Adaptive Multilevel Collaborative Passenger Flow Control in Peak Hours for a Subway Line

Table 1

The symbols involved in the model.

Symbols	Definition
Sets/parameters
	Set of directions, the up direction (), the down direction ().
	Operating train set on direction, .
	The current passenger flow control level, .
	Station set on direction, .
	Discrete time range of the study, .
	The maximum capacity of the train.
	The minimum fluctuant range of each gate at the timestamp allowing passengers to enter the control area of station on direction.
	The maximum fluctuant range of each gate at the timestamp allowing passengers to enter the control area of station on direction.
	The key area of the station, .
	The acreage of area at station .
	The acreage of area at station occupied by the passengers on direction.
	The actual departing time of the train at the station on direction.
	The maximum passing capacity of each gate at the timestamp on direction allowing passengers to enter the control area of station .
	Under the current control level , the number of passengers arrived at area of station on direction at timestamp .
	Under the current control level , the number of passengers arrived at area of station with trip on direction at timestamp .
	Under the current control level , the percentage of the acreage at area assigned to the passengers along direction.
	The timestamp index of the actual departing time .
	The length of two adjacent timestamps.
	Safety limitation factor.
	The dynamic percentage of passengers with trip accounting for the total passengers boarding train at station on direction.
Intermediate variable
	The number of passengers alighting from train i at station k on g direction.
	The number of accumulated passengers entering the platform between departure time of train i-1 and i on g direction at timestamp t.
	The boarding passengers for train i at station k on g direction.
	Under the current control level L, the total passengers arriving at area of station k from timestamp 1 to t.
	Under the current control level L, the total passengers arriving at area of station k on g direction from timestamp 1 to t.
	Under the current control level L, the total passengers allowed to enter the control area of station k on g direction from timestamp 1 to t.
	The total passengers allowed to enter platform and board train i at station k on g direction.
	The loading passengers in train i between station k and k +1 on g direction.
	The waiting time on platform for passengers to board train i on g direction.
	The waiting time for passengers in area of station k on g direction.
	Under the current control level L, the total passenger waiting time at station k on g direction.
	Under the current control level L, the number of waiting passengers at area of station k on g direction from timestamp 1 to t.
Decision variable
	The number of passengers allowed to enter the control area of station k on g direction at the timestamp t.