In this paper, the queuing theory is used to model cloud computing environment. The aim of this job is to analyze the response time as a measure of the Quality of Service (QoS) of computer services. In the cloud computing, multi resources need to be allocated simultaneously to multiple customers. When a customer requests for a service, if servers are busy, the requested job enters into the waiting line until a server completes its service. So, this may lead to a bottleneck in the network. By modeling cloud platforms by a queuing network, it can be easy to determine and to measure the QoS. The arrival rate and the service rate of processing servers are two main parameters that can affect the performance of the model; so, they are used to analyze the performance of the model. This paper proposes a queuing model which is applied at multiple servers in order to analyze the response time and also to improve the network performance and QoS effectively in a cloud computing environment.