Consider the two$-$link network shown in following figure.

This network represents one origin$-$destination pair connected by two alternative routes. Let t $1$ and t $2$

represent the travel time on links $1$ and $2,$ respectively, and let x$1$ and x$2$ represent the traffic flow on

these links. The total origin$-$destination flow is designated by$,$ where q$=$x$\_(1)+$x$\_(2).$ The performance

functions on these links t$\_(1)($x$\_(1))$ and t$\_(2)($x$\_(2))$ are represented in the following figure. The travel time

increases as the flow rate on each link increases. For the case of User Equilibrium, where drivers chose

routes with minimum travel time, plot the travel time in the system when the total flow rate q increase

gradually from $1$ to Q $.$