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Caching is an important means to scale up the growth of the Internet. Weak consistency is a major approach used in Web caching and has been deployed in various forms. The paper investigates some fundamental properties and performance issues associated with an expiration-based caching system. We focus on a hierarchical caching system based on the time-to-live expiration mechanism and present a basic model for such system. By analyzing the intrinsic timing behavior of the basic model, we derive important performance metrics from the perspectives of the caching system and end users, respectively. Based on the results for the basic model, we introduce threshold-based and randomization-based techniques to enhance and generalize the basic model further. Our results offer some important insights into a hierarchical caching system based on the weak consistency paradigm.