Devise a two$-$way bus service scheme on a regional route $\{$A$-$B$-$C; C$-$B$-$A$\}$ offering service with even but different headways on links A$-$B$-$A and on links B$-$C$-$B$.$ The target service frequency on A$-$B$-$A is $12$ buses$/$h$,$ and on B$-$C$-$B$,8$ buses$/$h$.$ To do this, some buses will shuttle back and forth between A and B and others will travel the complete route $($A$-$B$-$C$-$B$-$A$).$ Buses can be held at B for as long as necessary to produce the requisite even departures from B in both directions. If the trip times from A$-$B$,$ B$-$A$,$ C$-$B$,$ and B$-$C are each $30$ min, then depict a set of bus trajectories that will meet the stated requirements, i$.$e$.,$ have regular headways on all legs. You need to determine how much to delay each bus at B$,$ and if a bus just came from A$,$ whether to turn it around at B$.$ How many buses are required to accommodate your scheme?