Metro disruption management: Optimal initiation time of substitute bus services under uncertain system recovery time

Determining the initiation time of substitute bus (SB) services is critical for metro disruption management, especially under uncertain recovery time. This study develops a mathematical formulation to determine the optimal initiation time (OIT) of SB services by trading-off their initiation cost and passenger delay cost, thereby minimizing the total system cost. Given the probability distribution of metro disruption duration, we determine the OIT by formulating an optimization problem to minimize the expected total system cost. We then conduct sensitivity analyses of the initiation cost of SB services, passenger value of time, and SB services rate. The results show that SB services ought to be activated only if the metro incident lasts longer than a certain time interval, depending on the factors mentioned earlier, and the OIT should advance with the predicted incident duration. This paper derives analytical results for the case of linear passenger arrival, and determines the results numerically for the case of non-linear passenger arrival when analytical closed-form solutions are not available. The findings will facilitate transit operators to develop response plans in the aftermath of a metro disruption.