Equity-Oriented Train Timetabling with Collaborative Passenger Flow Control: A Spatial Rebalance of Service on an Oversaturated Urban Rail Transit Line
Table 1
Notations used throughout the paper.
Sets and indices
Sets of stations indexed by ,;
Sets of train services indexed by ,;
Sets of discrete time intervals indexed by ;
Parameters
,
The minimum and maximum headways between two adjacent trains
The maximum variation for two adjacent headways
The headway threshold for implementing passenger flow control
,
Departure times at the start terminal station for the first and last trains
Dwelling time at station
Running time from station to station
Number of passengers arriving at station in time interval
Maximum capacity of facilities at station for one-unit interval
Proportion of arrival passengers at station whose destination is station
Maximum train loading capacity
Maximum capacity of the platform at station
Average train load factor of the segment between station and station
The penalty for passengers who miss trains, which should be a monotone increasing function of
A large positive number
Intermediate variables
Departure time of train at station
Binary variable, which is 1 if time interval is larger than the departure time of train at station and no larger than the departure time of train at the same station and is 0 otherwise
Number of arrival passengers at station between train and train
Binary variable, which is 1 if all passengers arriving at station between train and train have entered the platform when train departs from the same station and is 0 otherwise
Number of passengers entering the platform at station between train and train
Number of passengers boarding train at station
Number of passengers alighting from train at station
Number of passengers on train after departing from station
Decision variables
Headway between train and train at the start terminal station
Number of passengers arriving at station between train and train who enter the platform between the subsequent train and train
