A new computer system is put in place at a toll booth. The system comes online at $9$:$00$am $($with no vehicles in the queue$)$ and vehicles arrive at a rate of $\backslash$lambda $($t$)=120\mathrm{.}4$t $($with $\backslash$lambda $($t$)$ in veh$/$min and t in min$).$ Due to a computer system failure, cars are not serviced until $9$:$10$am$.$ Between $9$:$10$ and $9$:$20$ they are serviced at $3$ veh$/$min$.$ After $9$:$20$ they are serviced at $15$ veh$/$min$.$ Assuming D$/$D$/1$ queuing, what is the total vehicle delay in veh$-$min?