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For integrated service systems supporting real-time (RT) and non-real-time (NRT) traffic, evaluating the performance of the NRT traffic is often challenging. An approximation based on a fluid model - the so-called Fluid Approximation (FA) - can be used when RT traffic has much larger successful call arrival rate than the NRT traffic, while otherwise it may introduce errors. In this paper, we propose a Generalized Fluid Approximation (GFA), extending the use and improving the accuracy of FA. It can also be used to trade off the computational complexity and the accuracy. Benefits achieved by GFA are demonstrated by extensive numerical examples.