These two extensions, although seemingly subtle, marked a fundamental departure from
static assignment in traffic representation and algorithmic design. The first extension required the
development of efficient ways of describing time-varying network traffic condition and finding
shortest (least time) routes in networks where link travel times change over time. Describing
time-varying network traffic condition requires careful treatment to ensure that, while network
traffic is propagated forward in time, key traffic flow properties—in particular, flow
conservation (e.g., total amount of link outflow at the present time cannot be greater than the
total amount of inflow from the previous time step) and the fundamental relationship of traffic
flow variables (e.g., flow equals the product of average speed and density)—are preserved
temporally. This requirement motivates various network loading models including both
analytical- and simulation-based approaches.