  Accurate forecasting of passenger flow (i.e., ridership) is critical to the
operation of urban metro systems. Previous studies mainly model passenger flow
as time series by aggregating individual trips and then perform forecasting
based on the values in the past several steps. However, this approach
essentially overlooks the fact that passenger flow consists of trips from each
individual traveler. For example, a traveler's work trip in the morning can
help predict his/her home trip in the evening, while this causal structure
cannot be explicitly encoded in standard time series models. In this paper, we
propose a new forecasting framework for boarding flow by incorporating the
generative mechanism into standard time series models and leveraging the strong
regularity rooted in travel behavior. In doing so, we introduce returning flow
from previous alighting trips as a new covariate, which captures the causal
structure and long-range dependencies in passenger flow data based on travel
behavior. We develop the return probability parallelogram (RPP) to summarize
the causal relationships and estimate the return flow. The proposed framework
is evaluated using real-world passenger flow data, and the results confirm that
the returning flow -- a single covariate -- can substantially and consistently
improve various forecasting tasks, including one-step ahead forecasting,
multi-step ahead forecasting, and forecasting under special events. And the
proposed method is more effective for business-type stations with most
passengers come and return within the same day. This study can be extended to
other modes of transport, and it also sheds new light on general demand time
series forecasting problems, in which causal structure and long-range
dependencies are generated by the user behavior.
