Sudden passenger demand at a bus stop can lead to numerous passengers gathering at the stop, which can affect bus system operation. Bus system operators often deal with this problem by adopting peer-to-peer service, where empty buses are added to the fleet and dispatched directly to the stop where passengers are gathered (PG-stop). However, with this strategy, passengers at the PG-stop have a long waiting time to board a bus. Thus, this paper proposes a novel mathematical programming model to reduce the passenger waiting time at a bus stop. A more complete stop-skipping model that including four cases for passengers’ waiting time at bus stops is proposed in this study. The stop-skipping decision and fleet size are modeled as a dynamic program to obtain the optimal strategy that minimizes the passenger waiting time, and the optimization model is solved with an improved ant colony algorithm. The proposed strategy was implemented on a bus line in Harbin, China. The results show that, during the evacuation, using the stop-skipping strategy not only reduced the total waiting time for passengers but also decreased the proportion of passengers with a long waiting time (>6 min) at the stops. Compared with the habitual and peer-to-peer service strategies, the total waiting time for passengers is reduced by 31% and 23%, respectively. Additionally, the proportion of passengers with longer waiting time dropped to 43.19% by adopting the stop-skipping strategy, compared with 72.68% with the habitual strategy and 47.5% with the peer-to-peer service strategy.
An Iterative Approach for Reconstruction of Arbitrary Sparsely Sampled Magnetic Resonance Images
