On the SteadyState of Cache Networks

Abstract—A shift has recently begun taking place regarding the manner in which researchers are thinking about network-ing in the Internet. In addition to the traditional host-to-host communication that has endured for more than four decades, many researchers have begun to focus on Content Networking- a networking model in which host-to-content interaction is the norm. A central component of such an architecture is a large-scale interconnected caching system. To date, very little is understood about the way these networks of such caches behave and perform. In this work, we demonstrate that certain cache networks are non-ergodic in that their steady-state characterization depends on the initial state of the system. We then establish several important properties of cache networks, in the form of three sufficient conditions for a cache network to be ergodic. Each property targets a different aspect of the system- topology, admission control and cache replacement policies. Perhaps most importantly we demonstrate that cache replacement can be grouped into equivalence classes, such that the ergodicity (or lack-thereof) of one policy implies the same property holds for all policies in the class. I