On the Distributions of the Stochastic Components in SUE Traffic Assignment Models
NIELSEN O A, Technical University of Denmark, Denmark
The Stochastic User Equilibrium traffic assignment, SUE, as formulated by Daganzo & Sheffi (1977) and Sheffi & Powell (1982) is widely recognised due to its ability to han- dle both the speed-flow relationship and the stochastic element in route choice (N
The Stochastic User Equilibrium traffic assignment, SUE, as formulated by Daganzo & Sheffi (1977) and Sheffi & Powell (1982) is widely recognised due to its ability to han- dle both the speed-flow relationship and the stochastic element in route choice (Nielsen, 1996 and Slavin, 1996). In addition it is able to handle the problems with overlapping routes (Sheffi, 1985), which are common in full-scale networks. SUE was developed further by (Nielsen, 1996) to simulate differences in road users utility functions.
In order to model differences in road users perceived travel resistance's Sheffi & Powell (1982) assumed that the perceived travel times on each link are normally distributed. This leads to a multivariate normal distribution of the perceived travel times on all paths connecting each O-D pair. Hereby, the concept of SUE equals alprobit-based assign- ment in the case of no congestion (zero speed-flow relationship). The solution algo- rithm use Monte Carlo simulation where draws from the Normal distribution are trun- cated because link-times cannot be negative. Other distributions have been suggested to avoid the truncation (Gamma by Sheffi, 1985, Rectangular by van Vuren, 1994, and Tri- angular by Tatineni et.al. 1997), and to speed up calculation time (Rectangular, Trian- gular and Gumbel by Nielsen, 1994). However, no thorough discussions and compara- tive tests of the different distributions seems to have been made.
The paper starts in section 2 with a short review of the link-based SUE. Section 3 dis- cusses desired characteristics for the distributions, e.g. the need for symmetry and repro- ductively. Following this, section 4 accentuates problems with the distributions on small simplified networks while section 5 refers to tests on a Nil-scale model. As conclusion, the paper provides recommendations and guidelines for use of SUE.
Association for European Transport