A new type of fair service, referred to as Statistically-Fair Service (SFS), is proposed in this paper. The SFS discipline is given based on the SFS criterion. Compared to "strict" fair service available, SFS is mainly characterized by its flexible suitability for the nature of statistically-multiplexed networks. By its statistically-fair service to users, therefore, SFS can ensure well end-to-end QoS requirements on a statistical basis with a benefit of enhancement in network utilization. Two useful properties of SFS is presented. One of them, the property of retaining Exponentially Bounded Burstiness(EBB), can facilitate end-to-end delay estimation of EBB-type traffic. Finally, some numerical results obtained from a simulation study on SFS shows that an SFS-equipped node in steady states will in deed retain the EBB attribute of any input flow.
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