Cloud computing became a popular computing technology, that provides efficient resource utilization to deliver IT services. Each user requests cloud computing system for use of resources. If the system is busy, then user needs to wait until current user finishes the job. This may result in waiting time increase and drop of request Thus, cloud computing service provider needs tools to evaluate and reduce waiting and processing times. In the paper, each request is assumed to consist of several independent sub-requests according to the number of virtual cloud servers in the system. All sub-requests of the same request arrive simultaneously and each server receives exactly one sub-request in its queue. One of the main performance measures of cloud computing system is a maximum waiting and processing time of all sub-requests, which is called response time of the request. In order to evaluate this characteristic, we develop a model in terms of queuing system with multiple queues and batch arrivals. We provide algorithm to obtain steady-state probabilities that allow evaluating various performance measures. © 2014 IEEE.