The IEEE 802.15.5 MAC enables high-rate mesh communications between devices in a wireless personal area network (WPAN). The channel time allocation (CTA) scheduler plays an important role in sizing CTAs within each superframe. In this paper, we propose an efficient admission control and centralized CTA mechanism for a hop-2 mesh communication in the IEEE 802.15.5. The proposed algorithm is executed between the mesh Piconet Coordinators (MPNC)s and their piconets' member mesh devices (MDEV)s s to provides a reliable resource allocation mechanism for the piconets at the hop-2 of the IEEE 802.15.5. This mechanism induces satisfaction and fairness among the requesting hop-2 Real-time (RT) and non-RT (NRT) MDEVs. It introduces the use of a novel priority Flag metric and takes the channel requests rejection rate into consideration. We evaluate the performance of the proposed algorithm through simulations and the results show that the proposed approach achieves good performance in terms of satisfaction and fairness.