In this paper, we investigate the stochastic stability of linear hyperbolic conservation laws governed by a finite-state Markov chain. Both system matrices and boundary conditions are subject to the Markov switching. The existence and uniqueness of weak solutions are developed for the stochastic hyperbolic initial-boundary value problem. By means of Lyapunov techniques some sufficient conditions are obtained by seeking the balance between the boundary condition and the transition probability of the Markov process. Particularly, boundary feedback control of a stochastic traffic flow model is developed for the freeway transportation system by integrating the on-ramp metering with the speed limit control. (C) 2017 Elsevier Ltd. All rights reserved.