Motivated by the virtual machine scheduling problem in today's computing systems, we propose a new setting of stochastic bin-packing in service systems that allows the item sizes (job resource requirements) to vary over time. In this setting, items (jobs) arrive to the system, vary their sizes, and depart from the system following certain Markovian assumptions. We focus on minimizing the expected number of non-empty bins (active servers) in steady state, where the expectation in steady state is equal to the long-run time-average with probability $1$ under the Markovian assumptions. Our main result is a policy that achieves an optimality gap of $O(\sqrt{r})$ in the objective, where the optimal objective value is $\Theta(r)$ and $r$ is a scaling factor such that the item arrival intensity scales linearly with it. When specialized to the setting where the item sizes do not vary over time, our result improves upon the state-of-the-art $o(r)$ optimality gap. Our technical approach highlights a novel policy conversion framework that reduces the policy design problem to that in a single-bin (single-server) system.

翻译：受当代计算系统中虚拟机调度问题的启发，我们提出了一种服务系统随机装箱的新设定，允许物品尺寸（作业资源需求）随时间变化。在该设定下，物品（作业）到达系统后尺寸可变，并遵循特定马尔可夫假设离开系统。我们聚焦于稳态下最小化非空容器（活跃服务器）的期望数量，在马尔可夫假设下，该稳态期望以概率$1$等于长期时间平均。主要结果是一个策略，其目标函数的最优间隙为$O(\sqrt{r})$，其中最优目标值为$\Theta(r)$，$r$为缩放因子（物品到达强度与之线性缩放）。当特化为物品尺寸不随时间变化的场景时，我们的结果改进了现有最优间隙$o(r)$。技术方法凸显了一种新型策略转换框架，将策略设计问题简化为单容器（单服务器）系统问题。