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.

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