Modeling Random Exit Selection in Intercity Expressway Traffic with Quantum Walk

Abstract

In intercity expressway traffic, the multiplicity of available routes leads to randomness in exit selection. Random exit selection by drivers is hard to observe, and thus it is a challenge to model intercity expressway traffic sufficiently. In this paper, we developed a Random Quantum Traffic Model (RQTM), which modeled the stochastic traffic fluctuation caused by random exit selection and the residual regularity fluctuation with the quantum walk and autoregressive moving average model (ARMA), respectively. The RQTM considered the random exit selection of a driver as a quantum stochastic process with a dynamic probability function. A quantum walk was applied to update the probability function, which simulated when and where a driver will leave the expressway. We validated our model with hourly traffic data from seven exits from the Nanjing–Changzhou expressway in eastern China. For the seven exits, the coefficients of determination of the RQTM ranged from 0.5 to 0.85. Compared with the classical random walk and the ARMA model, the coefficients of determination were increased by 21.28% to 104.98%, and the relative mean square error decreased by 11.61% to 32.92%. We conclude that the RQTM provides new potential for modeling traffic dynamics with consideration of unobservable random driver decision making.

Analyzing the multi‐scale characteristic for online car‐hailing traffic volume with quantum walk

“…Then, Li et al. [36] proposed a random quantum traffic model (RQTM) to simulate the stochastic traffic fluctuation caused by the random exit choices of drivers. For traffic control, Karafyllidis et al.…”

“…For traffic simulation and prediction, Yu et al [35] innovatively proposed a small granularity traffic volume simulation model based on quantum walks, which realized the consideration of the drivers' driving habits heterogeneity and decision randomness. Then, Li et al [36] proposed a random quantum traffic model (RQTM) to simulate the stochastic traffic fluctuation caused by the random exit choices of drivers. For traffic control, Karafyllidis et al [37] developed quantum walk models for autonomous driving and traffic control.…”