The Core Stateless Fair Queuing (CSFQ) is a distributed approach of fair queuing. The limitations of CSFQ include its inability to estimate fairness during large traffic flows which are short and bursty (VoIP or video) and also it utilizes the single FIFO queue at the core router. For improving the fairness and efficiency, the authors propose an Extended Core Stateless Fair Queuing (ECSFQ) with multiple queue priority scheduler. Initially priority scheduler is applied to the flows entering into the ingress edge router. If it is real time flow i.e. VoIP or video flow, then the packets are given higher priority, otherwise lower priority.