Table 1 Set, indexes, parameters of the...

Table 1

Set, indexes, parameters of the model

Symbols	Definitions
$N$	Set of stations on the line
$K$	Set of trains
$K_{n}$	Set of low-speed grade trains (300km/h) $K_{n} \subset K$
$K_{b}$	Set of high-speed grade trains (350km/h) $K_{b} \subset K$
$K_{j}$	Set of flagship trains, $K_{j} \subset K_{b}$
$i, j$	Station index, $i, j \in N$
$m$	Total number of trains running on the line
$k, k^{'}$	Train index, $k, k^{'} \in K$
$N_{k k^{'}}$	Set of stations commonly passed by trains $k$ and $k^{'}$ ⁠, $k, k^{'} \in K$
$o_{k}$	Origin station of train $k$
$d_{k}$	Terminal station of train $k$
${S T}_{k i}$	Stopping status of train $k$ at station $i$ ⁠, 0 means passing without stopping, 1 means stopping
$F_{i}$	Minimum number of stops required at station $i$ within the specified time
${T r}_{i, i + 1}^{k}$	Pure running time of train $k$ in section $(i, i + 1)$
$t i_{k}$	Departure time of train $k$ ⁠, generally taken as whole hours, i.e. 420min, 480min, etc., $t i_{k} \in T I$
$S_{k i}$	Starting additional time of train $k$ at station $i$
$B_{k i}$	Stopping additional time of train $k$ at station $i$
${T s}_{i}^{\min}$	Minimum dwell time of trains at stations
${T s}_{i}^{\max}$	Maximum dwell time of trains at stations
$T_{i}^{\min}$	Upper limit of operation time window at station $i$
$T_{i}^{\max}$	Lower limit of operation time window at station $i$
$I_{d d}$	Minimum train departure interval
$I_{d p}$	Maximum train passing interval
$I_{p d}$	Minimum passing-to-departure interval
$I_{a a}$	Minimum arrival-to-arrival interval
$I_{a p}$	Minimum arrival-to-passing interval
$I_{p a}$	Minimum passing-to-arrival interval
$I_{p p}$	Minimum passing-to-passing interval
$M$	A large positive number
$L {s v}_{k}$	Train-kilometer conversion coefficient for train $k$
$T I$	Set of whole hour times

Symbols	Definitions
$N$	Set of stations on the line
$K$	Set of trains
$K_{n}$	Set of low-speed grade trains (300km/h) $K_{n} \subset K$
$K_{b}$	Set of high-speed grade trains (350km/h) $K_{b} \subset K$
$K_{j}$	Set of flagship trains, $K_{j} \subset K_{b}$
$i, j$	Station index, $i, j \in N$
$m$	Total number of trains running on the line
$k, k^{'}$	Train index, $k, k^{'} \in K$
$N_{k k^{'}}$	Set of stations commonly passed by trains $k$ and $k^{'}$ , $k, k^{'} \in K$
$o_{k}$	Origin station of train $k$
$d_{k}$	Terminal station of train $k$
${S T}_{k i}$	Stopping status of train $k$ at station $i$ , 0 means passing without stopping, 1 means stopping
$F_{i}$	Minimum number of stops required at station $i$ within the specified time
${T r}_{i, i + 1}^{k}$	Pure running time of train $k$ in section $(i, i + 1)$
$t i_{k}$	Departure time of train $k$ , generally taken as whole hours, i.e. 420min, 480min, etc., $t i_{k} \in T I$
$S_{k i}$	Starting additional time of train $k$ at station $i$
$B_{k i}$	Stopping additional time of train $k$ at station $i$
${T s}_{i}^{\min}$	Minimum dwell time of trains at stations
${T s}_{i}^{\max}$	Maximum dwell time of trains at stations
$T_{i}^{\min}$	Upper limit of operation time window at station $i$
$T_{i}^{\max}$	Lower limit of operation time window at station $i$
$I_{d d}$	Minimum train departure interval
$I_{d p}$	Maximum train passing interval
$I_{p d}$	Minimum passing-to-departure interval
$I_{a a}$	Minimum arrival-to-arrival interval
$I_{a p}$	Minimum arrival-to-passing interval
$I_{p a}$	Minimum passing-to-arrival interval
$I_{p p}$	Minimum passing-to-passing interval
$M$	A large positive number
$L {s v}_{k}$	Train-kilometer conversion coefficient for train $k$
$T I$	Set of whole hour times

Source(s): Author’s own work

[ViewLarge]

Sharing Unavailable