<p>Cluster-based systems have been extensively used to provide parallel processing of jobs. A distinguishing feature of such systems is that jobs consist of tasks that should run in parallel on different servers. A job does not start execution unless the required number of idle servers is available. This paper proposes a new continuous-time Markov chain that accurately models such cluster-based system with finite buffer size. Extensive performance evaluation is conducted where the influence of several model parameters on a number of performance measures is investigated. Performance measures include the blocking probability of jobs, the average delay of jobs in the queue and the utilization of the servers in the cluster. The application of the model to cloud centers with thousands of servers is shown possible under a typical heterogeneous workload where jobs require either 10 or 100 servers each.</p>