Abstract. The current paper addresses the problem of quality of service (QoS) provisioning in a general purpose operating system (GPOS), in this case GNU/Linux. Particularly, we propose to change the CPU allocation in that OS by reserving a percentage of a CPU capacity in order to ensure the QoS provisioning according to the QoS demand of each process. In order to investigate the effectiveness of that approach, Markovian models are proposed to represent the dynamics of the systems. Results show that the OS with reservation outperforms the system without it, but also that there is a performance tradeoff in the OS with reservation in such a way that an improvement in the QoS perceived by processes using the reserved capacity is done at a cost of a degradation in the QoS perceived by the other processes.