze the stability of stationary states in a diverge-merge network. Finally we present an example to show that LTM is not well-defined with non-invariant junction models. We can see that Newell’s model and continuous LTM complement each other and provide an alternative formulation of the network kinematic wave theory. This study paves the way for further extensions, analyses, and applications of LTM in the future.     

A kinematic wave approach to traffic statics and dynamics in a double-ring network

Recently there has been much interest in understanding macroscopic fundamental diagrams of stationary road networks. However, there lacks a systematic method to define and solve stationary states in a road network with complex junctions. In this study we propose a kinematic wave approach to defining, analyzing, and simulating static and dynamic traffic characteristics in a network of two ring roads connected by a 2 × 2 junction, which can be either an uninterrupted interchange or a signalized intersection. This study is enabled by recently developed macroscopic junction models of general junctions. With a junction model based on fair merging and first-in-first-out diverging rules, we first define and solve stationary states and then derive the macroscopic fundamental diagram (MFD) of a stationary uninterrupted network. We conclude that the flow-density relationship of the uninterrupted double-ring network is not unique for high average network densities (i.e., when one ring becomes congested) and unveil the existence of infinitely many stationary states that can arise with a zero-speed shockwave. From simulation results with a corresponding Cell Transmission Model, we verify that all stationary states in the MFD are stable and can be reached, but show that randomness in the retaining ratio of each ring drives the network to more symmetric traffic patterns and higher flow-rates. Furthermore we model a signalized intersection as two alternate diverge junctions and demonstrate that the signalized double-ring network can reach asymptotically periodic traffic patterns, which are therefore defined as “stationary” states in signalized networks. With simulations we show that the flow-density relation is well defined in such “stationary” states, and asymptotic traffic patterns can be impacted by signal cycle lengths and retaining ratios. But compared with uninterrupted interchanges, signalized intersections lead to more asymmetric traffic patterns, lower flow-rates, and even gridlocks when the average density is higher than half of the jam density. The results are consistent between this study and existing studies, but the network kinematic wave model, with appropriate junction models, is mathematically tractable and physically meaningful. It has offered a more complete picture regarding the number and type of stationary states, their stability, and MFD in freeway and signalized networks.     

Stability and bifurcation in network traffic flow: A Poincaré map approach

Previous studies have shown that, in a diverge-merge network with two intermediate links (the DM network), the kinematic wave model always admits stationary solutions under constant boundary conditions, but periodic oscillations can develop from empty initial conditions. Such contradictory observations suggest that the stationary states be unstable. In this study we develop a systematic approach to investigate the stability property of stationary states in this and other networks within the framework of network kinematic wave theories. Based on the observation that kinematic waves propagate in a circular path when only one of the two intermediate links is congested, we derive a one-dimensional, discrete Poincaré map in the out-flux at a Poincaré section. We then prove that the fixed points of the Poincaré map correspond to stationary flow-rates on the two links. With Lyapunov’s first method, we demonstrate that the Poincaré map can be finite-time stable, asymptotically stable, or unstable. When unstable, the map is found to have periodical points of period two, but no chaotic solutions. We further analyze the bifurcation in the stability of the Poincaré map caused by varying route choice proportions. We apply the Poincaré map approach to analyzing traffic patterns in more general (DM)ⁿ and beltway networks, which are sufficient and necessary structures for network-induced unstable traffic and gridlock, respectively. This study demonstrates that the Poincaré map approach can be efficiently applied to analyze traffic dynamics in any road networks with circular information propagation and provides new insights into unstable traffic dynamics caused by interactions among network bottlenecks.     

Robust transit network design with stochastic demand considering development density

This paper analyzes the influence of urban development density on transit network design with stochastic demand by considering two types of services, rapid transit services, such as rail, and flexible services, such as dial-a-ride shuttles. Rapid transit services operate on fixed routes and dedicated lanes, and with fixed schedules, whereas dial-a-ride services can make use of the existing road network, hence are much more economical to implement. It is obvious that the urban development densities to financially sustain these two service types are different. This study integrates these two service networks into one multi-modal network and then determines the optimal combination of these two service types under user equilibrium (UE) flows for a given urban density. Then we investigate the minimum or critical urban density required to financially sustain the rapid transit line(s). The approach of robust optimization is used to address the stochastic demands as captured in a polyhedral uncertainty set, which is then reformulated by its dual problem and incorporated accordingly. The UE principle is represented by a set of variational inequality (VI) constraints. Eventually, the whole problem is linearized and formulated as a mixed-integer linear program. A cutting constraint algorithm is adopted to address the computational difficulty arising from the VI constraints. The paper studies the implications of three different population distribution patterns, two CBD locations, and produces the resultant sequences of adding more rapid transit services as the population density increases.     

