The most simple method for assigning traffic to a network is the all-or-nothing assignment method. It directly manifests the assumption that all travellers on a network will act to minimise their travel cost.
A shortest path tree is created between each origin and destination pair in a transport network - based on the generalised cost of using different links. An all-or-nothing assignment then assigns traffic to these routes. All other routes are ignored - mimicking a traveller that would like to minimise their travel cost. The following assumptions are made in an AON assignment model:
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There are no congestion effects,
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all travellers consider the same factors for route cost,
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these factors are weighted the same for each traveller.
Based on these assumptions all drivers travelling between an O-D pair will travel on the same route. Thus, each link along a shortest path between an OD pair will have the traffic from the origin assigned to it, until the final link which ends at the destination. Two such AON assignments were created in this research project, named the IAON code and the CAON code.
The most commonly used heuristic that attempts to take into consideration the effect of congestion when assigning traffic to a transport network is the method of successive averages (MSA). It is an algorithm that iteratively completes all-or-nothing assignments until a convergence criteria has been met and has been the traditional method for modelling a stochastic user equilibrium (SUE) due it's property of allowing non-shortest routes to carry positive flow (Liu et al. (2009)).
MSA's are able to do this as the volumes assigned to each link for each successive iteration are based upon a linear combination of the flows assigned in previous iterations and an all-or-nothing assignment completed for the current iteration. Link costs are then updated based on the new iteration's volume's and new volumes are assigned. Thus, certain iterations will assign demand to a sub-optimal route - modelling the "probabilistic errors in travellers perception of route cost." (Liu et al. (2009)). A generic algorithm for a MSA is as follows (adapted from de Dios Ort~Aozar and Willumsen (2011)):
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Step 1: An initial set of current link costs is selected based on free- ow travel times. All traffic flows, V are equal to 0 and n (the number of iterations) equals 0.
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Step 2: A set of minimum cost trees is built based on the current link costs. Make n = n + 1.
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Step 3: All volumes from the O-D matrix are loaded onto the minimum cost trees via an AON assignment. This assignment provides the auxiliary ows Fa.
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Step 4: Current flows are then calculated using the current link costs function:
where V is the new set of current link flows for all links a of iteration n. phi is the step size of choice.
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Step 5: New current link costs are generated based upon the new set of current link flows V . If the convergence criteria of choice is met, stop. If the convergence criteria is not met, the process reverted to step 2.
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Both the IAON AON code and the CAON AON code were extended based on this algorithm for use in an MSA assignment. They retained their names of IAON and CAON as the AON assignment makes up the core of both of the codes.
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Method of successive averages heuristic
All-or-nothing assignment
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