The emergence and spread of Internet of Things (IoT) technologies along with the edge computing paradigm has led to an increase in the computational load on sensor end-devices. These devices are now expected to provide high-level information instead of just raw sensor measurements. Therefore, the processing tasks must share the processor time with the communication tasks, and both of them may have strict timing constraints. In this work, we present an empirical study, from the edge computing perspective, of the process management carried out by an IoT Operating System (OS), showing the cross-influence between the processing and communication tasks in end-devices. We have conducted multiple tests in two real scenarios with a specific OS and a set of wireless protocols. In these tests, we have varied the processing and communication tasks timing parameters, as well as their assigned priority levels. The results obtained from these tests demonstrate that there is a close relationship between the characteristics of the processing tasks and the communication performance, especially when the processing computational load is high. In addition, these results also show that the computational load is not the only factor responsible for the communication performance degradation, as the relationship between the processing tasks and the communication protocols timing parameters also plays a role. These conclusions should be taken into account for future OSs and protocol developments.