Elastic paging

Abstract

We study a generalization of the classic paging problem where memory capacity can vary over time -a property of many modern computing realities, from cloud computing to multi-core and energy-optimized processors. We show that good performance in the "classic" case provides no performance guarantees when memory capacity fluctuates: roughly speaking, moving from static to dynamic capacity can mean the difference between optimality within a factor 2 in space, time and energy, and suboptimality by an arbitrarily large factor. Surprisingly, several classic paging algorithms still perform remarkably well, maintaining that factor 2 optimality even if faced with adversarial capacity fluctuations -without taking those fluctuations into explicit account!

Online Caching with Convex Costs

“…Accordingly, much research has been devoted to understand and analyze caching algorithms that work well in practice [4,1,17]. Recently, there has been some interest in developing caching algorithms for cloud computing scenarios [18,5]. The latter references consider scenarios where the memory available to an algorithm can vary over time.…”

Tight Bounds for Parallel Paging and Green Paging

“…Related Work on Green Paging. The last decade has seen a surge in interest for paging models where memory capacity is not static, but can instead change over time [2,4,5,9,14,21,25,26]. One justification for such models is the increased popularity of virtualization/cloud services: the amount of physical memory allotted to a specific virtual machine often varies considerably over time based on the number and priority of other virtual machines supported by the same hardware.…”

“…This problem has been investigated by López-Ortiz and Salinger [21] and later, in the more general version where pages have sizes and weights, by Gupta et al [14]. Subsequent work, and in particular the elastic paging of [25,26], showed that one can effectively decouple page replacement from memory allocation: even if the latter is chosen adversarially, LFD is still optimal, and a number of well-known paging algorithms like LRU or FIFO are optimally competitive, with a competitive ratio that is extremely close albeit not quite equal to the classic k/(k − h + 1). A similar line was taken by adaptive caching [5] with a slightly different cost model.…”

“…A similar line was taken by adaptive caching [5] with a slightly different cost model. These results [5,25,26] imply that green paging is a problem of memory allocation: once memory is allocated, one can simply use LRU for page replacement-as its cost will be within a factor O(1) of the optimal (for that memory allocation).…”