It is known that the commonly used NaSch cellular automaton （CA） model and its modifications can help explain the internal causes of the macro phenomena of traffic flow. However, the randomization probability of veh...It is known that the commonly used NaSch cellular automaton （CA） model and its modifications can help explain the internal causes of the macro phenomena of traffic flow. However, the randomization probability of vehicle velocity used in these models is assumed to be an exogenous constant or a conditional constant, which cannot reflect the learning and forgetting behaviour of drivers with historical experiences. This paper further modifies the NaSch model by enabling the randomization probability to be adjusted on the bases of drivers＇ memory. The Markov properties of this modified model are discussed. Analytical and simulation results show that the traffic fundamental diagrams can be indeed improved when considering drivers＇ intelligent behaviour. Some new features of traffic are revealed by differently combining the model parameters representing learning and forgetting behaviour.展开更多
We investigate some relations between two kinds of semigroup regularities, namely the e-property and the eventual continuity, both of which contribute to the ergodicity for Markov processes on Polish spaces.More preci...We investigate some relations between two kinds of semigroup regularities, namely the e-property and the eventual continuity, both of which contribute to the ergodicity for Markov processes on Polish spaces.More precisely, we prove that for Markov-Feller semigroup in discrete time and stochastically continuous MarkovFeller semigroup in continuous time, if there exists an ergodic measure whose support has a nonempty interior,then the e-property is satisfied on the interior of the support. In particular, it implies that, restricted on the support of each ergodic measure, the e-property and the eventual continuity are equivalent for the discrete-time and the stochastically continuous continuous-time Markov-Feller semigroups.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 70821061)the National Basic Research Program of China (Grant No. 2006CB705503)
文摘It is known that the commonly used NaSch cellular automaton （CA） model and its modifications can help explain the internal causes of the macro phenomena of traffic flow. However, the randomization probability of vehicle velocity used in these models is assumed to be an exogenous constant or a conditional constant, which cannot reflect the learning and forgetting behaviour of drivers with historical experiences. This paper further modifies the NaSch model by enabling the randomization probability to be adjusted on the bases of drivers＇ memory. The Markov properties of this modified model are discussed. Analytical and simulation results show that the traffic fundamental diagrams can be indeed improved when considering drivers＇ intelligent behaviour. Some new features of traffic are revealed by differently combining the model parameters representing learning and forgetting behaviour.
基金supported by National Natural Science Foundation of China (No.11731009, No.12231002)Center for Statistical Science,Peking University。
文摘We investigate some relations between two kinds of semigroup regularities, namely the e-property and the eventual continuity, both of which contribute to the ergodicity for Markov processes on Polish spaces.More precisely, we prove that for Markov-Feller semigroup in discrete time and stochastically continuous MarkovFeller semigroup in continuous time, if there exists an ergodic measure whose support has a nonempty interior,then the e-property is satisfied on the interior of the support. In particular, it implies that, restricted on the support of each ergodic measure, the e-property and the eventual continuity are equivalent for the discrete-time and the stochastically continuous continuous-time Markov-Feller semigroups.
