We apply the Metropolis-Hastings algorithm to efficiently sample from arbitrary paths distributions in a general network. Paths can be generalized into all-day travel plans through, e.g., an appropriate network expansion. The Metropolis-Hastings algorithm creates a Markov chain of paths, which resembles DTA simulations that can also be phrased as Markov chains. A combination of both chains could lead to better understood DTA simulations that avoid the arbitrariness of current choice set generation procedures.