List-based caches can offer lower miss rates than single-list caches, but their analysis is challenging due to state space explosion. In this setting, we propose novel methods to analyze performance for a general class of list-based caches with tree structure, non-uniform access to items and lists, and random or first-in first-out replacement policies. Even though the underlying Markov process is shown to admit a product-form solution, this is difficult to exploit for large caches. Thus, we develop novel approximations for cache performance metrics, in particular by means of a singular perturbation method and a refined mean field approximation. We compare the accuracy of these approaches to simulations, finding that our new methods rapidly converge to the equilibrium distribution as the number of items and the cache capacity grow in a fixed ratio. We find that they are much more accurate than fixed point methods similar to prior work, with mean average errors typically below 1.5% even for very small caches. Our models are also generalized to account for synchronous requests, fetch latency, and item sizes, extending the applicability of approximations for list-based caches.

中文翻译：

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具有非一致访问的基于列表的缓存的性能分析方法

基于列表的缓存可以提供比单列表缓存更低的未命中率，但是由于状态空间的爆炸性，它们的分析具有挑战性。在这种情况下，我们提出了新颖的方法来分析具有树结构，对项目和列表的非均匀访问以及随机或先进先出替换策略的基于列表的缓存的一般类的性能。即使底层的马尔可夫过程已被证明可以接受产品形式的解决方案，但是对于大型缓存而言，这很难利用。因此，我们针对缓存性能指标开发了新颖的近似值，尤其是借助奇异摄动方法和精确的平均场近似值。我们比较了这些方法进行仿真的准确性，发现随着项目数量和缓存容量以固定比率增长，我们的新方法迅速收敛到平衡分布。我们发现它们比定点方法要精确得多，类似于先前的工作，即使对于非常小的缓存，平均平均错误也通常低于1.5％。我们的模型也被通用化以解决同步请求，获取延迟和项目大小，从而扩展了基于列表的缓存的近似适用性。