Geometry of Packet Switching: Maximal Throughput Cone Scheduling Algorithms

In this chapter, we discuss the key ideas underlying some recent developments in packet switching. They concern algorithms for scheduling packets through switching fabrics, primarily to maximize throughput and support differentiated quality of service. We first develop a model capturing the packet queueing and scheduling dynamics of the switch in a ‘vectorized’ framework, which allows for the rich geometry of the switching problem to emerge. We then present a class of algorithms that dynamically schedule packets for transfer through the switching fabric, based on which conic space the packet backlog vector resides. Appropriate construction of the cones leads to maximum throughput. Cone algorithms subsume the well known ‘maximum weight matching’ ones for packet switching as a special case. We discuss various aspect of cone algorithms including robustness, scalability, throughput and quality of service support.