Deployment of Single Board Computer Mesh Networks for Remote Cyber Operations

Operators can buy commercial-off-the-shelf (COTS) single board computers (SBCs) cheaply, off the shelf, and on short notice, without waiting on a lengthy development cycle. Networked together, these devices deliver flexible communication and cyber capabilities. Three constraints shape how operators use them: battery life, physical stealth, and radio-frequency (RF) stealth. Batteries matter because operators emplace mesh networks forward, in hostile terrain, with no chance to recharge. Stealth—both physical and RF— matters because exposure is costly. An adversary who spots a device on patrol or direction-finds its signal through signals intelligence not only neutralizes it, but also can infer friendly intent and capability in the area.

Optimal placement of SBC devices can enable lower cost, increased stealth, and longer battery life while ensuring coverage of the target area. This paper presents a two-phase decision framework to find and test optimal placement. Phase I formulates an integer set-cover problem minimizing the number of deployed SBC devices while enforcing full coverage of all demand locations, a maximum effective range constraint, a soft minimum range constraint for stealth, and a 2-edge-connectivity requirement on the resulting communication network. This model often leads to numerous equally optimal solutions that cannot be solved with linear programming. We must use the simulation in Phase II to evaluate the candidate solutions under stochastic conditions to include random target arrival, distance-dependent effect probabilities, and energy depletion from both active engagements and passive battery drain. The simulation produces a comparative table of operational metrics including average engagement rate, energy cost per engagement, and average time to system failure, enabling operators to make an informed selection among placements that the integer program alone cannot distinguish.

Determining where to place a finite set of networked devices to serve a defined operational area is a foundational problem in operations research and graph theory. The SBC mesh-placement problem addressed in this paper is a member of this family, and the literature most directly relevant to it is the node-placement work in wireless sensor networks: research driven by reducing coverage gaps that leave portions of the target area unaddressed and excessive redundancy that drives up cost, radio-frequency signature, and battery load without operational benefit. This problem extends past the frame of wireless sensor networks to the broader topic of facility location. Toregas et al. (1971) used the set-cover problem to find optimal placement of emergency services locations. The set-cover problem takes a set of candidate locations and a set of demand locations as input, and selects the smallest subset of candidates such that every demand location is covered by at least one selected candidate. With binary decision variables indicating which candidates are chosen, the problem is formulated as a 0–1 integer program and can be solved with standard optimization software. Kumari and Srirangarajan (2024) extended this approach to wireless sensor networks by defining a mixed-integer linear program that jointly places static and mobile nodes to achieve full area coverage. They weighted boundary cells higher to drive static-node coverage towards the edges, while mobile nodes handle central cells, establishing integer programming as a valid method of finding efficient placements of static nodes.

Li et al. (2009) emphasized that minimizing the number of nodes is important for reducing the total dollar and energy cost of the network similar to our goal. However, a wireless sensor network (WSN) that covers its target area is not necessarily resilient. A network is “k-vertex-connected” if each node in the network can communicate with each other node even if k – 1 nodes are removed. Joint optimization of coverage and k-vertex-connectivity has been studied in the WSN literature: Li et al. (2007) formulate the k-vertex-connected target coverage problem, in which a minimum set of sensors must both cover every target and induce a k-vertex-connected communication graph. Similarly, a network is “k-edge-connected” if each node in the network can communicate with each other node even if k – 1 communication links are removed. The higher the k value, the more fault tolerant the network is. This paper adopts k-edge-connectivity as opposed to vertex-connectivity to model the possibility of a communications disrupted environment that may cause link-level outages due to signal jamming and not device-level outages.

Where optimization models produce feasible placements, simulation can evaluate how those placements perform under uncertain operating conditions. Hyink (2007) defined a discrete event simulation to model performance of different defensive strategies against a vehicle mounted weapon of mass destruction within the greater Washington, D.C. area. The paper used geospatial data to create a graph of vertices and edges which represents the actual road layout of the city. Detection probability was driven by a function of the speed of the vehicles and their distance separation at the time of encounter. This provides a precedent for simulation as a means of evaluating different candidate placements.

