Time Coordination of Periodic Passenger Train Connections in Conditions of Single-Track Lines

Table 1

Summary of mathematical model notation.

Symbol	Meaning	Unit
	The incidence matrix representing whether train connections from the set can pass one another in the opposite directions or not
	The element of the incidence matrix ; when passing of trains and is possible, then , if not, then
	The set of nodes where passing train connections from the set one another is possible
	The set of nodes where passing the train connection with the train connection in the opposite direction is possible
	Volume of the transfer passengers who arrived to coordination node by train connection and who are transferring to train connection that is departing in direction
	Nonnegative variable that models the time loss of passengers who are transferring in transfer node from train connection to train connection that is departing in direction	(min)
	Set of train connections arriving to node
	Set of train connections operated within the network in question
	Set of train connections, with which connection included in I^GW are coordinated in the set of nodes
	Set of train connections of external transportation providers that service node
	Set of train connections departing from node in direction
	Set of nodes, in which transfer of passengers among train connections are planned
	Subset of transfer nodes of set , in which transfers of passengers between train connections of the transportation provider in question and train connections of external transportation providers are planned
	Subset of transfer nodes of set in which transfers of passengers among train connections of the transportation provider in question are planned
	Set of the initial nodes of individual train connections
	Set of nodes, in which passengers will transfer from train connection
	Binary variable that models the passing plan of the train connections coming from opposite directions and ; in node
N	Maximal permitted change of individual train connections	(min)
	Number of train connections leaving from initial node
	Nonnegative variable that models the time loss incurred due to two train connections passing each other in the opposite direction and ; in node
	Set of nonnegative numbers
	Set of the directions, in which individual train connections leave from transfer node
	Regular time interval among connections that service the routes within the network in question	(min)
	Earliest possible departure time of train connection from its initial node	(min)
	Transfer time for node	(min)
	Trip time of train connection from its initial node to transfer node	(min)
	Nonnegative variable that models the time change of the departure of train connection from the initial node	(min)
	Binary variable that models the origin of a transfer relation between train connection and train connection that departs in direction in node
	Trip time of train connection from the initial node to node	(min)