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The authors develop an efficient reduced load fixed-point technique to obtain approximations for blocking probabilities in large multirate loss systems. The point of departure is that for large systems they exploit a single-link approximation based on large deviation techniques for which computational complexity does not scale with the size of the system. The explicit characterisation then allows the authors to prove the convergence of the reduced load fixed point algorithm. The accuracy of the approach is demonstrated on several examples. Comparison of the results to those obtained by the Erlang fixed point and stochastic knapsack methods clearly demonstrate the effectiveness of the approach.