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Study the effects of concurrent voice connections on the performance metrics of communication network such as queue length, waiting time, packets service time and is very important. Mathematical analysis of such network especially with long-tail traffic will help us for a good capacity planning and also lead to an accurate admission control algorithms. In this study a mathematical model of a communication network supporting VoIP and back-ground traffic with long-tail service time is considered. Some problems of previous mathematical models are identified and a new queueing system is proposed in which specifically the coexisting of heavy-tail and voice flows is addressed. The long-tail service time is approximated via hyper-Erlang distribution and also to achieving an accurate performance model a Markov reward model is introduced. The available bandwidth for long-tail distribution varies according to the Markov chain, describing the utilisation factor of voice connection. Numerical results show a comparison between exponential and heavy-tail service time and finally the effects of concurrent voice connections on the service time of heavy-tailed back-ground packets is shown. [ABSTRACT FROM AUTHOR]