# Communication Infrastructure Design for Reliable UAV Operations in Air Mobility Corridors
## 2 Materials and Methods
### Markov Modeling of Communication Reliability and Estimation of Availability Metrics
#### 2.2.1 Markov State-Transition Diagrams for Different Deployment Strategies  
Strategy 1.  
The system is modeled as a continuous-time Markov chain where each state, \(H_{ij}\), describes the status of a single radio station and the number of UAVs currently connected to it for communication (Figure 6).  
Each system state is denoted as \(H_{ij}\), where \(i\) indicates the failure status of the radio station (0 for operational, 1 for failed), and \(j\) represents the number of UAVs currently engaged in communication within the station's coverage area. The model assumes a maximum number of simultaneously supported UAV sessions, denoted as \(m\).  
Communication requests from UAVs are modeled as a Poisson process with an average interarrival time \(T_{c}\), resulting in an arrival rate of \(\phi=1/T_{c}\). The duration of each communication session follows an exponential distribution with a mean of \(t_{c}\), corresponding to a service rate of \(\psi=1/t_{c}\). The communication load on the system is characterized by the traffic intensity parameter of \(\rho=\phi/\psi\), which indicates the expected number of concurrent sessions in a stable system.  
The reliability of the radio station itself is captured through two additional parameters: the failure rate \(\lambda\), and the repair rate \(\mu\), both expressed as exponential rates. These parameters govern the transitions between the operational and failed states of the re  
Figure 6: Markov chain representation of UAV communication for Strategy 1.  
peater. Together, this set of parameters enables the construction of a two-dimensional continuous-time Markov chain that captures both system availability and communication capacity dynamics.  
Strategy 2.  
The Markov chain shown in Figure 7 models the communication reliability for Strategy 2, where each point in the UAV corridor is simultaneously covered by two independent radio stations. Communication is considered available as long as at least one of the two stations is operational.  
This Markov model accounts for redundant coverage, allowing UAVs to maintain communication even if one station fails. Communication becomes unavailable only in states \(H_{2j},~{}\forall j\), where both radio stations are failed (i.e., \(i=2\)).  
Strategy 3.  
The transition graph shown in Figure 8 models the system behavior under Strategy 3, where radio repeater stations are deployed with alternating redundancy: every second station is duplicated, while others are single. At any given point along the UAV corridor, a UAV may be covered by up to three independent radio stations depending on its position relative to the station layout.  
This model reflects the key feature of Strategy 3--mixed redundancy, where coverage alternates between full, partial, and minimal redundancy based on the position in the corridor. In the worst-case scenario, communication becomes unavailable only when all three covering stations fail, i.e., in states \(H_{3j},\forall j\).  
Strategy 4.  
Figure 8: Markov chain representation of UAV communication for Strategy 3.  
Figure 7: Markov chain representation of UAV communication for Strategy 2.  
The transition graph shown in Figure 9 represents Strategy 4, in which each radio repeater station in the UAV corridor is duplicated, and these stations are placed at intervals of \(R\), providing full overlapping coverage. This means each point in the corridor is simultaneously covered by four independent radio units--two at the current location and two from the adjacent one. The system is designed to provide maximum reliability and remain operational even if multiple stations fail.