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.