Development Economics X Paper Model Twenty
Transportation is the art of moving people and goods across space and time, but it is also a reflection of the political and economic forces. Sometimes, these forces are smooth and predictable, like a well-designed highway. Other times, they are rough and chaotic, like a bumpy road or a turbulent crisis. In either case, we propose to model the behavior of transportation systems using obliquely reflected Brownian motion in nonsmooth domains with fractional and subfractional noise, which captures the randomness, the constraints, and the complexity of the real world. We apply and extend important results from the probability and statistics literature on obliquely reflected Brownian motion in nonsmooth planar domains to account for fractional and subfractional noise. We consider understudied realistic scenarios that involve complex road network topologies, different traffic conditions at the boundary, and memory effects in the drivers’ behavior. We use a multiple connected domain to capture the presence of holes or islands in the road network, a switching or regime-switching model to account for absorption or tangential motion at the boundary, and a fractional Brownian motion or a fractional diffusion process to incorporate long-range dependence or memory in the process. We construct and analyze the generalized obliquely reflected Brownian motion in these settings and explore its potential applications to queuing theory and traffic flow optimization, especially in settings such as transportation in large urban centers.
Opoku-Agyemang, Kweku (2023). "Obliquely Reflected Brownian Motion in Nonsmooth Domains with Fractional and Subfractional Noise: An Transportation Systems Framework." Development Economics X Paper Model Twenty.
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