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.
Highlights
Introduction published maps and institutional affilWhen a driver heads to his/her destination via intercity expressways, despite the fact that the destination is often deterministic, the multiplicity of available routes leads to randomness in exit selection
By integrating the random exit selection from an interactive quantum probability perspective, we developed the Random Quantum Traffic Model (RQTM) to simulate the stochastic traffic fluctuation caused by random exit selection by a quantum walk (QW) model and the residual regularity fluctuation by an autoregressive moving average (ARMA) model
Based on the experiment configuration, the average statistics of the quantum walk simulation with different ∆k values are listed in Table 2, and when ∆k = 0.13, the statistics were the best, so the optimal fitting parameter ∆k of quantum walk for the seven exits was set to 0.13
Summary
When a driver heads to his/her destination via intercity expressways, despite the fact that the destination is often deterministic, the multiplicity of available routes leads to randomness in exit selection. A driver will pick the travel route from multiple candidates based on considerations of economy, timeliness, and traffic conditions [1]. Under such a scenario, the exit section is randomly induced by route selection, contrary to the conventional deterministic exit selection. The aggregation of the random exit selection by individual drivers will affect the distributions of traffic flow in space-time along the expressway [2]. The combined effect of a large number of individual random decisions at different destinations/exits along the expressway makes the overall traffic iations
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