We propose a new concept of performance evaluation based on deterministic analysis using inverse functions of the input and output of systems. Traffic theory and queuing theory depend heavily on the probabilistic behavior of systems and users. In general, only the probabilistic features of delay and loss can be obtained by probalisctic arguments. Now many new application, especially streaming servises such as VoIP and Broadcasting over internet, requires a deterministic guarantee of their performance. Hence, many researches start to focus on deterministic analysis such (σ, p)-calculus, where inputs to systems are described by some deterministic manners. In this paper, we use inverse functions of input and output of systems to evaluate its performance. Especially, we apply these concept to the case of multi-inputs sharing an FIFO queue, and evaluate the delay of each input.
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