Traffic analysis, where eavesdroppers retrieve networking information such as source-destination pairs and paths of data flow, severely compromises user privacy and can equip an adversary to launch more powerful network attacks. Anonymous communication, where users exchange information without revealing the communicating parties is essential in any data network. Chaum Mixing, where relay nodes or proxy servers use cryptographic and batching strategies to mask source identities, is a well technique to provide anonymous communication on the Internet. The mathematical analysis of Chaum mixes and the design of mixing strategies have utilized an information theoretic measure of anonymity based on Shannon entropy. In this work, a statistical signal processing framework is proposed to study optimal mixing strategies and the achievable anonymity. Using the detection time of an adversary as a metric, the maximum achievable anonymity of a mix is characterized as a function of its available memory and the allowed rate of dummy transmissions. It is shown that, in the absence of dummy transmissions, the maximum allowable time for anonymous transmission increases quadratically with the buffer size, and for a fixed buffer size, the system approaches perfect unobservability at a rate inversely proportional to the rate of dummy transmissions.