Near-Optimal Stochastic Bin-Packing in Large Service Systems with Time-Varying Item Sizes

TL;DR

This paper introduces a near-optimal scheduling policy for large service systems with jobs having time-varying resource needs, achieving an asymptotic optimality gap of O(√r) in stochastic bin-packing.

Contribution

It proposes the Join-Requesting-Server (JRS) policy for scheduling jobs with Markovian resource variability, providing theoretical guarantees in large-scale systems.

Findings

JRS achieves an O(√r) optimality gap in large systems.

The policy improves upon previous results for constant resource requirements.

A novel policy conversion framework reduces the problem to a single-server analysis.

Abstract

In modern computing systems, jobs' resource requirements often vary over time. Accounting for this temporal variability during job scheduling is essential for meeting performance goals. However, theoretical understanding on how to schedule jobs with time-varying resource requirements is limited. Motivated by this gap, we propose a \emph{new setting} of the stochastic bin-packing problem in service systems that allows for \emph{time-varying} job resource requirements, also referred to as `item sizes' in traditional bin-packing terms. In this setting, a job or `item' must be dispatched to a server or `bin' upon arrival. Its resource requirement may vary over time while in service, following a Markovian assumption. Once the job's service is complete, it departs from the system. Our goal is to minimize the expected number of active servers, or `non-empty bins', in steady state. Under our problem formulation, we develop a job dispatch policy, named Join-Reqesting-Server (JRS). Broadly, JRS lets each server independently evaluate its current job configuration and decide whether to accept additional jobs, balancing the competing objectives of maximizing throughput and minimizing the risk of resource capacity overruns. The JRS dispatcher then utilizes these individual evaluations to decide which server to dispatch each arriving job to. The theoretical performance guarantee of JRS is in the asymptotic regime where the job arrival rate scales large linearly with respect to a scaling factor $r$. We show that JRS achieves an additive optimality gap of $O(\sqrt{r})$ in the objective value, where the optimal objective value is $\Theta(r)$. When specialized to constant job resource requirements, 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 into a single-server problem.