Point queue models: A unified approach

In transportation and other types of facilities, various queues arise when the demands of service are higher than the supplies, and many point and fluid queue models have been proposed to study such queueing systems. However, there has been no unified approach to deriving such models, analyzing their relationships and properties, and extending them for networks. In this paper, we derive point queue models as limits of two link-based queueing model: the link transmission model and a link queue model. With two definitions for demand and supply of a point queue, we present four point queue models, four approximate models, and their discrete versions. We discuss the properties of these models, including equivalence, well-definedness, smoothness, and queue spillback, both analytically and with numerical examples. We then analytically solve Vickrey’s point queue model and stationary states in various models. We demonstrate that all existing point and fluid queue models in the literature are special cases of those derived from the link-based queueing models. Such a unified approach leads to systematic methods for studying the queueing process at a point facility and will also be helpful for studies on stochastic queues as well as networks of queues.     

Junction interactions and monotonicity in traffic assignment

We consider the traffic equilibrium problem when the travel demand is inelastic and stationary in time. Junction interactions, which abound in urban road networks, are permitted. We prove that the set of equilibria (solutions to the assignment problem) is convex when certain monotonicity and continuity conditions are statisfied at each junction.     

Effect of providing traffic information estimated by a stochastic network equilibrium model with stochastic demand

To estimate travel times through road networks, in this study, we assume a stochastic demand and formulate a stochastic network equilibrium model whose travel times, flows, and demands are stochastic. This model enables us to examine network reliability under stochastic circumstances and to evaluate the effect of providing traffic information on travel times. For traffic information, we focus on travel time information and propose methods to evaluate the effect of providing that information. To examine the feasibility and validity of the proposed model and methods, we apply them to a simple network and the real road network of Kanazawa, Japan. The results indicate that providing ambulance drivers in Kanazawa with travel time information leads to an average reduction in travel time of approximately three minutes.     

Induced road traffic in Spanish regions: A dynamic panel data model

Distinguishing between traffic generated exclusively from the expansion of the road network (induced demand) and that resulting from other demand factors is of crucial importance to properly designed transport policies. This paper analyzes and quantifies the induced demand for road transport for Spain’s main regions from 1998 to 2006, years that saw mobility in Spain attain its highest growth rate. The lack of research in this area involving Spain and the key role played by the sector, given its high level of energy consumption and the negative externalities associated with it (accidents, noise, traffic congestion, emissions, etc.), endow greater relevance to this type of research. Based on a Dynamic Panel Data (DPD) reduced-form model, we apply alternative approaches (fixed and random effects and GMM-based methods) for measuring the induced demand. The results obtained provide evidence for the existence of an induced demand for transport in Spain, though said results vary depending on the estimating method employed.     

Congestion mechanism and demand adjustment strategies for double-cell system with bottlenecks

In this paper, ramp systems on the Beijing 3rd ring road are described as double-cell ramp systems with a bottleneck. By analyzing empirical data for the Beijing 3rd ring road, we found that the initial states have an important impact on the final convergence states of the ramp systems. Then, we studied the dynamic process of the ramp systems, determined the congestion mechanism, and then designed a ramp control method based on the obtained mechanism. Under a feasible demand, double-cell ramp systems exhibit two typical cases, including an upstream-bottleneck system (in which the bottleneck cell is upstream) and a downstream-bottleneck system (in which the bottleneck cell is downstream). Then, a cell transmission model is used to analyze the dynamic evolution processes, starting from different initial states, and determine the congestion mechanism for each case. It is proven that the two systems have different possible equilibrium sets and congestion mechanisms. In an upstream-bottleneck system, the downstream always converges to the uncongested equilibrium, while the upstream bottleneck cell may experience congestion under certain initial states. In a downstream-bottleneck system, the congestion starts downstream, and then gradually propagates upstream. Furthermore, based on the different congestion mechanisms, two demand adjustment strategies are proposed, which redistribute the stationary feasible demand. The simulation results indicate that both systems can converge to uncongested equilibriums after demand adjustment. The ramp demand adjustment methods provide a scientific basis for urban traffic system management.     

Vulnerability analysis for large-scale and congested road networks with demand uncertainty

To assess the vulnerability of congested road networks, the commonly used full network scan approach is to evaluate all possible scenarios of link closure using a form of traffic assignment. This approach can be computationally burdensome and may not be viable for identifying the most critical links in large-scale networks. In this study, an “impact area” vulnerability analysis approach is proposed to evaluate the consequences of a link closure within its impact area instead of the whole network. The proposed approach can significantly reduce the search space for determining the most critical links in large-scale networks. In addition, a new vulnerability index is introduced to examine properly the consequences of a link closure. The effects of demand uncertainty and heterogeneous travellers’ risk-taking behaviour are explicitly considered. Numerical results for two different road networks show that in practice the proposed approach is more efficient than traditional full scan approach for identifying the same set of critical links. Numerical results also demonstrate that both stochastic demand and travellers’ risk-taking behaviour have significant impacts on network vulnerability analysis, especially under high network congestion and large demand variations. Ignoring their impacts can underestimate the consequences of link closures and misidentify the most critical links.     

