  Performance evaluation of caching systems is an old and widely investigated
research topic. The research community is once again actively working on this
topic because the Internet is evolving towards new transfer modes, which
envisage to cache both contents and instructions within the network. In
particular, there is interest in characterizing multi-cache systems, in which
requests not satisfied by a cache are forwarded to other caches.
  In this field, this paper contributes as follows. First, we devise a simple
but accurate approximate analysis for caches fed by general "renewal" traffic
patterns. Second, we characterize and model the traffic statistics for the
output (miss) stream. Third, we show in the simple example case of tandem
caches how the resulting output stream model can be conveniently exploited to
analyze the performance of subsequent cache stages. The main novelty of our
work stems in the ability to handle traffic patterns beyond the traditional
independent reference model, thus permitting simple assessment of cascade of
caches as well as improved understanding of the phenomena involved in cache
hierarchies.
