Dynamic Origin-Destination Matrix Estimation Based on Urban Rail Transit AFC Data: Deep Optimization Framework with Forward Passing and Backpropagation Techniques

Table 1

Sets, indices, variables, vectors, and parameters.

	Definitions
Indices
i	Index of nodes (origin stations),
j	Index of destination stations,
t	Index of departure time intervals,
	Index of travel time,
p	Index of paths,
Sets
N	Set of stations (origin stations)
D	Set of destination station indices
	Set of destination station indices for the departure time t
T	Set of departure time indices
	Set of departure time indices for the origin station i
	Set of departure time indices from the origin station i to the destination station j
	Set of travel time indices
	Set of travel time indices for the path p
P	Set of path indices
	Set of path indices for the destination station j
	Set of path indices from origin station i to the destination station j at departure time t
Variables
	Number of passengers entering (tap-in) the system at origin station i
	Number of passengers departing at time t
	Number of passengers exiting (tap-out) the system at destination station j
	Number of passengers choosing the path p
	Number of passengers spending the travel time
Vectors
X	The vector of the input layer,
	The vector of hidden layer 1,
	The vector of hidden layer 2,
	The vector of hidden layer 3,
Y	The vector of the output layer,
Parameters
	The proportion of passengers departing at time t to the passengers entering (tap-in) the system at node i
	The proportion of passengers exiting (tap-out) the system at node j to the passengers departing at time t
	The proportion of passengers choosing the path p to the passengers exiting (tap-out) the system at node j
	The proportion of passengers with the travel time to the passengers choosing the path p
	Learning rate
	A gradient of hidden layer 1
	A gradient of hidden layer 2
	A gradient of hidden layer 3
	A gradient of the output layer
	The updated value of
	The updated value of
	The updated value of
	The updated value of
	The matrix of the departure time layer proportion
	The matrix of the destination station layer proportion
	The matrix of the path layer proportion
	The matrix of the travel time layer proportion
	Number of real passengers spending the travel time from AFC records