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Buffered crossbar switches are a special type of crossbar switches. In such a switch, besides normal input queues and output queues, a small buffer is associated with each crosspoint. Due to the introduction of crosspoint buffers, output and input contention is eliminated, and the scheduling process for buffered crossbar switches is greatly simplified. Moreover, since different input ports and output ports work independently, the switch can easily schedule and transmit variable length packets. Compared with fixed length packet scheduling, variable length packet scheduling has some unique advantages: higher throughput, shorter packet latency, and lower hardware cost. In this paper, we present a fast and practical scheduling scheme for buffered crossbar switches called Localized Independent Packet Scheduling (LIPS). With LIPS, an input port or output port makes scheduling decisions solely based on the state information of its local crosspoint buffers, i.e., the crosspoint buffers where the input port sends packets to or the output port retrieves packets from. The localization feature makes LIPS suitable for a distributed implementation and thus highly scalable. Since no comparison operation is required in LIPS, scheduling arbiters can be efficiently implemented using priority encoders, which can make arbitration decisions quickly in hardware. Another advantage of LIPS is that each crosspoint needs only L (the maximum packet length) buffer space, which minimizes the hardware cost of the switches. We theoretically analyze the performance of LIPS and, in particular, prove that LIPS achieves 100 percent throughput for any admissible traffic with speedup of two. We also discuss in detail the implementation architecture of LIPS and analyze the packet transmission timing in different scenarios. Finally, simulations are conducted to verify the analytical results and measure the performance of LIPS.