In flow-based mix networks, flow correlation attacks have been proposed earlier and have been shown empirically to seriously degrade mix-based anonymous communication systems. In this paper, we theoretically analyze the effectiveness of a mix network under flow correlation attacks. Our formulae clearly show how a mix network will ultimately fail when an adversary has access to sufficiently long flow samples, independently of the type of flows (TCP or UDP). We illustrate the analysis methodology by modelling a continuous-time mix, which randomly delays each incoming packet. Our queuing-model-based analysis can provide useful guidelines for designers who develop and deploy anonymity systems.