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To fulfill the missing part in cascading failures based reliability study of bus transit network (BTN), this paper is devoted to establishing a novel cascading failures model under route failure perspective, as well as considering the link prediction effect on failure load dynamic redistribution (FLDR). First, for advancing the route failure perspective, the weighted bus transit route network (weighted BTRN) is established through modifying the Space R method. Thereby, the represented passenger flow system of BTN can adapt to the demand of investigating the cascading failures under route failure perspective, because the node actually denotes the route under weighted BTRN perspective. Second, through analyzing the general evolution process of FLDR under time step scale perspective and providing the overall evolution steps of the proposed cascading failures model, the cascading failures analytical framework under time step scale perspective is further proposed. Furthermore, through embedding the effect of structural similarity based link prediction indices on evaluating the existence possibility relative size of all optional evacuation links, FLDR pattern considering link prediction effect is proposed. Finally, the case study of Jinan’s BTRN is conducted to verify the adaptability of the proposed cascading failures model. This interdisciplinary study between transportation engineering and system science provides a strong link between two important study areas of complex network theory- cascading failures and link prediction, and helps to improve the engineering applicability of cascading failures based reliability model in actual BTN operation.

This paper establishes a multi-parameter controlling cascading failures (CFs) model for measuring interdependent public transit network (PTN) reliability under mesoscopic perspective. First, we abstract the weighted PTN and geospatial PTN into a double-layered passenger flow system that considers the influences of the transportation infrastructure and the interaction between the passenger flow transited via the public transit mode and that transited via all other urban traffic modes. Second, for embedding the congestion, time-delay interaction and self-organization effects in the CFs model of an interdependent PTN, we propose the failure load dynamic redistribution (FLDR) considering the congestion effect in each sub-network, define the interaction way (another FLDR form) considering time-delay effect between two sub-networks and establish the CFs judging method considering the self-organization effect in the interdependent PTN. Furthermore, the multi-perspective measurement indicator system (i.e., (i) the global and local perspectives and (ii) the aggregated and discretized perspectives) is defined to provide a full viewing perspective for better understanding and capturing the CFs process. Finally, through a simulation analysis of Jinan’s PTN, the adaptability of the proposed CFs model is verified, and the significant nonlinearity is found, i.e., there is a threshold value of the station load tolerance parameter $$\lambda _C$$ , making the cascading survivability of interdependent PTN significantly increase, when the actual station load tolerance parameter is larger than $$\lambda _C$$ ; moreover, increasing the control parameter of the connected edge transit capacity (parameter $$\theta $$ ) can speed up the process of finding this $$\lambda _C$$ of an interdependent PTN. This nonlinearity provides the simulation evidence of the CFs controllability in the interdependent PTN.

The complexity and resilience of urban public transit network (PTN) are the interdisciplinary study area between transportation engineering and system science, which is a good demonstration of applying complex network theory to promote the development of engineering science. The deep understanding of this study helps to provide a new perspective for analyzing the reliability of urban PTN. Following study process of the complexity and resilience of complex network, this paper reviews the complexity and resilience of PTN from four topics, i.e., the PTN complexity, the static resilience of PTN, the dynamic resilience (cascading failures based resilience) of single layered PTN, and the dynamic resilience of interdependent PTN. In the literature review, multiple key items are, respectively, extracted for each topic, and the engineering applicability of each topic is also analyzed, which are both for obtaining the key features of this study area. Finally, in order to realize the development trend of cyclic and forward—complex network theory, network resilience theory, transforming into a realistic model and method that is close to actual public transit operation, engineering application and practice, and contributing to complex network theory, the study status is summarized and the future development trend is prospected.

In order to construct weighted public transit network, this work introduces bus routes density and departure frequency relative value to modify the traditional space L method. Then, the station initial load and capacity are defined based on station intensity, and the cascading failure model of weighted public transit network under single station deliberate attacks is given. Finally, Jinan city's weighted public transit network is taken as sample to analyze the station intensity distribution, which can get that the intensity average value and variance of stations are both divergent, the network follows power-low distribution with exponent λ = 1.66 and has the characteristics of scale-free network; by case simulation experiment, the authors give the cascading failure simulation analysis under three kinds of station attack strategies, get the intensity value size of failure station, the station load tolerance parameter α and the station load distribution control parameter β having important influences on cascading survivability, and verify the feasibility of cascading failure model.

The Braess paradox is an important phenomenon in the traffic network, and the robustness is a characteristic that measures the network system performance under interference. Study of traffic network paradox and its robustness is an important topic of traffic assignment. In this paper, we investigate the traffic network under elastic demand, its robustness and paradox under stochastic user equilibrium. Using the Logit model and Braess’ network, we find that paradox occurs when the congestion of a newly added road meets certain criterion. Paradox severity and the ranking of the network components are both affected by the new congestion. This finding can be applied in the planning of urban traffic network.

