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arXiv · 2305.08555

Mean Payoff Optimization for Systems of Periodic Service and Maintenance

David Klaška·Antonín Kučera·Vít Musil·Vojtěch Řehák
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Abstract

Consider oriented graph nodes requiring periodic visits by a service agent. The agent moves among the nodes and receives a payoff for each completed service task, depending on the time elapsed since the previous visit to a node. We consider the problem of finding a suitable schedule for the agent to maximize its long-run average payoff per time unit. We show that the problem of constructing an $\varepsilon$-optimal schedule is PSPACE-hard for every fixed $\varepsilon \geq 0$, and that there exists an optimal periodic schedule of exponential length. We propose randomized finite-memory (RFM) schedules as a compact description of the agent's strategies and design an efficient algorithm for constructing RFM schedules. Furthermore, we construct deterministic periodic schedules by sampling from RFM schedules.

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David Klaška, Antonín Kučera, Vít Musil, Vojtěch Řehák. 2023-05-15. Mean Payoff Optimization for Systems of Periodic Service and Maintenance. https://arxiv.org/abs/2305.08555

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