Complex networks are now the focus of many branches of research. Particularly, the scale-free property of some networks is of great interest, due to their importance and pervasiveness. Recent studies have shown that in some complex networks, e.g., transportation networks and social collaboration networks, the degree distribution follows the so-called “shifted power law” (or Mandelbrot law) $P(k)\propto (k+c{)}^{-\gamma }$. This study analyzes some evolving networks that grow with linear preferential attachments. Recent results for the quotient Gamma function are used to prove the asymptotic Mandelbrot law for the degree distribution in certain conditions. The best fit values for the scaling exponent, γ, and the shifting coefficient, c, can be directly calculated using Bernoulli polynomial functions. The study proves that the degree distribution of some complex networks follows an asymptotic Mandelbrot law with linear preferential attachment depicted by $P(k)\propto {\left(k+\frac{b+a+1}{2}\right)}^{-(b-a)}$.

Two characteristics of traffic flows make the vehicle departure headways in Beijing, China different from that in Atlanta, USA. Urban traffic flows in China are often hindered by pedestrians at intersections and queuing vehicles often cannot be totally discharged during the green time, so most signalized intersections are over-saturated in the day time. The first characteristic makes the departure headways of the first and second vehicles in Beijing depend heavily on the start-up situations (with or without interference). The departure headways of the 3rd to 5th vehicles in Beijing have similar characteristics to those in Atlanta. The second characteristic makes the departure headways after the 5th vehicle significantly different from those in Atlanta. These comparisons show that the conventional delay estimate methods and signal control algorithms may not fit Chinese scenarios, which makes imported intelligent traffic control systems not work well in China without calibrations.

This paper describes a location specific cell transmission model of freeway traffic based on the observed variability of fundamental diagrams both along and across freeway segments. This model extends the original cell transmission model (CTM) mechanism by defining various shapes of fundamental diagrams to reproduce more complex traffic phenomena, including capacity drops, lane-by-lane variations, nonhomogeneous wave propagation velocities, and temporal lags. A field test on a Canadian freeway was used to demonstrate the validity of the location specific CTM. The simulated spatio-temporal evolutions of traffic flow show that the model can be used to describe the traffic dynamics near bottlenecks more precisely than the original model.

Two characteristics of Chinese mixed traffic invalidate the conventional queuing delay estimates for western countries. First, the driving characteristics of Chinese drivers lead to different delays even though the other conditions are the same. Second, urban traffic flow in China is often hindered by pedestrians at intersections, such that imported intelligent traffic control systems do not work appropriately. Typical delay estimates for Chinese conditions were obtained from data for over 500 vehicle queues in Beijing collected using charge coupled device (CCD) cameras. The results show that the delays mainly depend on the proportion and positions of heavy vehicles in the queue, as well as the start-up situations (with or without interference). A simplified delay estimation model considers vehicle types and positions that compares well with the observed traffic delays.

The modeling of headway/spacing between two consecutive vehicles in a queue has many applications in traffic flow theory and transport practice. Most known approaches have only studied vehicles on freeways. This paper presents a model for the spacing distribution of queuing vehicles at a signalized junction based on random-matrix theory. The spacing distribution of a Gaussian symplectic ensemble (GSE) fits well with recently measured spacing distribution data. These results are also compared with measured spacing distribution observed for the car parking problem. Vehicle stationary queuing and vehicle parking have different spacing distributions due to different driving patterns.

One key function of intelligent transportation systems is to automatically detect abnormal traffic phenomena and to help further investigations of the cause of the abnormality. This paper describes a robust principal components analysis (RPCA)-based abnormal traffic flow pattern isolation and loop detector fault detection method. The results show that RPCA is a useful tool to distinguish regular traffic flow from abnormal traffic flow patterns caused by accidents and loop detector faults. This approach gives an effective traffic flow data pre-processing method to reduce the human effort in finding potential loop detector faults. The method can also be used to further investigate the causes of the abnormality.