This paper deals with a main limitation of Markovian traffic assignment (MTA) models: when the network includes cyclic structures and the link costs are small enough, the fact that the MTA models assign traffic flows to all feasible paths causes computational challenges. This study addresses this issue by proposing a method of restricting path set based on the concept of choice-based prism. To achieve a prism-based path set, a novel network description and the constraints are introduced. These are flexible and compatible with the MTA operation, meaning that our method does not extinguish the mathematical and computational advantages of the MTA models. Our network description allows the expected minimum cost to take a value specific for each state, or a pair of node and choice-stage. This enables us to perform traffic assignment with a simple solution procedure, regardless of parameter setting or network structure. The numerical experiments show that our method solves the computational challenges of the MTA models and that the incorporation of the prism constraints does not increase computational effort required, or rather, it is computationally efficient even when considering the correlation among path utilities. (C) 2019 Elsevier Ltd. All rights reserved.