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A new method for identifying the stable state in distributed arbitration schemes as used in modern multiprocessor buses like Futurebus is suggested. It exploits the dependence of the arbitration time on the arbitration numbers. The method allows a reduction in bus acquisition time without considerable changes to the system, for example by more than a factor of 1.3 for Futurebus. This method also improves the performance of standard buses by only introducing individual arbitration delays for bus requestors.