Next train arrives in the same station will have to satisfy Methyl acetylacetate Autophagy Equation (six): ai,j – di-1,j xi-1,j xi,j Ida + (1 – xi-1,j ) xi,j Ita + xi-1,j (1 – xi,j ) Idt 3.1.three. Overtaking Judgement and Adjustments Due to the express trains have fewer stop stations and run quicker than nearby trains, express trains will catch up together with the local trains once they are running on the very same route. At this moment, the express trains really need to overtake the nearby trains. The overtaking judgment situation could be defined as follows: when the arrival interval between two successive trains can not satisfy the necessary secure interval tmin at the final station, the rear train desires to overtake the front train (as shown in Equation (7)). 1. Overtaking judgement situation:- tiN 1,i = ai,N – ai-1,N – Iaa(five)(6)(7)Appl. Sci. 2021, 11, x FOR PEER REVIEW6 of1.Appl. Sci. 2021, 11,Overtaking judgement condition:i tN-1,i = ai, N – ai-1, N – Iaa6 of(7)where , may be the value made use of to determine whether or not the interval amongst the arrival times – of trains (i iN 1,i is the at the employed to decide whether or not satisfies the essential the ( , times exactly where t – 1) and i worth last station (i.e., station N) the interval in between tmin arrival 0 , signifies that (i – 1) and i at the last station (i.e.,-station N) satisfies thethat train ti doesn’t 0 0 implies needed min (ti-1,i of trains train i wants to overtake train (i 1); N overtake train (i – 1)). requires to overtake train (i – 1); ti-1,i 0 suggests that train i doesn’t signifies that train i N two. overtake train (i – 1)). places with the overtaking stations Determination in the two. Determination from the areas it the overtaking stations When overtaking is deemed important, ofis necessary to decide the areas in the When overtaking is deemed necessary, it really is essential to ascertain overtaking station. Two scenarios demand overtaking to take place (Figure 2). the places with the overtaking station. Two scenarios demand overtaking to take place (Figure 2).(a)(b)Figure 2. Two scenarios exactly where thethe express train overtakes the regional train: (a) Situation 1; (b) Situation 2. Figure 2. Two scenarios exactly where express train overtakes the neighborhood train: (a) Scenario 1; (b) Scenario 2.Situation 1: When the departing interval in between the nearby train as well as the behind express train at stationWhen the the security requirement, nonetheless, the arrival interval at the station Situation 1: j satisfies departing interval among the neighborhood train and also the behind (j + train at happy, the express train requirement, nonetheless, the train interval j, express1) will not be station j satisfies the security demands to overtake the localarrivalat stationat as theshown in + 1) isn’t happy, the expressovertake theto overtake at stationtrain at station by station (j Figure 2a. No 3-Methylbenzaldehyde Autophagy matter whether the train i train wants neighborhood train the regional j is calculated Equation (eight). j, as shown in Figure 2a. No matter whether the train i overtake the nearby train at station j is calculated by Equation (8). 1, tddij-1,i xi,j Idd + (1 – xi,j ) Idt and taaij-1,i Iaa +1 yi,j = (eight) 1, tdd ij-1,i x , I d + (1 – x , j ) I d t and taai -1,i I aa 1 yi , j = 0, tddij–1,i ixji,j Idd + (1 i- xi,j ) Idt and ji +taaij-1,i Iaa (eight) 0, tdd i 1,i x I + (1 – x ) I and taa -1,i +1 I aa i, j dd i, j dt j j +1 where tddi-1,i the departing interval amongst the two successive trains at at station j and where j, is could be the departing interval in between the two successive trains station j and , taaij-1,i the arrival interval among two trains at in the station + 1).1).