Traffic Assignment Methods
2.2 Traffic Assignment Methods
Traffic assignment method options for SIDRA ASSIGN include the following:
2.2.1 All-or-Nothing Assignment
All-or-Nothing (AON) Assignment starts with processing the Network with the Initial Vehicle 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 movement travel times and cost estimates after the Assign Trips have been loaded. It is therefore very likely that new shortest path routes can be discovered after the completion of the AON Assignment.
AON solution is the recommended method for cases wherein there is only one viable route between O-D pairs. In cases where there are competing alternative routes between O-D pairs, the AON solution may not satisfy Wardrop's First Principle of Traffic Equilibrium and AON is not suitable to use in these cases.
2.2.2 Incremental Assignment
Incremental Assignment (IA) is a technique where small and equal proportions of the Assign Trips are loaded to the network. The process starts by loading Initial Vehicle Volumes and Fixed Trips and processing the Network. The resulting movement travel times and cost are used to find the shortest Route between O-D pairs. The first proportion of Assign Trips is assigned to the shortest Route. The network is then reprocessed and the movement travel times or costs are updated. The process of incrementally loading proportions of Assign Trips and reprocessing the network is repeated until all Assign Trips are loaded. The Number of Increments parameter 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 satisfies Wardrop's First Principle.
The Assign Routes that trips were assigned at each iteration are not changed. It is therefore possible that the IA solution may include route flows that do not satisfy Wardrop's 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.
2.2.3 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 Vehicle Volumes and Fixed Trips which are loaded first before Assign Trips are loaded. 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. 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 iteration will also terminate if the Maximum Number of UE Iterations is reached, even if 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 as the solution gets closer to satisfying Wardrop's First Principle.
2.2.4 Stochastic User Equilibrium
Stochastic User Equilibrium Assignment (SUE) is an assignment method that apportions Assign Trips to alternative routes based on probabilistic route choice preferences. A choice set of viable routes is defined and the proportion of Assign Trips that will use each route is calculated according to the attractiveness (or utility) of the route.
SUE is an extension of the UE method and it also seeks to find a solution that satisfies Wardrop's First Principle but with the assumption that information and perception of Route travel time amongst Trips varies. The SUE method can result in more realistic Route flows than the UE method when alternative routes have comparable Route travel times. The SUE method will proportionately assign O-D Volumes between them using a Route choice model, whereas the UE method will assign all the O-D Volumes to the lowest travel time Route only.
The route choice model is a logit model with the utility function expressed as follows:
Utility = Travel Time Coefficient x Travel Time, minutes + error
The probability of a route being selected is calculated as follows:
Prob(route) = Exp(Utility of route) / Sum of Exp(Utility) of all routes in the choice set
The Travel Time Coefficient sets the sensitivity of Trips to differences in Travel Time of alternative Routes. Figure 2.2.1 illustrates the case where there are two alternative routes for an O-D Pair, i.e. Route 1 and Route 2. If the route travel times are equal, then each route will get a share of 50% of the Assign Trips. If the travel on Route 1 is higher or lower than Route 2, then the share of Route 1 of the Assign Trips will increase or decrease accordingly. The degree of change in route share is dependent on the Travel Time Coefficient. Large negative values of the coefficient increase the sensitivity of route share to travel time differences between alternative routes.
Figure 2.2.1 — Route Share Given Difference in Travel Time between the Routes
Route flows determine route travel costs; and route travel costs determine the route flows. The SUE applies an iterative method to find a traffic assignment solution such that the routes flows, and route travel costs (or time) are mutually consistent.
The SUE iterations are terminated, and the solution is accepted when the Duality Gap is lower than the Duality Gap Tolerance set by the user. The iteration will also terminate if the Maximum Number of SUE Iterations is reached even if the Duality Gap Tolerance was not satisfied.
2.2.5 Fixed Route Assignment
Fixed Route Assignment (FRA) is an assignment method wherein the routes and the proportion of Trips using the routes are user-defined. Fixed Route Assignment can be done in conjunction with another Traffic Assignment Method. Fixed Route Assignment is useful for modelling public transport routes. Fixed Trips are loaded first before Assign Trips are loaded in the Network.
For a Network Route to be used as a Fixed Route, it needs to start from an Origin Zone and end at a Destination Zone. The Movement Class for the Fixed Route must also be enabled for every Site Movement along the Network Route. The Fixed Route Volumes are calculated as the product of the Fixed O-D Volume and the Fixed Trip Proportion of the Route. The sum of Fixed Trip Proportions of all enabled Fixed Routes between an O-D Pair must equal to 100%.
2.2.6 Utility Function of Routes
The utility function of Routes is an equation that quantifies the attractiveness of a Route relative to other alternative Routes between O-D Pairs. This utility function can include various attributes of Routes, such as travel time, distance, cost, stops, etc. In many cases the utility function accounts for the sum of the travel time and the time value equivalent of toll cost. The utility function is the basis for the shortest path search algorithm in traffic assignment.
The SIDRA ASSIGN utility function of Routes includes travel time only. To include other factors in the SIDRA ASSIGN utility function, the Extra Midblock Delay in the Calibration Tab of the Site Vehicle Movement Data dialog can be used. For example, toll costs can be converted to a travel time equivalent (i.e. toll cost divided by value of time) and input as Extra Midblock Delay. ASSIGN can then incorporate the toll cost in the utility function.
2.2.7 Convergence Metrics
There are two types of convergence metrics: indicating either proximity or stability. Duality Gap is a proximity convergence metric. Duality Gap is independent of traffic assignment solutions of prior iterations. It is referred to as proximity convergence metric because it measures how close the traffic solution is to meeting a traffic equilibrium principle, in this case Wardrop's First Principle. Duality Gap is applicable to AON, IA, UE and SUE, and it is reported for all of these traffic assignment methods. However, Duality Gap is used as a terminating condition for UE and SUE only.
Stability convergence metrics on the other hand measure the changes to the traffic assignment solution between successive iterations. These metrics only apply to UE and SUE methods. Stability convergence metrics do not apply to AON and IA. Stability convergence metrics include:
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Consistency Index (%), which is an indicator of the consistency between of the route flows and route travel cost of the traffic assignment solution.
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Absolute total travel time change for Assign Trips (%) between successive iterations, All MC
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Maximum change in route flows for any Assign Routes in veh/h between successive iterations, All MC
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Maximum change in Site Movement Flows for any Movement in the Network in veh/h between successive iterations, All MC
These metrics indicates if the traffic assignment solution is stabilising in the last few iterations of the traffic assignment method. It is desirable that these metrics are close to zero, indicating that the traffic solution is not changing significantly in the last few iterations. Stability convergence metrics are reported by ASSIGN; but they are not used as a terminating condition for any traffic assignment method.
Increasing the Maximum Number of Iterations for UE and SUE or increasing the Number of Increments for IA tends to improve convergence.
In addition to reviewing ASSIGN Convergence Metrics, it is also important to check Network Model Variability to ensure that the Network Model has converged. Network Model Variability issues will affect the reliability of ASSIGN traffic assignment solutions. Refer to the SIDRA INTERSECTION User Guide for more information regarding Network Model Variability.