Delays caused by motorized vehicles unable to clear intersections in China: Graphical analysis

In many Chinese cities,motorized vehicles （M-vehicles） move slowly at intersections due to the interference of a large number of non-motorized vehicles （NM-vehicles）.The slow movement makes a part of M-vehicles fail to leave intersections timely after the traffic signal tums red,and thereby conflicts between vehicles from two directions occur.The phenomenon was analyzed graphically by using the cumulative vehicle curve.Delays in three cases were modeled and compared：NM-vehicle priorities and M-vehicle priorities with all-red intervals unable to release all vehicles,and longer all-red intervals ensuring release all vehicles.Marginal delays caused by two illegal behaviors that occasionally happened in mixed traffic intersections were also investigated.It is concluded that increasing the speed of M-vehicles leaving intersections and postponing the entering of NM-vehicles are the keys in mathematics,although they are uneasy in disordered mixed traffic intersections due to a dilemma between efficiency and orders in reality.The results could provide implications for the traffic management in the cities maintaining a large number of M-and NM-vehicles.

Inequalities for L_p Mixed Intersection Bodies

Haberl and Ludwig defined the notions of L_p intersection bodies. In this paper,we introduce the L_p mixed intersection bodies, and establish some geometric inequalities for L_p mixed intersection bodies. Furthermore, the Busemann-Petty type problem for L_p mixed intersection bodies are shown.

Analysis of occupation time of vehicles at urban unsignalized intersections in non-lane-based mixed traffic conditions

In India, traffic flow on roads is highly mixed in nature with wide variations in the static and dynamic characteristics of vehicles. At unsignalized intersections, vehicles generally do not follow lane discipline and ignore the rules of priority. Drivers generally become more aggressive and tend to cross the uncontrolled intersections without considering the conflicting traffic. All these conditions cause a very complex traffic situation at unsignal- ized intersections which have a great impact on the capacity and performance of traffic intersections. A new method called additive conflict flow （ACF） method is suitable to determine the capacity of unsignalized inter- sections in non-lane-based mixed traffic conditions as prevailing in India. Occupation time is the key parameter for ACF method, which is defined as the time spent by a vehicle in the conflict area at the intersection. Data for this study were collected at two three-legged unsignalized intersections （one is uncontrolled and other one is semi- controlled） in Mangalore city, India using video-graphic technique during peak periods on three consecutive week days. The occupation time of vehicles at these intersections were studied and compared. The data on conflicting traffic volume and occupation time by each subject vehicle at the conflict area were extracted from the videos using image processing software. The subject vehicles were divided into three categories： two wheelers,cars, and auto-rickshaws. Mathematical relationships were developed to relate the occupation time of different cate- gories of vehicles with the conflicting flow of vehicles for various movements at both the intersections. It was found that occupation time increases with the increasing con- flicting traffic and observed to be higher at the uncontrolled intersection compared to the semicontrolled intersec- tion. The segregated turning movements and the presence of mini roundabout at the semicontrolled intersection reduces the conflicts of vehicular movements, which ulti- mately reduces the occupation time. The proposed methodology will be useful to determine the occupation time for various movements at unsignalized intersections. The models developed in the study can be used by practitioners and traffic engineers to estimate the capacity of unsignalized intersections in non-lane-based discipline and mixed traffic conditions.

INEQUALITIES FOR MIXED INTERSECTION BODIES

In this paper, some properties of mixed intersection bodies are given, and inequalities from the dual Brunn-Minkowski theory (such as the dual Minkowski inequality, the dual Aleksandrov-Fenchel inequalities and the. dual Brunn-Minkowski inequalities) are established for mixed intersection bodies.

A Quasi-Funk's Section Theorem in n-Complex Space

The Funk＇s section theorem in the n-complex space Cn is investigated. It turns out that this theorem does not admit an extension for the class of general origin-symmetric star bodies in Cn but for a class of star bodies called generalized complex intersection bodies. A quasi-version of Funk＇s section theorem in Cn is established then.