In the methodology of urban rail transit network (URTN), the study on the hour-scale based time-varying characteristic of topology complexity (HTCTC) dynamics is a missing part. This paper proves the existence of HTCTC and analyzes its dynamics through establishing the testing framework in Nanjing’s weighted URTN. Furthermore, a novel network structure entropy based on station strength that characterizes the uniformity of energy distribution is proposed for capturing and understanding the HTCTC dynamics. Its availability is proved by conducting Pearson correlation analysis between it and a series of traditional weighted topology complexity indicators. This programmed analytical framework can contribute to improving the processible time and space scales of complex system, and can be widely applied to other cities.

In this paper, an evolution traffic network model considering the influence of the next-nearest neighbor is constructed. Using the model, we focus on studying the topology of the evolution traffic network in order to understand the traffic dynamics better. First, the influence of the next-nearest neighbor on the cumulative degree distribution is investigated by altering the values of the sensitivity coefficients; then the influence of some important parameters (density, the maximum velocity, etc.) is also discussed; subsequently, we study the trend of the degree of the hub when the values of the parameters change; some hubs of the evolution network are given at last. In this model, the hub is denoted as the node whose ranking of the degree is at the top a fixed percentage. By studying the statistical properties of the traffic network, we can grasp the traffic dynamics so as to take the appropriate methods for the better traffic situations.

This work explores the synchronization behavior in discrete systems with both discrete time and discrete state. In order to describe the self-driven function of the node’s state, a state transfer matrix is introduced. Three typical network structures (random network, small-world network and scale-free network) are numerically studied in order to investigate the impact of network structure. Simulation results show that, according to the phase synchronization index, the coupling strength is divided into four regions: the increasing region, the maximum region, the decreasing region and the oscillation region. Moreover, the size of the oscillation region seems to be changeless, independent of the network structure and a parameter describing the number of total node’s states.

In this work, we study the effect of congestion on the behavior of cascading failures in scale-free networks, where a capacity is assigned on each node (controlled by a tolerance parameter α), and traffic flows are governed by user equilibrium instead of going along the shortest paths. The effect of congestion can be described by link cost function, which denotes the time needed to travel along the link. Here we focus on studying the effect of link's practical capacity, which is a parameter in link cost function. Two different kinds of link's practical capacity are investigated, i.e. uniform case and nonuniform case. In the uniform case, each link has the same value of practical capacity. While in the nonuniform case, we assume that link's practical capacity and degrees of the link's endpoints are correlated (controlled by parameter θ, which governs the heterogeneity of link's practical capacity). Simulation results show that, in the uniform case, scale-free networks are more prone to cascading failures when increasing the value of link's practical capacity. In the nonuniform case, cascading failures in scale-free networks are very sensitive to α when θ > 0; while θ < 0, scale-free networks may suffer from serious cascading failures, regardless of α.

In this work, we propose and study a model for the diffusion of congestion in complex networks. According to the proposed model, the level of congestion on each node will be self-organized into the same value. The diffusion of congestion throughout various networks with different topologies is investigated analytically and by numerical tests. The flow fluctuations in complex networks are studied. We recover a power-law scaling relation between the standard deviation and mean flow, which is consistent with the previous studies. Finally, we extend our model by adding two constraints, which may be effective strategies for diffusing the local and the global congestion in complex networks, respectively.

Delay, as an inevitable real-world phenomenon, is usually ignored in transport network design. A model of urban hybrid transport system with stochastic delay was created on the basis of the idealized public transport system design. After formulating the total trip time cost composed of accessing time in the sub-region of the city, waiting time at the public transport station, and in-vehicle time in the public transit network, the analytical properties of the total trip time cost function were investigated. The results show that in the urban hybrid transport network design, the total trip time cost reaches its approximate minimum in a δ-neighbourhood of buffer time of 1.5 min, and that through modelling optimal delay in hybrid transport system, the maximal synchronization can be achieved and operational efficiency and passenger satisfaction can be improved. The proposed modelling and analytical investigations are attempts to contribute to more realistic modelling of future idealized public transport system that involves more practical constraints.

In this paper, we extend a fiber bundle model to study the propagation of traffic jams on scale-free networks. For the special distributions of traffic handling capacities of the links and traffic load on the nodes, the critical behavior of the jamming transition on scale-free networks is studied analytically. It is found that the links connecting to the nodes with larger degrees are more prone to suffering from traffic jams. This feature is associated with a propagation that follows a precise hierarchical dynamics. Finally, the average failure rate of the networks, which is defined as the fraction of total broken links of the network, is investigated analytically and by simulations in scale-free networks. We mainly find that, when β > γ (β and γ are the scaling exponents of the load distribution and degree distribution, respectively), there is a scaling between the average failure rate of the scale-free networks 1 - G and the network size N, 1 - G ~ N-1, independent of γ.

