Based on the classical Nagel–Schreckenberg model, we in this paper propose an improved cellular automaton (CA) model to study the influences of a multi-point tollbooth on traffic flow. The numerical results show that the multi-point tollbooth can be looked at as a bottleneck and that it can improve the road capacity compared with other tolling stations, which shows that the proposed model is more effective than other traffic flow models. In addition, the results can help readers to better understand the effects of a multi-point tollbooth on traffic flow and help traffic engineers to reasonably design the tolling station.
As an integrated kind of railway signal-control pattern, the four-aspect fixed autoblock system has been used in many train control systems. This paper takes the four-aspect fixed autoblock system as the research object and proposes the cellular automata model of the fixed autoblock system based on the existing theoretical researches on different train systems and traffic systems by means of the analytical study of the classical cellular automata model. The CA (cellular automata) models combine complexity of passenger railway line with the theory of cellular automata and introduce some new CA models into the existing control systems. After analyzing the relevant simulation results, we study thoroughly and obtain efficiently the needed data for the variation of the section carrying capacity, the average train delay and the train speed which have been affected by redundant time on the operation of passenger trains with different speeds.
We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero.