Traffic Assignment Models

Traffic assignment models aim to determine the number of trips on different links (road sections) of the network given the travel demand between different pairs of nodes (zones). These models try to mathematically describe the route choice phase of the sequential demand analysis procedure. There are various models of traffic assignment. All of these models assume that travel time on the link is the only factor which trip makers consider while choosing a route. These models, however, differ in their assumptions regarding the variation in link travel times with the link volume (or link flow). In this section, three models are discussed, namely, (i) all-or-nothing assignment model, (ii) incremental assignment model, and (iii) user-equilibrium model. The notation used (other than those used in the earlier sections) in describing these models is as follows:

$x_a$ : 		 Flow (or volume) on link $a$. 

$x_a^k$ : 		  Flow (or volume) on link $a$ as estimated in the $k^{th}$iteration.

$\tau_a(x_a)$ : 		 Travel time on link $a$ when flow on link $a$ is$x_a$. 

$t_{ij}$ : 		 The total demand (or number of trips) between origin $i$ anddestination $j$. 

$\delta_{a,k}^{i,j}$ : 		 Indicator variable which is 1 if link $a$ is apart of the $k^{th}$ route between 


origin $i$ and destination $j$; otherwise it is zero. 

$\Phi_k^{i,j}$ : 		 Flow between $i$ and $j$ which uses the $k^{th}$ route.