This paper presents an improvement of the Bandwidth Inheritance Protocol (BWI), the natural extension of the well-known Priority Inheritance Protocol (PIP) to resource reservation schedulers. The modified protocol allows for a better management of nested critical section, removes unneeded overheads in the management of task block and unblock events, and introduces a run-time deadlock detection mechanism at no cost. Also, an implementation of the new protocol on the Linux kernel is presented, along with experimental results gathered while running some synthetic application load. Presented results prove the effectiveness of the proposed solution in reducing latencies due to concurrent use of resources and in improving temporal isolation am...