  In intercity expressway traffic, a driver frequently makes decisions to
adjust driving behavior according to time, location and traffic conditions,
which further affects when and where the driver will leave away from the
expressway traffic. Spontaneous exit choices by drivers are hard to observe and
thus it is a challenge to model intercity expressway traffic sufficiently. In
this paper, we developed a Spontaneous Quantum Traffic Model (SQTM), which
models the stochastic traffic fluctuation caused by spontaneous exit choices
and the residual regularity fluctuation with Quantum Walk and Autoregressive
Moving Average model (ARMA), respectively. SQTM considers the spontaneous exit
choice of a driver as a quantum stochastic process with a dynamical probability
function varies according to time, location and traffic conditions. A quantum
walk is applied to update the probability function, which simulates when and
where a driver will leave the traffic affected by spontaneous exit choices. We
validate our model with hourly traffic data from 7 exits from the
Nanjing-Changzhou expressway in Eastern China. For the 7 exits, the
coefficients of determination of SQTM ranged from 0.5 to 0.85. Compared with
classical random walk and ARMA model, the coefficients of determination were
increased by 21.28% to 104.98%, and relative mean square error decreased by
11.61% to 32.92%. We conclude that SQTM provides new potential for modeling
traffic dynamics with consideration of unobservable spontaneous driver's
decision-making.
