AI 中文总结
本文针对异构HBM系统构建精确多状态可靠性框架，提出TP-mBAT算法并通过实验验证其在存储效率上的显著优势，同时揭示忽略状态间相关性会高估可靠性8.73个百分点。
AI 中文摘要
高带宽内存（HBM）系统可呈现部分服务状态，而非仅全服务或完全隔离：由于子通道隔离、通道重映射或保护开销，控制器可见的服务单元可能提供全带宽、降低后的带宽或零带宽。本文构建了精确多状态可靠性框架，其中每个服务单元承载任意有限带宽状态集，可靠性定义为总提供带宽满足需求的概率。该框架可将二元k-out-of-n模型作为特例，而闭式二元映射误差关系可量化平均带宽失真，并为更简单的抽象提供筛选测试。针对精确单阈值评估，提出了阈值剪枝多状态二进制加法树（TP-mBAT）算法，该算法具有明确的场景特异性：在紧凑公共网格上，固定网格动态规划更适用，其中16单元相称控制仅需273次剪枝动态规划更新，而TP-mBAT需362506次节点访问；在可复现的14单元不相称基准测试中，将TP-mBAT与遵循相同阈值规则的动态规划对比，二者均扩展相同状态空间，分别为6862个节点与6861次更新，差异仅在于保留状态：中心需求处TP-mBAT需17次遍历条目，而动态规划需412121个概率状态，测得峰值存储从25.02 MB降至1152 B；精确概率转移灵敏度可确定将质量从降级状态转移至高带宽状态时，系统成功概率的变化情况，预留单元下限模型允许第三条精确剪枝规则，若无此类下限则该规则无效；潜在封装状态混合捕捉共享应力，忽略相关性会高估可靠性达8.73个百分点。
英文摘要
High Bandwidth Memory (HBM) systems can exhibit partial service rather than only full service or complete isolation: a controller-visible service unit may deliver full, reduced, or zero bandwidth because of sub-channel isolation, lane remapping, or protection overhead. This paper develops an exact multistate reliability framework in which each service unit carries an arbitrary finite set of bandwidth states and reliability is the probability that aggregate delivered bandwidth meets a demand. The binary k-out-of-n model is recovered as a special case, while closed-form binary-mapping error relations quantify mean-bandwidth distortion and provide a screening test for the simpler abstraction. For exact single-threshold evaluation a threshold-pruned multistate Binary-Addition-Tree (TP-mBAT) algorithm is proposed. It is deliberately regime-specific: fixed-grid dynamic programming is preferable on a compact common grid, where a 16-unit commensurate control required 273 pruned-DP updates versus 362,506 TP-mBAT node visits. On a reproducible 14-unit incommensurate benchmark, TP-mBAT is compared against a dynamic program carrying the same threshold rules, so that no baseline is weakened. Both expand the same state space, 6,862 nodes against 6,861 updates, and the separation lies entirely in retained state: 17 traversal entries against 412,121 probability states at central demand, reducing measured peak storage from 25.02 MB to 1,152 B. An exact probability-transfer sensitivity identifies when moving mass from a degraded state to a higher-bandwidth state changes system success, and a reserved-unit floor model admits a third exact pruning rule that is vacuous without such floors. A latent package-state mixture captures shared stress, where ignoring dependence overstates reliability by 8.73 percentage points.
