Research Article

Optimal Bus-Bridging Service under a Metro Station Disruption

Algorithm 1

Solution algorithm of the passenger behavior model.
Initialization: initialize the corresponding parameters of discrete choice behavior model, and K.
Procedure:
  if    then
   Define a temporary set List_k;
   for    do
   if  s==O  then
   Calculate the   based on the Eq. (21).
   else if  s==D  then
   Calculate the based on the Eqs. (19) ~(20).
   else
   Calculate the based on the Eqs. (22)~(24).
   if the number of elements in List_k is not exceeding K, add the into the set List_K and sort the elements
from smallest to largest;
   if the number of elements in List_k equals K, and the last value of List_k is larger than  , remove the last
value of List_k and add to the List_k.
   end if.
   end for.
   Calculate the based on the using the Eqs. (25)~(26).
   Then, calculate based on Eqs. (27).
   Calculate the joint probability , , based on Eqs. (28)~ (30).
Using the Roulette method to generate an alternative travel decision:
   (1) Construct a cumulative probability set R based on , , , where m=,
and .
  
  .
  
   (2) Generate a random variable r.
   (3) Determine the behavior choices:
   if , passenger will give up the metro journey and take a bus instead to the destination and ;
   if , passenger will give up the metro journey and take the transport mode m instead to
the destination, ;
   if , passenger will take an alternative station k as his new origin station of
metro journey, and he will take the transport mode m to the new origin station from the planned origin
station, the entry time at new origin is the original entry time added by the time consumption of the
transport mode m, ;
   if , passenger will wait at the planned origin station.
   else if    then
   Define a temporary set List_k, and we set the O as the passengers’ current station at the current time. If
passenger p is now in train, we set the O as the next station the train will stop at.
   Judge whether the travel time from the current station to the destination is larger than the closure duration?
if yes, the passenger p need not to change his travel behavior. If not, go on executing the following part.
   for    do
   if  s==O  then
   Calculate the   based on the Eqs. (19)~ (20).
   else if  s==D  then
   Set , where W is a very big constant.
   else
   Calculate the based on the Eqs. (22)~(24).
   if the number of elements in List_k is not exceeding K, add the into the set List_K and sort the elements
from smallest to largest;
   if the number of elements in List_k equals K, and the last value of List_k is larger than  , remove the last value
of List_k and add to the List_k.
   end if.
   end for.
   Calculate the based on the using the Eqs. (25)~(26).
   Then, calculate based on Eq. (27).
   Calculate the joint probability , , based on Eqs. (28)~(30).
   Using the Roulette method to generate an alternative travel decision:
   (1) Construct a cumulative probability set R based on , , , where m=,
and .
  , m=
  , m=, .
   (2) Generate a random variable r.
   (3) Determine the behavior choices:
   if , passenger will give up the metro journey and take a bus instead to the destination from current
station, ;
   if , passenger will give up the metro journey and take the transport mode m instead to
the destination from current station, ;
   if , passenger will take an alternative station k as his new
destination station of metro journey, and he will take the transport mode m to the planned destination
station from the new destination station, ;
   end if.