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Demand for Traffic
The demand for traffic - or, more general, a spatial interaction pattern - comprises the demand for transportation from every source node i to every distinct destination node j. In telecommunications networks, for example, the demand is recorded in so-called end-to-end matrices. Regarding (road) traffic networks the trip table is usually denoted by a vector.
A system optimal traffic pattern represents the global viewpoint of a network provider who is interested in the efficient usage of network resources. In doing so a private or public network carrier would arrange goods movements possibly by virtue of some sort of peak load pricing so as to internalize external costs of congestion. Nevertheless, negative effects external to the network are not necessarily taken into account. Thus, a first-best traffic pattern requires further instruments to internalize the latter external effects.
The origin-destination-trips are allocated to available routes with the objective to minimize total travel cost, where interactions between flows sharing the same links or nodes are taken into account. (normative traffic assignment)
Traffic or trip assignment is a procedure to forecast the traffic loads on a network of transportation facilities given predicted travel demands comprised in so-called trip tables. Each number of trips from a particular origin to a particluar destination must be assigned to the alternative routes connecting this pair of nodes. The result is twofold. While path flows are of particular interest from the travelers' point of view, the network designer is usually more interested in the corresponding link flows to detect bottlenecks.
User Optimality or Wardrop Equilibrium
A user optimal traffic pattern refers to the individual point of view of each motorist who tends to be unaware of, or at least to be unresponsive to, certain costs he imposes on others. Hence, the driver will rationally not take into account these costs in his travel related decisions. Drivers are only concerned with the private cost they must bear themselves such as petrol costs, the time costs of making the trip and maintaining their vehicle. Consequently, motorists tend to underestimate the social cost of trips that should include all impacts of their activities on others. (descriptive traffic assignment)
A path flow is called a Wardrop equilibrium (or user equilibrium) when no
driver has a less costly alternative route.
As no unused path has lower cost the Wardrop equilibrium may be restated as follows: each path in use operates at minimum cost and each unused path shows at least minimum cost.
Wardrop's first performance criterion is based upon the assumption of
rational traveler behavior with respect to each user of the congested
traffic network seeking to minimize his/her own travel time, and it is
therefore also known as the user optimum, or equilibrium principle.
Wardrop's second performance criterion is the minimization of the average
travel time (or, equivalently, the total travel time for a given number of
trips), and it is therefore referred to as the system optimum principle.
Wardrop's first principle: The journey times on all the routes actually used are equal and less than those which would be experienced by a single vehicle on any unused route.
Wardrop's second principle: The average journey time is a minimum.
Literature: Wardrop (1952)