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Piecewise polynomials have been used to visually link and classify network traffic. The advantage of using piecewise polynomials to approximate traffic is that significantly less storage space is required when compared to traditional packet captures. However, when representing discrete data with continuous approximations, error is introduced. We analyze this error through the creation and examination of polynomials for client, server, and bidirectional traffic, where each polynomial represents a single TCP connection. An application of the piecewise polynomial technique is traffic classification. In this initial work, we use traffic attributes of packet length and arrival time to represent Instant Messaging, Video, and Basic Web Page traffic. We then examine the error introduced by using polynomials to represent each of these traffic types. The initial results also show that this technique can reduce standard packet trace sizes by up to four orders of magnitude. An understanding of the error involved and the amount of memory saved by using this technique is a necessary step toward an automated process for traffic classification that utilizes piecewise polynomial approximations.