Traffic Assignment Methods
ASSIGN includes the following traffic assignment methods:
- All-or-Nothing Assignment (AON)
- Incremental Assignment (IA)
- User Equilibrium (UE)
- Stochastic User Equilibrium Assignment (SUE)
- Fixed Route Assignment (FRA)
All-or-Nothing Assignment
All-or-Nothing (AON) Assignment starts with processing the Network with the Initial Volumes and Fixed Trips loaded. Movement travel times and cost are then used to determine the shortest path between O-D pairs. Assign Trips are then loaded on the shortest path. The Network is then processed one more time which completes the AON Assignment.
AON Assignment does not update the route choice of Assign Trips based on the latest movement travel times and cost estimates. In cases where there are competing routes between O-D pairs, the AON solution may not satisfy Wardrop’s First Principle of Traffic Equlibrium. AON solution is useful method to apply for cases wherein there is only one viable route between O-D pairs.
Incremental Assignment (IA)
Incremental Assignment (IA) is a technique where small proprotions of the Assign Trips are loaded to the network. The process starts by loading Initial Volumes and Fixed Trips and processing the Network. The resulting movement travel times and cost are used to find the shortest path between O-D pairs. The first proportion of Assign Trips is then assigned to the shortest path. The network is the reprocessed; and, the movement travel times and costs are updated. The process of incrementally loading proprtions of Assign Trips and reprocessing the network is repeated until all of the Assign Trips are loaded. Assign Trips are loaded in equal increments. The Number of Increments is set by the user. A higher Number of Increments may result in a traffic assignment solution that is a good approximation of a solution that satifies Wardops First Principle.
The Assign Routes that trips were assigned to for each iteration are not changed. It is therefore possible that the IA solution may include routes that do not satisfy Wardops First Principle. IA is useful to find an approximate solution to an ASSIGN Network quickly when User Equilibrium or Stochastic User Equilibrium techniques are taking a long time to find a solution.
User Equilibrium
User Equilibrium (UE) is an assignment method which apportions Assign Trips to routes that satisfy Wardrop’s First Principle. The UE process factors in the Initial Volumes and Fixed Trips. A UE solution is a close approximation of real-world routes choices given trips have perfect information of alternative route travel times and cost.
UE applies an iterative method to find a trtaffic assignment solution that satisfies Wardrops’s First Principle. The UE iterations are terminated, and the solution is accepted when the Duality Gap is lower than the Duality Gap Tolerance set by the user. The iteraration will also terminate if the Maximum Number of UE Iterations is reached, although this indicates that the Duality Gap Tolerance was not satisfied.
The Duality Gap is the percentage difference between the total trip travel cost and the theoretical total trip travel cost assuming shortest travel cost for all trips. The Duality Gap approaches zero the closer the solution is to satisfying Wardop’s First Principle.