The urban expressway network is an important part of the urban transport system which carries huge traffic pressure. It is also the key to the efficiency of the urban transport system. In this paper, the mesoscopic traffic flow models are improved by integrated with variable speed limits strategy to simulate the dynamic of vehicles on urban expressway network. The models include static queuing model, the velocity model and the vehicle movement model. Moreover the corresponding variable speed limits values can be obtained by proposed simulation method which can aid traffic managers to develop a network traffic flow control strategy. In the end, the elevated expressway network of Jinan city is used as a simulation example. We investigated the performance of the transport system with averaged density, speed and flow on link. We also analyzed the dynamic of the traffic system on expressway network at different demand level. The simulation results show that the proposed models and method are feasible and effective. The variable speed limits strategy can successfully alleviate the traffic congestion in some extent. The operational efficiency of the transportation system is greatly improved.

Urban congestion is a major and costly problem in many cities both in China and other countries. The purpose of building urban expressway is to alleviate the growing traffic pressure. In this paper, the mesoscopic traffic flow models are improved by variable speed limits strategy for the dynamic of vehicles on urban expressway network. The models include static queuing model, the velocity model, and the movement model of the vehicle. Moreover the method of the simulation is also proposed. So that we can get the corresponding variable speed limits values and aid traffic managers in making decisions to develop a network traffic flow control strategy. In the end, the elevated expressway of Jinan city is used as a simulation example. We investigated the performance of the transport system with averaged density, speed, and flow on link. We also analysed the dynamic of the traffic system on expressway network at different demand levels. The simulation results show that the models are feasible and effective and the variable speed limits strategy can successfully alleviate the traffic congestion in some extent. The operational efficiency of the transportation system is greatly improved.

Taking urban public transit network as research perspective, this work introduces the influences of adjacent stations on definition of station initial load, the connected edge transit capacity, and the coupled capacity to modify traditional load-capacity cascading failures (CFs) model. Furthermore, we consider the coupled effect of lower layered public transit network on the CFs of upper layered public transit network, and construct CFs coupled model of double layered public transit network with “interdependent relationship”. Finally, taking Jinan city’s public transit network as example, we give the dynamics simulation analysis of CFs under different control parameters based on measurement indicator of station cascading failures ratio (abbreviated as CF) and the scale of time-step cascading failures (abbreviated as [Formula: see text]), get the influencing characteristics of various control parameters, and verify the feasibility of CFs coupled model of double layered public transit network.

Many traffic problems in China such as traffic jams and air pollutions are mainly caused by the increasing traffic volume. In order to alleviate the traffic congestion and improve the network performance, the analysis of traffic state and congestion propagation has attracted a great interest. In this paper, an improved mesoscopic traffic flow model is proposed to capture the speed-density relationship on segments, the length of queue, the flow on links, and so forth, The self-developed dynamic traffic simulation software (DynaCHINA) is used to reproduce the traffic congestion and propagation in a bidirectional grid network for different demand levels. The simulation results show that the proposed model and method are capable of capturing the real traffic states. Hence, our results can provide decision supports for the urban traffic management and planning.

In this work, we have collected 195 bus routes and 1433 bus stations of Jinan city as sample date to build up the public transit geospatial network model by applying space L method, until May 2014. Then, by analyzing the topological properties of public transit geospatial network model, which include degree and degree distribution, average shortest path length, clustering coefficient and betweenness, we get the conclusion that public transit network is a typical complex network with scale-free and small-world characteristics. Furthermore, in order to analyze the survivability of public transit network, we define new network structure entropy based on betweenness importance, and prove its correctness by giving that the new network structure entropy has the same statistical characteristics with network efficiency. Finally, the "inflexion zone" is discovered, which can be taken as the momentous indicator to determine the public transit network failure.

Regional traffic signal optimization has been always a hot research field. The study of signal control in urban traffic network is a fundamental work to enhance traffic efficiency and depress traffic congestion. In this paper, the optimization goal which can be used to optimize the network performance index, includes average vehicle travel delay, queue lengths, intersection throughputs, etc. The improved mesoscopic traffic simulation model is presented to simulate the processes of traffic movement. And the SPSA(Simultaneous Perturbation Stochastic Approximation) algorithm is improved to the timing schemes of signal controllers in a network. And the first time the complex network theory is used to find the evolution of network topology interactive with optimal signal. The simulation results present that the optimal signal timings and optimal network topology can both alleviate traffic congestion and more effective on improve average network journey velocity.