Increasingly enterprises rely on software applications to support their business processes. Since such processes are continually evolving to keep up with market dynamism, companies strive to increase their efficiency, for example, by optimising the integration of applications supporting these processes. Integration platforms are specialised software tools that allow creating integration processes so that applications can share data and functionality. However, this integration involves several challenges, especially when large volumes of heterogeneous data should be integrated and shared. The performance of an integration process, in terms of message processing, is directly related to the run-time system of the integration platform. This article investigates the impact of the volume of messages and the number of threads used by a run-time system on makespan and performance of an integration process. The greater is the number of messages per second received by the integration process, the high is the volume of messages. The study was based on a run-time system with task-based execution model and follows a strict protocol to conduct and report our empirical study. We observed an increment of makespan when increasing the volume of messages to integration processes and different behaviours when increasing the number of threads used in their executions. Makespan reduces as the number of threads increases, but only when the volume of inbound messages is not very high. We confirmed that there is a performance gain by increasing the number of threads to execute an integration process, but observed that the continuous increment of threads leads to degradation of the performance in this model.