In this paper, we introduce Quality of Service(QoS) analytic model of a distributed system that decentralizes the process nodes performing each task and communicates through a network for cooperation. The model advances a service reliability model of Dai et a1.(2003) by means of considering the processing time. The service is assumed to be provided by a centralized heterogeneous distributed system which is composed of some subsystems managed by a control center. The QoS is defined as the probability that a service is provided successfully in an allowed time, we consider the hardware/software reliability and the processing time which include program execution time, data transfer time. We derive the processing time distribution for a required service through convolution of corresponding probability density function. An application example is used to explain the procedure of computing quality of service.