A Coupon Collector based approximation for LRU cache hits under Zipf requests

The Least Recently Used (LRU) policy is widely used in caching, since it is computationally inexpensive and can be implemented ‘on-the-fly.’ However, existing analyses of content- wise hit-rates under LRU have expressions whose complexity grows rapidly with the buffer size. In this paper, we derive a simple yet accurate approximation for the LRU content-wise hitrates under Zipf-distributed requests, in the regime of a large content population. To this end, we map the characteristic time of a content in the LRU policy to the classical Coupon Collector’s Problem (CCP). We justify the accuracy of these approximations by showing analytically that the characteristic time concentrates sharply around its mean. Our bounds highlight and quantify the impact of cache-size scaling as well as the variations in content popularity on the accuracy of the hit-rate estimates. Specifically, we show that these estimates become more accurate with a decrease in Zipf parameter β or an increase in the cache-size scaling. Finally, our analysis of the CCP with Zipf-distributed coupons could be of independent interest.