Performance modeling of recent computer and communication system development has become more complicated as the size and complexity of the system has increased, (see  and ). Finite source queueing models are efficiently used for performance evaluation of computer systems (see , ,  and ). Realistic consideration of certain stochastic systems, however, often requires the introduction of a random environment, sometimes referred as to Markov-modulation, where system parameters are subjected to randomly occuring fluctuations or bursts. This situation may be attributed to certain changes in the physical environment such as personal changes and work load alterations. Gaver et al.  proposed an efficient computational approach for the analysis of a generalized structure involving finite state space birth-and-death processes in a Markovian environment. This paper deals with a First-Come, First-Served (FCFS) queueing model to analyze the behaviour of heterogeneous finite-source system with a single server. The clients (request sources) and the server are supposed to operate in independent random environments, respectively, allowing the arrival and service processes to be Markov-modulated ones. Each request of the clients is characterized by its own exponentially distributed source and service time with parameter depending on the state of the corresponding environment, that is, the request generation and service rates are subject to random fluctuations. Our aim is to get the usual stationary performance measures of the system, such as utilizations, mean queue lengths, average response times. The main problem is that the state space of the underlying continuous-time Markov-chain will be very large, so we have the state space explosion problem.