The IETF 6TiSCH Working Group (WG) is currently standardizing a novel architecture to integrate IEEE 802.15.4e TSCH Wireless Networks into the Internet of Things. Within the proposed 6TiSCH architecture, a Scheduling Function (SF) is used to manage the allocation of communication resources (i.e., TSCH timeslots). Although many SFs have been proposed in literature, the 6 TiSCH WG is considering the On-The-Fly (OTF) Bandwidth Reservation Algorithm as the reference SF. In this paper, we carry out an extensive simulation analysis of OTF to evaluate if, in its current definition, it can ensure the low latency and high reliability requirements of critical applications targeted by TSCH. Specifically, we investigate how its performance is affected by the RPL protocol and the 6top protocol used for routing and distributed resource negotiation, respectively. Our results show that the OTF performance is significantly affected by (i) frequent changes in the preferred parent selected by RPL, and (ii) failures in resource negotiation. These events typically lead to congestion, from which the network can hardly recover. To overcome such limitations, we propose a modified version of the Bandwidth Reservation Algorithm, named Enhanced-OTF. We show that proposed modifications can effectively improve the overall network performance by allowing network nodes to recover from congestion in a short time.