The ability to deliver guaranteed QoS (Quality of Service) is crucial for the commercial success of cloud platforms. This paper presents a model based on queuing theory to study computer service QoS in cloud computing. Cloud platforms are modeled with an open Jackson network that can be used to determine and measure the QoS guarantees the cloud can offer regarding the response time. The analysis can be performed according to different parameters, such as the arrival rate of customer services and the number and service rate of processing servers, among others. Detailed results for the model are presented. When scaling the system and depending on the types of bottleneck in the system, we show how our model can provide us with the best option to guarantee QoS. The results obtained confirm the usefulness of the model presented for designing real cloud computing systems.