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

Mohammad Merati, David Castañón

TL;DR

This work addresses online task allocation for multi-robot systems with multiple locations, stochastic Bernoulli arrivals, and one-slot switching delays. By formulating a discounted-cost MDP and proving structural optimality results, the authors establish Exhaustive-Serve-Longest (ESL) as an optimal feedback policy under symmetry: robots serve exhaustively at their current nonempty location and switch to the longest unoccupied nonempty location when idle. Through simulations, ESL consistently outperforms baselines (FCFS and Cyclic) across different robot-to-location ratios and traffic loads, achieving lower discounted costs and shorter queues while maintaining a higher serving fraction with restrained switching. The findings support ESL as a practical default for real-time multi-robot scheduling, with future work exploring asymmetries and learning-augmented variants.

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.

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

TL;DR

This work addresses online task allocation for multi-robot systems with multiple locations, stochastic Bernoulli arrivals, and one-slot switching delays. By formulating a discounted-cost MDP and proving structural optimality results, the authors establish Exhaustive-Serve-Longest (ESL) as an optimal feedback policy under symmetry: robots serve exhaustively at their current nonempty location and switch to the longest unoccupied nonempty location when idle. Through simulations, ESL consistently outperforms baselines (FCFS and Cyclic) across different robot-to-location ratios and traffic loads, achieving lower discounted costs and shorter queues while maintaining a higher serving fraction with restrained switching. The findings support ESL as a practical default for real-time multi-robot scheduling, with future work exploring asymmetries and learning-augmented variants.

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.

Paper Structure

This paper contains 12 sections, 7 theorems, 37 equations, 1 figure, 2 tables.

Table of Contents

  1. INTRODUCTION
  2. Problem Formulation
  3. System description
  4. State dynamics
  5. Performance criterion
  6. Exhaustive Service and Switch-on-Empty
  7. Experiments and results
  8. Simulation Scenarios
  9. Evaluation Metrics
  10. Results
  11. CONCLUSIONS
  12. APPENDIX

Key Result

Proposition 1

Consider the $M$–robots, $N$–locations model. Let $g$ be any stationary deterministic policy under which, at some decision epoch and state a particular robot $r$ is located at location $i$ with $x_i>0$ and $g$ either switches$r$ away from $i$ or idles$r$. Then $g$ is strictly suboptimal.

Figures (1)

  • Figure 1: Policy comparison across loads $\alpha\in\{0.2,0.5,0.8\}$ for two robot–location ratios. Columns: discounted cost, mean queue length, action fractions. Top row: $M=2$; bottom row: $M=3$.

Theorems & Definitions (14)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Proposition 3
  • proof
  • Corollary 3.1
  • proof
  • Corollary 3.2
  • proof
  • ...and 4 more