A model‐based demand‐balancing control for dynamically divided multiple urban subnetworks

Traffic control is an effective and efficient method for the problem of traffic congestion. It is necessary to design a high‐level controller to regulate the network traffic demands, because traffic congestion is not only caused by the improper management of the traffic network but also to a great extent caused by excessive network traffic demands. Therefore, we design a demand‐balance model predictive controller based on the macroscopic fundamental diagram‐based multi‐subnetwork model, which can optimize the network traffic mobility and the network traffic throughput by regulating the input traffic flows of the subnetworks. Because the transferring traffic flows among subnetworks are indirectly controlled and coordinated by the demand‐balance model predictive controller, the subnetwork division can variate dynamically according to real traffic states, and a global optimality can be achieved for the entire traffic network. The simulation results show the effectiveness of the proposed controller in improving the network traffic throughput. Copyright © 2016 John Wiley & Sons, Ltd.     

The role of travel demand and network centrality on the connectivity and resilience of an urban street system

In the transportation literature, two major and parallel approaches exist to identify the critical elements of a transportation system. On the one hand, conventional transportation engineering emphasizes travel demand, often in terms of traffic volume (i.e., demand side). On the other hand, newer techniques from Network Science emphasize network topology (i.e., supply side). To better understand the relationship between the two approaches, we first investigate whether they correlate by comparing traffic volume and node centrality. Second, we assess the impact of the two approaches on the connectivity and resilience of a transportation network; connectivity is measured by the relative size of the giant component, and resilience is measured by the network’s adaptive capacity (the amount of extra flow it can handle). The urban road system of Isfahan (Iran) is used as a practical case study. Overall, we find that traffic volume indeed correlates with node centrality. In addition, we find that the weighted degree of a node, i.e., the sum of the capacities of its incident links (for small disruptions) and node betweenness (for large disruptions), best captures node criticality. Nodes with high weighted degree and betweenness should therefore be given higher priority to enhance connectivity and resilience in urban street systems. Regarding link criticality, roads with higher capacities showed a more important role as opposed to betweenness, flow, and congestion.

     

A cell transmission model for dynamic lane reversal with autonomous vehicles

Autonomous vehicles admit consideration of novel traffic behaviors such as reservation-based intersection controls and dynamic lane reversal. We present a cell transmission model formulation for dynamic lane reversal. For deterministic demand, we formulate the dynamic lane reversal control problem for a single link as an integer program and derive theoretical results. In reality, demand is not known perfectly at arbitrary times in the future. To address stochastic demand, we present a Markov decision process formulation. Due to the large state size, the Markov decision process is intractable. However, based on theoretical results from the integer program, we derive an effective heuristic. We demonstrate significant improvements over a fixed lane configuration both on a single bottleneck link with varying demands, and on the downtown Austin network.     

Feeder transit services: Choosing between fixed and demand responsive policy

The Demand Responsive Connector (DRC) connects a residential area to a major transit network through a transfer point and is one of the most often adopted types of flexible transit services. In this paper, analytical and simulation models are developed to assist planners in the decision making process when having to choose between a demand responsive and a fixed-route operating policy and whether and when to switch from one to the other during the day. The best policy is chosen to maximize the service quality, defined as a weighed sum of customer walking time, waiting time and ride time. Based on the results of one-vehicle operations for various scenarios, we have generated critical customer demands, which represent switching points between the competing service policies. Our findings show that the critical demands are in the range from 10 to 50 customers/mile²/h and that a demand responsive policy is more preferred during afternoon peak hours.     

Estimating road network accessibility during a hurricane evacuation: A case study of hurricane Irma in Florida

Understanding the spatio-temporal road network accessibility during a hurricane evacuation—the level of ease of residents in an area in reaching evacuation destination sites through the road network—is a critical component of emergency management. While many studies have attempted to measure road accessibility (either in the scope of evacuation or beyond), few have considered both dynamic evacuation demand and characteristics of a hurricane. This study proposes a methodological framework to achieve this goal. In an interval of every six hours, the method first estimates the evacuation demand in terms of number of vehicles per household in each county subdivision (sub-county) by considering the hurricane’s wind radius and track. The closest facility analysis is then employed to model evacuees’ route choices towards the predefined evacuation destinations. The potential crowdedness index (PCI), a metric capturing the level of crowdedness of each road segment, is then computed by coupling the estimated evacuation demand and route choices. Finally, the road accessibility of each sub-county is measured by calculating the reciprocal of the sum of PCI values of corresponding roads connecting evacuees from the sub-county to the designated destinations. The method is applied to the entire state of Florida during Hurricane Irma in September 2017. Results show that I-75 and I-95 northbound have a high level of congestion, and sub-counties along the northbound I-95 suffer from the worst road accessibility. In addition, this research performs a sensitivity analysis for examining the impacts of different choices of behavioral response curves on accessibility results.     

