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Network slicing is a novel key technology in 5G networks which permits to provide a multitude of heterogeneous communication services over a common network infrastructure while satisfying strict Quality of Service (QoS) requirements. Since radio spectrum resources are inherently scarce, the slicing of the radio access network should rely on a flexible resource sharing policy that provides efficient resource usage, fairness and slice isolation. In this article, we propose such a policy for bandwidth-greedy communication services. The policy implies a convex programming problem and is formalized to allow for session-level stochastic modeling. We developed a multi-class service system with service rates obtained as a solution to the optimization problem, a Markovian Arrival Process and state-dependent preemptive priorities. We use matrix-analytic methods to find the steady state distribution of the resulting continuous-time Markov chain and the expressions for important performance metrics, such as data rates. Numerical analysis illustrates the efficiency of the proposed slicing scheme compared to the complete sharing and complete partitioning policies, showing that our approach leads to a data rate about the double of that obtained under complete partitioning for the analyzed scenario.