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In cluster computing, a service provider must allocate necessary computing resources for large-scale scientific computations to process a customer's service request according to a service level agreement (SLA) that is a set of quality of services (QoS) and a fee agreed between a customer and a service provider. Thus, Resource allocation is a challenging but very necessary problem in cluster computing. In an effort to maximize a service provider's profit, it is commonplace and important to prioritize customer services in favor of those who are willing to pay higher fees. In this paper, we consider a set of computing resources owned by a service provider who serves differentiated customer services subject to an SLA for scientific applications that often require parallel computation. The QoS defined in the paper includes percentile response time and cluster utilization. We present an approach for optimal resource allocation in cluster computing systems in that we minimize the total cost of computing resources owned by a service provider while satisfying multiple priority customer service requirements. Our simulation experiments show that the proposed approach is applicable to the resource allocation in a cluster computing system with multiple customer services.