Equilibrium Flows on Urban Freeways

The equilibrium between supply and demand for travel on a roadway is reexamined without the usual assumption that the system is in a steady state. The demand for travel is treated as a function not only of the perceived cost of travel, but also of the time of day, with strong morning and evening peaks. In order to model typical urban freeway congestion, it is presumed that the peak demand will be sufficient to bring about capacity flow on some critical section of the roadway. Two different situations are studied, an afternoon case in which the travelers are on their way home from work and a morning case. It is shown that the duration of a trip made at a given time during the peak periods is not ordinarily a function of the flow at that particular time, but of the flows that existed prior to that time. Because of this, the equilibrium flows for the afternoon peak cannot be determined by finding the intersection of predetermined supply and demand functions, but only by solving an integral or differential equation. The results for the morning peak come closer to being a straightforward generalization of the usual steady state analysis.