In the case of a WSN designed to deliver cyber capabilities against targets, we must apply a targeting framework to give structure to the engagement process. Joint Publication 3-60: Joint Targeting defines the targeting steps as find, fix, track, target, engage, and assess. The detect-track-engage framework used in the simulation section of this paper is abstracted from this doctrinal cycle to model an SBC’s interaction with moving targets rapidly entering and leaving their range.

Optimization-based and simulation-based approaches to wireless sensor network deployment have developed largely in parallel. The optimization literature produces feasible placements but treats performance as out of scope. Similarly, the simulation literature evaluates pre-specified placements but does not generate them. This paper closes that gap by coupling a set-cover integer program, extended with a soft minimum-range stealth penalty and a 2-edge-connectivity requirement on the inter-node communication graph, with a discrete-time simulation that generates actionable metrics under stochastic target arrivals, distance-dependent effect probabilities, and battery depletion. The result is a single workflow that takes a target area and candidate location set as input and delivers an evaluable set of feasible deployment plans as output.

We utilize a two-phase process to aid operators to make informed decisions about SBC placement. Phase I, the integer optimization model, begins with a preprocessing step where the operator overlays the target area with a two-dimensional grid and extracts two sets of points within it — the demand locations the wireless effect must reach, identified from mission requirements, and the candidate locations where an SBC could feasibly be emplaced, identified from satellite imagery or geospatial data. The distance between every candidate and every demand is then precomputed, producing the finite network on which the remaining stages operate. Phase I treats this network as a set-cover problem and selects the smallest subset of candidate locations that satisfies coverage, range, stealth, and communication-resilience requirements. Because the formulation typically admits more than one optimal placement, Phase II evaluates each equally optimal solution through a discrete-time stochastic simulation that exercises it against randomly arriving moving targets, distance-dependent action outcomes, and battery depletion. This enables easy comparison between the set of equally optimal solutions.

Phase I: Integer Programming Model

The goal of Phase I is to generate efficient solutions given a target area and candidate areas. An efficient solution is one that places the minimum number of SBCs to ensure full coverage, with a stealth penalty. Efficient solutions are generated through an integer program. The sets, parameters, variables, and decision variables are defined below in Table 1.

Table 1. Notation Description

This model uses integer programming to solve the set-cover problem and find optimal placement of SBC devices to ensure full coverage of all demand locations while considering detection range, stealth, and communication reliability. The objective function of the model, Equation 1, is to minimize the number of SBC devices, while accounting for a stealth penalty.

The penalty weight for violating the minimum distance soft constraint, α, is multiplied by the distance amount of violation. This means that the larger the violation, the higher the penalty. Alpha is a parameter that must be tuned based on mission requirements and the characteristics of every individual objective.

Equation 3 is used for determining whether there is a “connection” between individual demand and candidate locations. This is based on the distance calculations from the preprocessing step.

The first constraint in the model, Equation 4, is to ensure that all demand locations are covered. This is what classifies our case as a set-cover problem. We must cover all demand locations because we can never be sure of the exact disposition and strength of enemy capabilities. Our method is robust because we cover all potential locations of enemy equipment, ensuring that our capabilities can be delivered throughout the entire target area. Based on capability testing of the SBC device, a single degree of coverage was determined to be sufficient.

The second constraint, Equation 5, enforces the maximum detection and cyber capability range of our SBC devices. This constraint ensures that we can reliably deliver wireless cyber capabilities on our target, without fear of being out of range. We use X_tc,tm so we can “turn on” this constraint only when we have determined that there should be a connection between the individual candidate location and the individual demand location.

