One of the essential requirements of wireless industrial Internet of Things (IoT) systems is to have an extremely high packet delivery rate, generally over 99.9% and comply with realtime deadline constraints. In industrial IoT networks, packets arriving after the deadline become part of packet loss and lose meaning when they arrive late. However, currently available industrial IoT proposals aim to minimize End-to-End delay without taking into account simultaneous realtime and reliability constraints. In this paper, we propose a new mechanism, called BDPC (Bounded Delay Packet Control) to tackle this challenge. BDPC combines the knowledge of a node's traffic delay to the destination (root) with the time budget of a data packet traversing the industrial IoT network, to allocate network resources to comply the system maximum delay requirements using an adaptive and distributed algorithm. Unlike the general aim to minimze end-to-end delay, we propose that data packets must arrive before the deadline, but not faster. Our results show, for example, that by using BDPC, the number of packets arriving before the deadline can be improved more than 2.6 times compared to the case when using the default Minimal Scheduling Function from the standard. As a further advantage, BDPC involves minor modifications to the 6TiSCH protocol stack, which makes it compatible with current implementations.