Maritime fleet tracking is a critical piece of naval operations. Leveraging the inherent spatial and temporal autocorrelation of vessels in a fleet, we use spatio-temporal Kriging, an interpolation technique, to estimate the likelihood of finding a vessel at a specific location. This estimation is based solely on the current and/or past locations of. other vessels within the fleet. We do this by first fitting covariance models to observed fleet movements. We then use spatio-temporal indicator Kriging to forecast the locations of vessels in a fleet at different times, with or without new information. Our results indicate a notable improvement in accuracy, ranging from 60 to 90% compared to a baseline model. We measure accuracy using ROC AUC values. Furthermore, our study reveals that tracking only a subset of vessels within a fleet significantly enhances understanding of the entire fleet’s movements. However, the number of vessels that needs to be tracked increases as we move further from the last observation of the entire fleet. Future extensions of our work include integrating additional situational information, using other spatio-temporal interpolation techniques, and expanding its application beyond maritime fleets.

We study the unmanned aerial vehicle (UAV) route planning problem for information collection missions performed in terrains with stochastic attributes. Uncertainty is associated with the availability of information, the effectiveness of the search and collection sensors the UAV carries, and the flight time required to travel between target regions in the mission terrain. Additionally, uncertainties in flight duration vary the detection threat exposed in missions performed in nonfriendly terrains. We develop a mixed integer programming model to maximize the expected information collection while limiting the risks of not completing the mission on time and of being detected and restricting the variance imposed on flight duration. The model allows multiple path alternatives between target pairs and revisits to the same target regions. Computational experiments are performed on randomly generated instances to investigate the impact of problem parameters and mission restrictions. We also develop a case study with a military and a civilian application, each of which with different specifications. In addition, we validate that the actual performance of the optimal solution of the model is close to the result reported by the solver via a simulation study. We conclude that the developed model is robust and can be used for practical-sized missions, and the failure rate of its optimal routes in actual missions is negligibly small. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplementary Information [ https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.1245 ] or is available from the IJOC GitHub software repository ( https://github.com/INFORMSJoC ) at [ http://dx.doi.org/10.5281/zenodo.7055494 .

Abstract In this paper, we study several statistical properties regarding the distance between events that take place on random locations along the edges of a given network. We derive analytical expressions for the arbitrary moments of such a distance, its probability density function, its cumulative distribution function, as well as their conditional counterparts for the cases in which the position of one event is known in advance. As part of this study, we implement our developments as a callable library for the Python language, to provide potential users with a computational engine able to calculate and visualize these statistics for any given network. We test our implementation on several networks of different sizes and topologies, analyze some of interesting properties we observed in our experiments, and discuss several applications for our proposed methodology. In particular, we focus our discussion on applications aimed to help with the optimal design of emergency response systems on infrastructure networks.

This paper considers the p-median problem on a general network with link demands. We construct the network in such a way that only transportation intersections are taken to be nodes and, therefore, both continuous and discrete link demands are allowed in our model. For such a model, we show that a nodal solution can be used to approximate the true optimal solution and an error bound which involves only the demands on a single link is given for the error caused by such an approximation. Based on nodal solutions, we demonstrate that a model with continuous link demands can be transformed into an equivalent discrete link demand model. Further, we propose a method to aggregate demands on each link in solving the p-median problem on a general network without introducing any aggregation errors to the problem solution. The implementation of the proposed approach with some heuristics is discussed. © 2000 John Wiley & Sons, Inc.

Abstract In this article, we study the problem of locating a server on a tree network that operates as a FIFO M/G/1 queue. The goal is to identify sets of efficient facility locations with respect to moments of the response time. The results are illustrated via an example. © 1993 by John Wiley & Sons, Inc.

Abstract This paper considers the problem of locating a single facility on a network that operates as an M/G/k queue, in which the average queueing delay is approximated by using a result in Nozaki and Ross [J. Appl. Prob. 15 (1978) 826–834]. Special consideration is given to the case of a tree network. Localization and sensitivity results are provided, together with appropriate intuitive explanations. We present an illustrative numerical example and provide a brief discussion of our computational experiences with the model. We also use discrete‐event simulation to test the effectiveness of the Nozaki and Ross approximation in the context of finding a good facility location—our results indicate that their approximation is adequate for this purpose.

Abstract This paper considers the problem of locating a single server on a network, relaxing the assumption that the server is always available for service, and explicitly accounting for queueing. The resulting queueing‐location model allows for an arbitrary number of priority classes. Properties of the objective function are developed and algorithms presented for obtaining the optimal location on tree and cyclic networks. Sensitivity analysis with respect to the average arrival rate of calls is investigated. A numerical example is presented to illustrate the results of this paper. The major conclusions of the paper include: (a) the optimal location need not be at a node of the network, (b) the optimal location changes as a function of the arrival rate of calls into the system, (c) the optimal location is usually different from that obtained by grouping all calls into one priority class.