Slow-start packet scheduling particularly applicable to systems including a non-blocking switching fabric and homogeneous or heterogeneous line card interfaces

Methods and apparatus are disclosed for slow-start scheduling packets, such as in systems having a non-blocking switching fabric and homogeneous or heterogeneous line card interfaces. In one implementation, multiple request generators, grant arbiters, and acceptance arbiters work in conjunction to determine the scheduling of packets. A set of requests for sending packets from a particular input is identified. The number of requests is possibly reduced to a value less than the number of packets that can be sent from the particular source if the particular input is not saturated. Otherwise, when the particular input is saturated, the number of requests remains the same or is reduced to the maximum number of packets that can be sent during a packet time.