Modeling the sojourn time of items for in-network cache based on LRU policy

To reduce network redundancy, in-network caching is considered in many future Internet architectures, such as Information Centric Networking. In in-network caching system, the item sojourn time of LRU (Least Recently Used) replacement policy is an important issue for two reasons: firstly, LRU is one of the most common used cache policy; secondly, item sojourn time is positively correlated to the hit probability, so this metric parameter could be useful to design the caching system. However, to the best of our knowledge, the sojourn time hasn't been studied theoretically so far. In this paper, we first model the LRU cache policy by Markov chain. Then an approximate closed-form expression of the item expectation sojourn time is provided through the theory of stochastic service system, which is a function of the item request rates and cache size. Finally, extensive simulation results are illustrated to show that the expression is a good approximation of the item sojourn time.