Bounded path-size q -product logit stochastic user equilibrium: theory and a path-based MSWA algorithm

Stochastic user equilibrium (SUE) models face three limitations: perception-error variance that does not scale with cost, path-size corrections distorted by unrealistic routes, and exogenous choice sets. We embed the bounded path-size q-product logit (BPSqPL) route-choice model, governed by four parameters, into a network-equilibrium framework, formulated as a variational inequality and solved by a path-based method of successive weighted averages. We prove existence via Brouwer’s theorem and subproblem uniqueness under a sufficient condition (Condition H) on the probability Jacobian. A proposition shows the equilibrium is independent of the initial flow once the active set stabilises, giving verifiable numerical uniqueness. On Sioux Falls, the model degenerates to five classical SUE models, with equilibrium reproducible across 270 parameter combinations within 0.1% maximum link-flow deviation. These persist on Winnipeg (1,052 nodes, 40× demand), where 91.7% of points meet a 1% criterion and aggregate deviations stay below 0.01%, bar one near-degenerate point.