Optimizing Server Locations in Spatial Queues: Parametric and Nonparametric Bayesian Optimization
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909915061157888 |
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| author | Hua, Cheng Swersey, Arthur J. Xing, Wenqian Zhang, Yi |
| author_facet | Hua, Cheng Swersey, Arthur J. Xing, Wenqian Zhang, Yi |
| contents | This paper presents a new model for solving the optimal server location problem in a spatial hypercube queueing model. Unlike deterministic location models, our approach accounts for server availability, varying utilization levels, and dependencies across servers. We prove that the problem is NP-hard and establish lower and upper bounds, as well as asymptotic results, by relating it to special cases of the classical $p$-Median problem. To address the computational challenge, we propose two Bayesian optimization approaches: (i) a parametric approach based on a sparse Bayesian linear model with second-order interactions, and (ii) a nonparametric approach using a Gaussian process surrogate with the $p$-Median objective as the prior mean function. We prove that both methods achieve sublinear regret and converge to the optimal solution. Numerical experiments and a case study using real-world data from the St. Paul, Minnesota, emergency response system show that our approaches consistently identify optimal solutions and outperform all baseline methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22249 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimizing Server Locations in Spatial Queues: Parametric and Nonparametric Bayesian Optimization Hua, Cheng Swersey, Arthur J. Xing, Wenqian Zhang, Yi Optimization and Control This paper presents a new model for solving the optimal server location problem in a spatial hypercube queueing model. Unlike deterministic location models, our approach accounts for server availability, varying utilization levels, and dependencies across servers. We prove that the problem is NP-hard and establish lower and upper bounds, as well as asymptotic results, by relating it to special cases of the classical $p$-Median problem. To address the computational challenge, we propose two Bayesian optimization approaches: (i) a parametric approach based on a sparse Bayesian linear model with second-order interactions, and (ii) a nonparametric approach using a Gaussian process surrogate with the $p$-Median objective as the prior mean function. We prove that both methods achieve sublinear regret and converge to the optimal solution. Numerical experiments and a case study using real-world data from the St. Paul, Minnesota, emergency response system show that our approaches consistently identify optimal solutions and outperform all baseline methods. |
| title | Optimizing Server Locations in Spatial Queues: Parametric and Nonparametric Bayesian Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2505.22249 |