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arXiv · 2509.25556

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

Mohammad Merati·David Castañón
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Abstract

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.

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BibTeXRIS

Mohammad Merati, David Castañón. 2025-09-29. Exhaustive-Serve-Longest Control for Multi-robot Scheduling Systems. https://arxiv.org/abs/2509.25556

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