Classicalnetworkreliabilityproblemsassumebothnetworksandcomponentshaveonlybinarystates,fullyworkingorfullyfailedstates.Butmanyactualnetworksaremulti-state,suchascommunicationnetworksandtransportationnetworks.Thenodesandarcsinthenetworksmaybeinintermediatestateswhicharenotfullyworkingeitherfullyfailed.Asimulationapproachforcomputingthetwo-terminalreliabilityofamulti-statenetworkisdescribed.Two-terminalreliabilityisdefinedastheprobabilitythatdunitsofdemandcanbesuppliedfromthesourcetosinknodesunderthetimethresholdT.Thecapacitiesofarcsmaybeinastochasticstatefollowinganydiscreteorcontinuousdistribution.Thetransmissiontimeofeacharcisalsonotafixednumberbutstochasticaccordingtoitscurrentcapacityanddemand.Tosolvethisproblem,acapacitatedstochasticcolouredPetrinetisproposedformodellingthesystembehaviour.Placesandtransitionsrespectivelystandforthenodesandarcsofanetwork.Capacitatedtransitionandself-modifiedtokencolourwithrouteinformationaredefinedtodescribethemulti-statenetwork.Bythesimulation,thetwo-terminalreliabilityandnodeimportancecanbeestimatedandtheoptimalroutewhosereliabilityishighestcanalsobegiven.Finally,twoexamplesofdifferentkindsofmultistatenetworksaregiven.
