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This paper addresses the problem of resource allocation in a multiservice optical network based on an overlapped code-division-multiple-access system. A joint transmission power and overlapping coefficient (transmission rate) allocation strategy is provided via the solution of a constrained convex quadratic optimization problem. The solution of this problem maximizes the aggregate throughput subject to peak laser transmission power constraints. The optimization problem is solved in a closed form, and the resource allocation strategy is simple to implement in an optical network. Simulation results are presented, showing a total agreement between the derived analytical solution and the one obtained using a numerical search method. In addition, analytical and numerical results show that the proposed resource allocation strategy can offer substantial improvement in the system throughput.