大型综合交通枢纽指路标志系统设置研究

城市大型综合交通枢纽由于其功能多样,辐射广泛,周边路网复杂,因此对其指路标志系统需要专门设计。文章以上海市虹桥综合交通枢纽指路标志系统为研究对象,从路网结构及交通流特性出发,将指路标志系统按出行者需求层次分为四级,并提出相应的指路标志设置原则及方法,供相关部门参考。     

Supporting real-time traffic in multihop vehicle-to-infrastructure networks

In this paper, a new Controlled Vehicular Internet Access protocol with QoS support (CVIA-QoS) is introduced. CVIA-QoS employs fixed gateways along the road which perform periodic admission control and scheduling decisions for the packet traffic in their service area. The CVIA-QoS protocol is based on Controlled Vehicular Internet Access (CVIA) protocol that was designed only for the best-effort traffic. The most important contribution of the CVIA-QoS protocol is providing delay bounded throughput guarantees for soft real-time traffic, which is an important challenge especially for a mobile multihop network. After the demands of the soft real-time traffic is met, CVIA-QoS supports the best-effort traffic with the remaining bandwidth. Simulation results confirm that in CVIA-QoS protocol, the real-time throughput is not affected from the best-effort load and its delay is much smaller than CVIA delay when both the real-time and best-effort load exist in the channel. It has been observed that, unlike, CVIA-QoS, IEEE 802.11e with multi-hopping suffers from lower throughput and high number of real-time packet drops.     

Rationing and pricing strategies for congestion mitigation: Behavioral theory,econometric model,and application in Beijing

Some travel demand management policies such as road pricing have been widely studied in literature. Rationing policies, including vehicle ownership quota and vehicle usage restrictions, have been implemented in several megaregions to address congestion and other negative transportation externalities, but not well explored in literature. Other strategies such as Vehicle Mileage Fee have not been well accepted by policy makers, but attract growing research interest. As policy makers face an increasing number of policy tools, a theoretical framework is needed to analyze these policies and provide a direct comparison of their welfare implications such as efficiency and equity. However, such a comprehensive framework does not exist in literature. To bridge this gap, this study develops an analytical framework for analyzing and comparing travel demand management policies, which consists of a mathematical model of joint household vehicle ownership and usage decisions and welfare analysis methods based on compensating variation and consumer surplus. Under the assumptions of homogenous users and single time period, this study finds that vehicle usage rationing performs better when relatively small percentages of users (i.e. low rationing ratio) are rationed off the roads and when induced demand elasticity resulting from congestion mitigation is low. When the amount of induced demand exceeds a certain level, it is shown analytically that vehicle usage restrictions will always cause welfare losses. When the policy goal is to reduce vehicle travel by a fixed portion, road pricing provides a larger welfare gain. The performance of different policies is influenced by network congestion and congestibility. This paper further generalizes the model to consider heterogenous users and demonstrates how it can be applied for policy analysis on a real network after careful calibration.     

On some traffic equilibrium theory paradoxes

We consider the asymmetric equilibrium problem with fixed demands in a transportation network where the travel cost on each link may depend on the flow on this as well as other links of the network and we study how the travellers' cost is affected by changes in the travel demand or addition of new routes. Assuming that the travel cost functions are strongly monotone, we derive formulas which express, under certain conditions, how a change in travel demand associated with a particular origin-destination (O / D) pair will affect the travelers' cost for any O / D pair. We then use these formulas to show that an increase in the travel demand associated with a particular O / D pair (all other remaining fixed) always results in an increase in the travelers' cost on that O / D pair, however, the travelers' cost on other O / D pairs may decrease. We then derive formulas yielding, under certain conditions, the change in travelers' cost on every O / D pair induced by the addition of a new path. These can be used to determine, whether Braess' paradox occurs in the network. We then show that when a new path is added, the travelers' cost associated with the particular O / D pair joined by this path will decrease (hence Braess' paradox does not occur) if a test matrix is positive semidefinite.     

Adding a new station and a road link to a road–rail network in the presence of modal competition

In this paper we study the problem of locating a new station on an existing rail corridor and a new junction on an existing road network, and connecting them with a new road segment under a budget constraint. We consider three objective functions and the corresponding optimization problems, which are modeled by means of mixed integer non-linear programs. For small instances, the models can be solved directly by a standard solver. For large instances, an enumerative algorithm based on a discretization of the problem is proposed. Computational experiments show that the latter approach yields high quality solutions within short computing times.