A fractional-order approximation framework for stochastic traffic assignment under uncertainty

This study develops a fractional-order approximation framework for static traffic equilibrium under stochastic network-element uncertainty. Random OD demand, link flow, link capacity, or travel time is propagated through nonlinear impedance functions, and non-integer BPR exponents require fractional moments of random variables. To improve upon conventional Taylor expansion, the proposed method combines fractional Taylor expansion with Padé rational approximation and introduces unified control of truncation, Padé, and re-expansion errors. Practical procedures for parameter selection and iterative implementation are also provided. Numerical experiments on the Nguyen and Dupuis and Sioux Falls networks examine stochastic link-flow and link-capacity settings under Gaussian mixture, inverse Gaussian, lognormal, Gamma, Weibull, and Pareto distributions. Results show lower and more stable travel-time approximation errors, more reliable equilibrium path flows and travel times, and higher computational efficiency than Taylor expansion and Monte Carlo sampling, particularly under strict convergence criteria and larger path sets.