Designing Ergodic Markov Chains for Sampling Household Schedules

Abstract

In activity-based models with household-level schedule choice, estimating discrete choice models requires realistic alternative schedules beyond those observed in finite samples. We propose a Metropolis–Hastings sampling algorithm for household schedules, grounded in Markov chain Monte Carlo theory. We define a finite schedule state space and a parsimonious set of elementary editing operations that jointly respect (i) spatiotemporal continuity, (ii) household-specific time-window constraints, (iii) asymmetry between licensed drivers and passengers in pick-up/drop-off behavior, and (iv) limits on the number of privately owned vehicles. Using tools from stochastic process theory, we prove that the Markov chain induced by these operations is irreducible. In our finitestate setting, together with the self-loop property of the Metropolis–Hastings kernel, this implies aperiodicity and positive recurrence, thereby establishing ergodicity. The framework provides a rigorous foundation for importance sampling of household schedules in OASIS-type models, enabling efficient estimation and robust policy analysis.