Problem $1$: Consider a transportation network designed to handle $40000$ vehicles per hour. An unprecedented flooding event after $5$ months of construction, has reduced the capacity of the network gradually to $10000$ vehicles per hour in $2$ days. If the disrupted network stays at this state for $2$ days and gradually increases back to pre$-$flood levels in $2\mathrm{.}5$ days, identify different terms as indicated in the figure below and calculate the performance loss due to the flooding.