1 Takashi Akamatsu, “Decomposition of Path Choice Entropy in General Transport Networks,” TRANSPORTATION SCIENCE 31 (4), 349-362 (1997).
This paper shows that the conventional entropy function defined by path flows can be decomposed into a function consisting only of link flows. The equivalence of the decomposed formulation of the logit-based traffic assignment is proved by using the Markov properties of Dial’s algorithm. Two methods for calculating the expected minimum cost without path enumeration is proposed.

2 Gary S. Chao and Terry L. Friesz, “Spatial price equilibrium sensitivity analysis,” Transportation Research Part B: Methodological 18 (6), 423-440 (1984).
The first order derivative of all decision variables with respect to parameter perturbations are shown to be a simple form which requires inversion of the Jacobian matrix of the Lagrangian function of the equivalent nonlinear program. The efficient computation of partial derivatives with respect to perturbations is done through a series of substitutions and manipulations of matrices.

3 Carlos F. Daganzo, “Unconstrained Extremal Formulation of Some Transportation Equilibrium Problems,” TRANSPORTATION SCIENCE 16 (3), 332-360 (1982).
The stochastic user equilibrium problem is reformulated as an unconstrained extremal problem. The expected maximum utility value and the inverse price function are both included in the objective. The equivalent unconstrained optimization can be formulated in path flow variables or link flow variable.

4 Yosef Sheffi and Carlos F. Daganzo, “Another “paradox” of traffic flow,” Transportation Research 12 (1), 43-46 (1978).
It is proved that the marginal expected perceived total cost with respect to the travel cost of a route is equal to the probability of choosing this route. The relationship between perceived travel cost and measured travel cost is similar to that of user equilibrium and system optimum.

5 Chao Yang and Anthony Chen, “Sensitivity analysis of the combined travel demand model with applications,” Eur.J.Oper.Res. 198 (3), 909-921 (2009).
The constrained nonlinear programming formulation of the combined travel demand model is employed in this paper (Oppenheim, 1995). The sensitivity analysis of the combined travel demand model followed the approach of Gary S. Chao (1984). However, they didn’t propose any efficient method to conduct the sensitivity analysis for large scale networks.

6 Jiang Qian Ying and Toshihiko Miyagi, “Sensitivity Analysis for Stochastic User Equilibrium Network Flows–A Dual Approach,” TRANSPORTATION SCIENCE 35 (2), 124-133 (2001).
The unconstrained extremal formulation of stochastic user equilibrium is employed in this paper. The Dial’s algorithm is adapted to compute the entries of the Hessian matrix of the objective. The derivation of the partial derivatives with respect to perturbations is essentially the same as Gary S. Chao (1984) and Chao Yang (2009).

7 Zhong Zhou, Anthony Chen and S. C. Wong, “Alternative formulations of a combined trip generation, trip distribution, modal split, and trip assignment model,” Eur.J.Oper.Res. 198 (1), 129-138 (2009).
The unconstrained optimization formulation of Carlos F. Daganzo (1982) is extended to represent the hierarchical structure of the combined travel demand model. The link travel cost function enters into the objective of this new formulation, while in the original formulation the inverse travel cost function is included. Another difference is that the decision variable of the new formulation is link flows, not the travel cost as in the original formulation.