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：受当前计算系统中虚拟机调度问题的启发，我们提出了一种允许物品尺寸（作业资源需求）随时间变化的服务系统随机装箱新设置。在此设置中，物品（作业）到达系统后其尺寸发生变化，并在特定马尔可夫假设下离开系统。我们重点最小化稳态下非空容器（活动服务器）的期望数量，其中在马尔可夫假设下稳态期望以概率1等于长期时间平均值。我们的主要成果是一种策略，该策略在目标函数上实现了$O(\sqrt{r})$的最优性差距，其中最优目标值为$\Theta(r)$，$r$为缩放因子，且物品到达强度随其线性缩放。当特化为物品尺寸不随时间变化的场景时，我们的结果改进了当前最优的$o(r)$最优性差距。我们的技术方法揭示了一种新颖的策略转换框架，可将策略设计问题简化为单容器（单服务器）系统中的问题。