Is +1 could be the arrival interval between two trains the station (j (j + Scenario two: When arrival interval among the regional train and also the behind Cyclohexanecarboxylic acid Endogenous Metabolite express Scenario two: When the the arrival interval amongst the nearby train along with the behind express train at station j satisfies security requirement, having said that, the departing interval at at station train at station j satisfies the the security requirement, nonetheless, the departing intervalstation j is j just isn’t happy, the express train demands to overtakelocallocal train at stationshown in not happy, the express train needs to overtake the the train at station j, as j, as shown in Figure this this scenario, regardless of whether the i overtake the the regional train at station Figure 2b. In2b. Inscenario, whether or not the train train i overtake local train at station j isj is calculated by Equation calculated by Equation (9).(9).-1, 1, i i- 1, taai1,i i xi , I aa + (1 – xi j ) I I and tdd ii–1,i x j I d + (1 – xi , ) I d yi , j =1, taa j ji -1,i xi,jj Iaa + (1 – x, i,j ) atat and tddjij-1,i i ,xi,j Idd + (1 -j xi,j ) tIdt 0, taa x I + (1 – x ) I and tdd yi,j = xi , j I d d + (1 – xi , j ) I d t i, j aa i, j at j j 0, taai-1,i xi,j Iaa + (1 – xi,j ) Iat and tddi-1,i xi,j Idd + (1 – xi,j ) Idt(9) (9)jjAdjustment in the train timetable soon after an overtaking three. Adjustment in the train timetable just after an overtaking If overtaking occurs, thethe tzthe the overtaken trainthe the overtaking station needsbe be If overtaking occurs, tz of of overtaken train at at overtaking station desires to to extended. The departure time of thethe overtaken trainthethe overtaking stationchanged extended. The departure time of overtaken train at at overtaking station is is changed to thethe original timewhich overtake train passes via thethe overtaking station plus Itd . to original time at at which overtake train passes via overtaking station plus Itd. The arrival and departure Valopicitabine manufacturer instances of thethe overtaken traineach subsequent station must towards the arrival and departure instances of overtaken train at at each and every subsequent station want be recalculated depending on on the corresponding inter-station travel time and tz . be recalculated based the corresponding inter-station travel time and tz. The timetable for for each and every subsequent train desires be be adjusted accordingly based on The timetable each and every subsequent train requires to to adjusted accordingly depending on thethe tconstraint. If the the interval constraint is unsatisfied, then the absolute value thethe tmin min constraint. If interval constraint is unsatisfied, then the absolute worth of of difference among thethe necessary and actual intervals requires be be added thethe present distinction amongst expected and actual intervals requires to to added to to existing arrival and departure times. The arrival and departure occasions at each and every subsequent station really need to be recalculated determined by the corresponding inter-station travel time and tz .3.two. Passenger Flow Parameters Our model calculations involve the following principal passenger flow parameters: the amount of waiting passengers at each station, the amount of boarding passengers, the3.Appl. Sci. 2021, 11,7 ofnumber of alighting passengers, the amount of onboard passengers, and the number of delayed passengers. 3.two.1. Quantity of Passengers Waiting in the Origin Station on the Line Beneath the assumption that passengers arriving at the origin station stick to a uniform distribution for the duration of the study period, the total quantity of passengers who enter the origin statio.