Our third constraint, Equation 6, is our soft minimum range constraint. The goal of this constraint is to ensure our SBC devices are not easily seen from the demand locations. However, sometimes placing a device further away means that it is in a less ideal place. By framing it as a soft constraint, we can allow placement where the device is very close to the demand location only if this allows the device to be in a significantly more advantageous location.

The final constraint, Equation 7, says that candidate locations can only cover demand locations if they are selected. This means that we only consider the connection between candidate locations and demand locations if we choose to place an SBC device in that candidate location.

The first step of running the model is to discretize the space into a two-dimensional grid. Within this grid, demand locations are placed based on mission requirements. These locations must be “covered” by at least one SBC device which can detect and affect signals at that location. We then determine a set of candidate locations where SBC devices may be placed. These locations can be determined by operators using satellite images or geospatial data.

We then precompute the distance between every candidate location tc and demand location tm. This allows us to conduct a feasibility check before initiating the Gurobi solver. The feasibility check returns an error if there is a demand location that cannot be covered by any candidate locations.
The next step is to run the Gurobi solver which returns the optimal objective, the number of solutions with that objective, and the indices of SBC devices for all equally optimal solutions. Depending on the scenario, this could result in many potential solutions. We can narrow down these feasible solutions by considering our communication range. In order to create a robust mesh communication network, we set the minimum edge connectivity of the network to be greater than or equal to two. This means that it would take at least two connections to break before any single node can be disconnected from the others. This creates a communication network that is resilient to unpredictable circumstances such as a communications denied, degraded, intermittent, or limited environment. Additionally, it reduces the number of feasible solutions and gives operators a more reasonable choice in which layout to select.

However, there are many situations where the number of equally efficient solutions is too high or the solutions are too complicated to meaningfully distinguish between them, as seen in Figure 1 below. This leaves operators guessing which solution would be truly best. To solve this problem, we created the simulation in Phase II.

Figure 1. Equally Optimal Solutions of an Illustrative Situation

Phase II: Simulation

This discrete-time simulation tests the efficient solutions generated in Phase I under stochastic conditions using object-oriented programming in Python, which allows each target and each SBC device to be considered individually. Simulation allows solutions to be compared using moving targets, which cannot be represented in the integer program. The output of the simulation is a table of summary statistics used to evaluate differences between the equally efficient solutions. At its current state, the parameters in this simulation such as maximum range of the SBC devices and battery drain of actions are assumed due to the inability to conduct robust testing in real-life. Additionally, many of these parameters must be tuned as, for example, the maximum range of SBCs depends on the type of antenna used and the environment (open areas, wooded areas, cities, etc.)

The simulation defines two object classes. One for the SBC devices and one for the Targets. The SBC device attributes include locations in Cartesian coordinates corresponding to the solution being evaluated, an identification number used to track performance through the simulation. Additionally, maximum range, capacity, and battery drain by action are defined as parameters so they can be changed based on different systems that are being tested. Capacity of a device is the number of targets it can detect, track, or attack simultaneously.

Targets are similarly given coordinates and an identification number, plus a speed. This speed is assigned on arrival using a uniform distribution between one and two to represent different types of targets such as someone walking, a vehicle, or a drone. Speed is a scalar quantity as all targets follow the same predetermined path through the simulation.

The simulation class controls the actions. The first step is to create the scene by adding each SBC device at its pre-decided position. If there is at least one SBC device with remaining battery and a set end time has not been reached, the simulation will continue to run. At each time step, a target has a chance of arriving into the system based on random chance. A uniform random number between zero and one is generated using the Python Random module and if the number falls above a set threshold, a target arrives. Distances between each target and each SBC device are calculated to determine which targets are in range. If a target is in range for a given SBC, the SBC will first attempt to detect it, then track it, and finally engage it. This detect-track-engage framework is based on the Joint Publication 3-60: Joint Targeting framework. Each action runs a subroutine to determine success or failure based on the distance between the target and SBC, where smaller distances equate to higher chances of success. Probability of success is defined as and is compared to a uniform random number between zero and one. If the probability of success is higher than the random number, the track or engagement is successful. If a track or engagement fails, the SBC must attempt to redetect the target before retrying the tracking or engagement step. The simulation keeps track of which targets are currently detected, tracked, or engaged, as well as their start and exit time from the simulation through the Event Log (Table 2).

