# Exhaustive-Serve-Longest Control for Multi-robot Scheduling Systems

arXiv: https://arxiv.org/abs/2509.25556 · HTML: https://mlsanity.com/paper/2509.25556/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Sep 2025.

## Built on by (most cited first, 1 of 1)

- [Multi-Robot Multi-Queue Control via Exhaustive Assignment Actor-Critic Learning](https://mlsanity.com/paper/2604.03605/) (2026)

## Abstract (arXiv)

We study online task allocation for multi-robot, multi-queue systems with stochastic arrivals and switching delays. Time is slotted; each location can host at most one robot per slot; service consumes one slot; switching between locations incurs a one-slot travel delay; and arrivals are independent Bernoulli processes. We formulate a discounted-cost Markov decision process and propose Exhaustive-Serve-Longest (ESL), a simple real-time policy that serves exhaustively when the current location is nonempty and, when idle, switches to a longest unoccupied nonempty location, and we prove the optimality of this policy. As baselines, we tune a fixed-dwell cyclic policy via a discrete-time delay expression and implement a first-come-first-serve policy. Across server-to-location ratios and loads, ESL consistently yields lower discounted holding cost and smaller mean queue lengths, with action-time fractions showing more serving and restrained switching. Its simplicity and robustness make ESL a practical default for real-time multi-robot scheduling systems.