On the maximal throughput of networks with finite buffers and its application to buffered crossbars

The advent of packet networks has motivated many researchers to study the performance of networks of queues in the last decade or two. However, most of the previous work assumes the availability of infinite queue-size. Instead, in this paper, we study the maximal achievable throughput in a flow-controlled lossless network with finite-queue size. In such networks, throughput depends on the packet scheduling policy utilized. As the main of this paper, we obtain a dynamic scheduling policy that achieves the maximal throughput (equal to the maximal throughput in the presence of infinite queue-size) with a minimal finite queue-size at the internal nodes of the network. Though the performance of the policy is ideal, it is quite complex and hence difficult to implement. This leads us to a design of simpler and possibly implementable policy. We obtain a natural trade-off between throughput and queue-size for this policy. We apply our results to the packet switches with buffered crossbar architecture. We propose a simple, implementable, distributed scheduling policy which provides high throughput in the presence of minimal internal buffer. We also obtain a natural trade-off between throughput, internal speedup and buffer-size providing a switch designer with a gamut of designs. To the best of authors' knowledge, this is one of the first attempts to study the throughput for general networks with finite queue-size. We believe that our methods are general and can be useful in other contexts.