Optimal Operation Scheme with Short-Turn, Express, and Local Services in an Urban Rail Transit Line

Table 2

Definition of sets, indices, parameters, and variables.

Notations	Description
Sets
	Set of service route nodes with index
	Set of physical stations in urban rail transit line with index , .  =  , where is the set of low-priority stations with medium or small volume of passenger flow and is the set of high-priority stations with large volume of passenger flow
	Set of physical stations that service route visited
	Set of the turn-back stations
	Set of service routes in urban rail transit service network with index .  =  , where is the set of express services and is the set of local services
	Set of sections in urban rail transit line with index
	Set of arcs in a service network with index .  =  , where is the set of boarding arcs, is the set of riding arcs, and is the set of alighting arcs
	Set of departing arcs in a service network in station
	Set of arriving arcs in a service network in station
	Set of inbound and outbound direction with index
	Set of the operational trains with index ,  = {1, 2, 3, …, f, …, }, denotes that th train to be operating in service route
	Set of O-D pairs with index , where denote the origin and destination
Parameters
	Capacity of each train
	The maximum number of service routes
	Maximum operation frequency of the interval
	Minimum operation frequency of the interval
	Minimum number of trains operation on the service route
	Train operation cost per unit time
	Service route operation cost per unit distance with index l and e
	Passenger waiting cost per unit time
	Passenger riding cost per unit time
	Passenger transfer penalty per person
	The turn-back capacity of station in the direction of
	The total number of available vehicles
	Train capacity surplus
	Maximum number of serving physical stations for service route in one direction
	Round-trip time of service route
	Round-trip distance of service route
	Time required to pass arc
	The number of passengers at station in urban transit line
	The volume of passengers flow in section in urban transit line
	The number of trips generated by O-D pair from station
	The number of trips generated by O-D pair
	Binary parameter, equals one if service route visits station
	Binary parameter, equals one if service route visits section
	Binary parameter, equals one if the service turns back at station to direction
Definitional variables
	Binary variable, equals one if the th service route is activated
	Binary variable, equals one if the th train is activated
	Binary variable, equals one if the th train operation is on service route
	Nonnegative continuous variable, flow of O-D pair over arc
	Nonnegative continuous variable, waiting time of O-D pair at station