# Erlang-U: Blocking Probability of UAV-Assisted Cellular Systems
## 6 Conclusions  
In this work, we analyzed, studied, and evaluated the blocking probability and average number of dropped calls of a UAV-assisted cellular system, considering that UAV temporarily provides additional channels whenever the traffic load increases in the coverage area. To this end, we develop the ErlangU formula that considers the main dynamics of the system, namely, arrivals and departures of voice calls, and the arrival and dwelling times of the drones. We provide clear guidelines for the design of the system by clearly calculating the number of fixed channels, \(S\), provided by the base station and mobile channels, \(M\), and also provided by the UAV to attain a target blocking probability. We can observe that as the number of mobile channels and/or the dwelling times of the drones increase, the blocking probability reduces. Hence, the system administrator can determine the adequate number of channels, capabilities of the drone to offer an adequate service, or even if more than one drone would be needed, reducing the average drone inter-arrival times. Also, we investigated the impact of the average dwelling times of the UAV and required time to reach the region of interest by introducing the UAV _traffic load_, \(a_{D}\). This is a helpful parameter to adequately choose the UAV specifications, since the flight time is  
Figure 5: Fraction between calls that are forced to finish, and the total offered calls for different UAV traffic load and additional channels provided by the UAV, \(M\).  
Figure 6: Portion of time that the drone is serving the cellular system for different UAV traffic load and additional channels provided by the UAV, \(M\).  
directly related to the weight, types, and number of rotors, as well as the battery capacity. Indeed, if the UAV does not leave sufficient time in the region (with the derived results presented in this work, we can clearly observe the adequate times for different system conditions), the impact of additional channels may not be relevant.  
As a future work, we intend to analyze UAV-assisted cellular systems using swarms of UAVs instead of the single UAV scenario, where the active communication and control between UAVs is required to avoid collisions and maintain the formation of the UAVs. Also, we plan to consider the case where UAV dwelling times in the system does not follow an exponential distribution. To this end, we will consider different effects such as wind and rain, as well as different types of trajectories of the UAVs inside the cell, that may impact the times that these devices can remain active in the system before they have to leave to recharge their batteries.  
[PERSON] contributed with the conceptualization, methodology, validation, formal analysis and writing of the manuscript, [PERSON] contributed with the conceptualization, formal analysis and writing (editing and review), [PERSON] contributed with writing, editing,and formal analisys, [PERSON]-[PERSON] contributed with investigation and writing, [PERSON] contributed with writing, review and editing, and formal analysis. All authors have read and agreed to the published version of the manuscript.  
This work was partially funded by project SIP 20240671 of the Instituto Politecnico Nacional.  
Not Applicable.  
This work is a theoretical work and no new data was created.  
The authors declare no conflicts of interest.