1. A method for designing a communication path to be used according to a service class on a network having a plurality of nodes being able to receive packets to be processed according to a plurality of service classes being different from each other with each of said packets being distinguished from each other and having a plurality of links serving as a transmission path used to establish connection between nodes each receiving packets to be processed according to said plurality of service classes being different from each other, said method comprising; a first step of producing a first constraint expression to be used as a constraint condition for selecting a communication path that satisfies a traffic demand containing requirements for said communication path; a second step of producing a second constraint expression to be used as a constraint condition based on a resource of said network to be shared according to said plurality of service classes; a third step of producing a third constraint expression to be used as a constraint condition based on a resource of said network to be provided according to said plurality of service classes; a fourth step of producing an objective function to be used as a reference for selection of optimized said communication path; and a fifth step of designing said communication path by solving a mathematical programming problem made up of said first constraint expression produced in said first step, said second constraint expression produced in said second step, said third constraint expression produced in said third step, and said objective function produced in said fourth step.