In-memory database management systems have the potential to reduce the execution time of complex operational analytical queries to the order of seconds while executing business transactions in parallel. The main reasons for this increase of performance are massive intra-query parallelism on many-core CPUs and primary data storage in main memory instead of disks or SSDs. However, database management systems in enterprise scenarios typically run a mix of different applications and users, of varying importance, concurrently. As an example, interactive applications have a much higher response-time objective compared to periodic jobs producing daily reports and should be run with priority. In addition to strict prioritization, enforcing a fair share of database resources is desirable, if several users work on applications that share a database. Solutions for resource management based on priorities have been proposed for disk-based database management systems. They typically rely on multiplexing threads on a number of processing units, which is unfavorable for in-memory databases on multi-cores, as single queries are executed in parallel and numerous context switches disrupt cache-conscious algorithms. Consequently, we propose an approach towards resource management based on a task-based query execution that avoids thread multiplexing. The basic idea is to calculate the allowed share of execution time for each user based on the priorities of all users and adjust priorities of tasks of incoming queries to converge to this share.