$(10$ points$)$ Given $29$ arrival epochs and $29$ departure epochs $($a total of $58$ trips$)$ at terminal

k between $6$:$00$ and $8$:$10$ a$.$m$.($see the following table$)$ and a maximum paid idle time of

Tmax $=35$ min

a$.$ Apply algorithm $TmF$ and find $D(k)$ and the maximum number of joinings at $k$ in which

$ij$ Tmax; list all joinings found.

b$.$ Use the FIFO rule for constructing the joinings at $k,$ list all joinings and compare the

results with those found in $($a$).($You must show your work and carefully justify your

answers. The correct answer without any work will receive little or no credit$)$