A Cluster is usually built by connecting a number of workstations (WSs) by a high speed network, and to run, computationally hungry applications on top of the system. A parallel application has to be built in a way that allows concurrent tasks to run in parallel on different nodes (i.e., WSs), and to have a main task coordinating their execution. This study aims at designing and evaluating a new processor allocation scheme for parallel applications executed on homogeneous nondedicated cluster in presence of local interactive processes. In such an environment, local interactive processes and parallel processes compete for the local processor. To handle the interactions between the two types of processes, the maximum response time is delimited by an upper bound, which is assumed to be given. This bound may be set by conducting empirical studies that determine the maximum time the user can wait till getting the response back from the system. Based on this response time a scheduling scheme that computes the appropriate quanta that satisfy both types of processes is presented. The scheme is modeled by a Colored Petri Net (CPN). In addition to the simulation model we have proposed an analytical model to confirm the simulation model results. The study started by studying the behavior of one single parallel job under different settings. After that, the model is relaxed to consider the presence of multiple prioritized parallel jobs in the cluster. The results of this study show that, there is a close agreement between the analytical and simulation models results. Both models' results have shown the effectiveness of the proposed scheme in preserving an acceptable speedup for the parallel job while maintaining the response time of the interactive processes. Also they have shown the performance of parallel jobs directly affected by several factors such as: cluster size, number of interactive processes at a cycle, number of parallel jobs, interactive processes demand, interactive processes arrival rate and parallel jobs priorities. Parallel job demand does not directly affect its speedup in case one single parallel job exists in the cluster. But it has a significant impact in case of multiple parallel jobs competing for the time quantum allocated for them.