In this paper we investigate the burstiness of the Transmission Control Protocol (TCP) and its impact on a network of finite TCP connections. A detailed TCP and network model is developed to quantify both the burstiness and throughput of TCP connections sharing a single bottleneck router. The range of parameters which are most important when considering burstiness are investigated. We find that under high loads the burstiness of the TCP protocol becomes a less significant performance factor. Extensive simulation is then used to validate our model over a wide range of parameters. 1