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Vector Spaces
Published in Crista Arangala, Exploring Linear Algebra, 2019
This is a discrete modeling technique for modeling systems that undergo transitions between a finite (or countable) number of states. Each Markov chain has a corresponding transition matrix. The transition matrix, M, is a probability matrix, where Mi,j is the probability of going from state j to state i. That is, M is of the form
Multiagent modeling of pedestrian-vehicle conflicts using Adversarial Inverse Reinforcement Learning
Published in Transportmetrica A: Transport Science, 2023
Payam Nasernejad, Tarek Sayed, Rushdi Alsaleh
The majority of active road user microsimulation models are based on the Cellular automata framework (Blue and Adler 2001; Burstedde et al. 2001; Nagel and Schreckenberg 1992) and social force models (Helbing and Molnar 1995). The Cellular automata is a grid-based or discrete modeling framework in which cells and states are the main components of the model. In this model, movement rules and cell occupancy conditions control the dynamic of the agents’ interactions. The social force models are based on physics law, in which pedestrians’ behavior is controlled by acceleration and repulsive forces. These forces originate from different incentives and obstacles in the model environment, and the collection of all influencing forces determines pedestrian moving speed and direction. Different adjustments and modifications were proposed to the CA and SFM frameworks to enhance the predictions’ accuracy. For example, Zeng et al. (2014) employed a modified SFM to reproduce pedestrian crossing behavior at signalised crosswalks. Zhou et al. (2019) examined the impact of flashing green signals on pedestrians’ behavior. The study found that the presence of approaching right-turning vehicles can significantly impact the pedestrian’s crossing velocity. Lu et al. (2016) proposed a CA model to simulate yielding and crossing behavior in pedestrian-vehicle interaction at unsignalized crosswalks. Xie et al. (2012) employed CA modeling approach to investigate different interaction mechanisms (e.g. risky or careful) that can occur between pedestrians and vehicles at signalised crosswalks.
Optimal urban expressway system in a transportation and land use interaction equilibrium framework
Published in Transportmetrica A: Transport Science, 2019
Tongfei Li, Huijun Sun, Jianjun Wu, Ziyou Gao, Ying-en Ge, Rui Ding
As shown in the previous literature listed in Table 1, there are two different kinds of methods for modeling integrated land use and the transportation systems, namely the discrete modeling approach and the continuous modeling approach. In the discrete modeling approach, the traffic network is discretized as many separated traffic zones connected by links; travel demand originating at each zone is assumed to be concentrated at the center of that zone. However, in the continuous modeling approach, the traffic network is assumed to be dense and is approximated as a continuum, over which commuters are continuously dispersed. Based on this assumption, Ho and Wong (2007) develop a bi-level model with housing allocation optimized to obtain the minimal negative utility, which included housing and transportation costs. In 2013, Yin et al. further extend it to be a new bi-level model to describe the relationships among housing allocation, traffic volume, and CO2 emissions in a polycentric city. Based on this model, they can get the optimal housing allocation to achieve minimum CO2 emissions (Yin et al. 2013). Compared to the continuous modeling approach, the discrete modeling approach better captures the realistic characteristics of transportation networks, and is thus more appropriate for the detailed planning and design of transportation systems (Li, Li, and Lam 2014). Therefore, in this paper, the discrete modeling approach has been adopted. The detailed description will be detailed in Section 3.2.