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Input characterization to describe the flow of incoming traffic in network systems, such as the grid and the WWW, is often performed by using Markov modulated poisson processes (MMPP). Therefore, to enact capacity planning and quality-of-service (QoS) oriented design, the model of the servers that receive the incoming traffic is often described as a MMPP/M/1 queue. In a work we have provided an approximate solution for the response time distribution of the MMPP/M/1 queue, which is based on a hyper-exponential process obtained via a weighted superposition of the response time distributions of M/M/l queues. Compared to exact solution methods, or simulative techniques, the aim of this approximation is to provide the potential for more efficient model solution, so to enable, e.g., real-time what-if analysis in system reconfiguration scenarios. In this paper, we show how fast the computation can be supported in practical settings by ad-hoc techniques allowing the hyper-exponential model to be solved with no iterative or numerical costly steps, which would otherwise be required in order to compute the length of transient phases due to state switches in the MMPP arrival process. An application to the context of performance analysis of a grid system is also shown, supporting the efficiency of our proposal.