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Common random numbers and the standard clock method are examples of effective variance reduction techniques that also share information and simulation resources when generating realizations of different simulated systems whose performances are being compared. This sharing of computing resources and the potentially widely different computational requirements for different simulation models are important considerations in allocating simulation replications among the candidate designs with the objective of maximizing the probability of selecting the best design, and we formulate the optimal computing budget allocation problem under this scenario. The resulting formulation leads to an optimization problem that can be viewed as a generalization of a correlated version considered in earlier work. An approximation to the problem is introduced to allow a tractable solution, for which a heuristic two-stage sequential allocation algorithm is proposed, and several numerical examples are used to illustrate the potential improvements that can be gained.