This paper uses trace-driven simulation and synthetic Web workloads to study the request arrival process at each level of a simple Web proxy caching hierarchy. The simulation results show that a Web cache reduces both the peak and the mean request arrival rate for Web traffic workloads. However, the variability of the request arrival pro-cess may either increase, decrease, or remain the same after the cache, depending on the input arrival process and the configuration of the cache. If the input request arrival process is self-similar, then the filtered request arrival process remains self-similar, though with reduced mean. Furthermore, the superposition of Web request streams from multiple child caches results in a bursty aggregate request stream. Finally, we find that a Gamma distribution provides a flexible means of modeling the request arrival count distribution in hierarchical Web caching architectures.