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In this paper, we discuss how to apply a novel and powerful technique -- Ordinal Optimization to the performance analysis issue of Gigabit ATM switching algorithms. In Ordinal Optimization, we focus on the order of the algorithms not their performance values. By doing so, we can achieve great savings in the simulation time. Also we are able to use a simple Surrogate Problem to replace the Original Problem and make the simulation even faster. The essential idea of the Ordinal Optimization is that by asking the soft questions and using Surrogate Problem, we can reduce our computational burden significantly while still obtain fruitful results. We compare eight different scheduling algorithms designed for the switch by simulation. We shows that by using Ordinal Optiniization, we can achieve the speed up of 100 times as compared to the conventional Cardinal Optimization. We employ the concepts of Schedulable Region and Quality of Service that will provide us with a framework for comparison for the different schedulers. We substitute our Original problem with a Surrogate problem that is faster and easier to solve but preserves the relative schedulers' rankings with a confidence probability whose estimates are also provided.