Research Article

A Short Turning Strategy for Train Scheduling Optimization in an Urban Rail Transit Line: The Case of Beijing Subway Line 4

Table 2

Subscripts and parameters.

symboldescription

index for train services in the up direction
index for train services in the down direction
oorigin
ddestination
A,B,Cdepots
Jtotal number of stations for short-turning
Ptotal number of stations for whole line
Ktotal number of time intervals
upup operation direction
dndown operation direction
total number of train services in the up direction
total number of train services in the down direction
set of train services in the up direction
set of train services in the down direction
running time for short turning trains in the up direction
running time for full-length trains in the up direction
running time for short turning trains in the down direction
running time for full-length trains in the down direction
dwell time for short turning trains in the up direction
dwell time for full-length trains in the up direction
dwell time for short turning trains in the down direction
dwell time for full-length trains in the down direction
the number of train services in the time interval for up direction
the number of train services in the time interval for down direction
predetermined departure time for the first train service at the origin station
predetermined departure time for the last train service at the origin station
minimal headway
maximal headway
expected headway of train services in area 2 during the time interval in the up direction
expected headway of train services in area 1 during the time interval in the up direction
expected headway of train services in area 2 during the time interval in the down direction
expected headway of train services in area 1 during the time interval in the down direction
minimal turnaround time
maximal turnaround time
Ma sufficiently large positive number