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This paper considers two methods for transmission service to the electric grid users. First, the service in which a transmission system provider is the main decision maker, and the second in which the system users indirectly control flows on the grid by deciding how much demand to exert for system use. In this paper the emphasis is on the process characterization, the assessment of the computational tools for solving the underlying stochastic optimization problems and their interpretation in light of market rules for transmission service in the electric power industry under restructuring. Copyright 2001 IFAC