We evaluate the QoS of a high user mobility through the calculation of the probability of success call completion (PSCC) when performs handover, but its call request needs to use both classical and quantum key distribution (QKD) networks resources. To this end, the formalism for PSCC estimation takes into account up to three elements: the probability to (i) leave the actual base station (BS), (ii) find the next BS inside the hysteresis time, and (iii) be blocked because others users try to occupy classic and QKD networks. Indeed, when the end user call needs to establish connection to a QKD hardware, the key management layer (KML) assumes the responsibility to provide continuous service by monitoring nodes between classical application and QKD layers. Thus, the QKD scheme is supported by the Bennett-Brassard protocol (BB84) which guarantees high QKD hardware efficiencies. In addition, the blocking probabilities are modeled with the Mellin transform. The results have demonstrated that the incorporation of a QKD network working together to a classical one, might to degrade the PSCC in up to 20% of nominal values, and that can be interpreted as the interaction between classic and QKD networks giving rise to an extra blocking effect.