Table 2. Illustrative Event Log

At each time step, the simulation completes one of the targeting actions and the targets move forward along a fixed path with a distance determined by their speed. SBCs will attempt to detect, track, and engage each target in its area until the target leaves. Each action will cost the SBC a portion of battery percentage. The SBCs also have a set battery drain of .01 percentage points per second, which is adjustable. All actions and battery statuses are captured in another event log called SBC Log (Table 3). The simulation concludes after a set time or all the SBCs run out of battery. At this point, the event log is finalized and summarized. From the summarized log, we can gain insight into the performance of the system. For each SBC, we can determine its final battery percentage, number of detections, tracks, and engagements, as well as the number of times these actions failed. This log can be found in Table 3 below.

Table 3. Illustrative SBC Log

For each target, we can determine its speed and the number of times it was detected, tracked, and engaged. This log can be found in Table 4 below.

Table 4. Illustrative Target Log

Through many simulations, we can determine the average time to failure, earliest system failure, energy cost per engagement, average detection rate, and average engagement rate. These metrics allow the different equally efficient solutions to be more easily compared based on goals. High success rate solutions may come at the cost of average time to failure and vice versa. An example of the final comparison table can be found below in Table 5.

Table 5. Illustrative Comparison Table

This paper presents a two-phase framework for the placement and operational evaluation of SBC devices in a tactical wireless sensor network. Phase I formulates a set-cover integer program enforcing full coverage, maximum range constraints, a stealth-motivated soft minimum range constraint, and a 2-edge-connectivity on the communication between devices. This formulation reliably produces a set of equally efficient solutions that satisfy all hard constraints at minimum node count. Phase II introduces a simulation that evaluates those solutions under stochastic conditions, modeling random target arrivals, action success as a function of target-to-SBC distance, and battery depletion from both engagement actions and passive drain. Through many runs of the simulation, summary metrics including average time to system failure, average engagement rate, and energy cost per engagement are calculated to enable quantitative differentiation among solutions the optimizer treats as equivalent.

A lack of three-dimensional consideration in the Phase I optimization model represents a meaningful limitation in environments with significant terrain variation. The current formulation computes inter-node and node-to-demand distances using two-dimensional Euclidean geometry, treating the operational area as a flat plane. In practice, line-of-sight obstructions introduced by terrain features such as ridgelines, valleys, and dense urban structures directly affect both the maximum effective range of SBC devices and the reliability of inter-node communication links. Consequently, solutions that satisfy all constraints under the current formulation may prove infeasible or significantly degraded when deployed in non-planar environments.

Phase II is limited by the lack of testing to determine maximum range, per-action battery drain, and passive discharge rate. Currently, these parameters are theoretical. Additionally, these parameters are sensitive to antenna type and deployment environment and must be updated as field testing data becomes available.

Future work should incorporate geospatial elevation data into the distance computation and replace the Euclidean range constraint with a line-of-sight feasibility check, ensuring that candidate placements are evaluated against terrain-realistic communication and coverage conditions. Secondly, further field testing of the SBC device will enable calibration of simulation parameters. Finally, simulation features and complexity can be increased to better simulate real-world conditions. This will bridge the gap between theoretical optimization and operational reality.

The author thanks LTC Jamie Grymes and CPT(P) William “Jamie” Reynolds of the Department of Mathematical Sciences at the United States Military Academy for their guidance, technical feedback, and continued support throughout the development of this research. Their mentorship shaped both the optimization formulation in Phase I and the simulation design in Phase II. The views expressed in this paper are those of the author and do not necessarily reflect the official policy or position of the United States Military Academy, the Department of the Army, the Department of Defense, or the U.S. Government.

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