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

Abstract

Abstract-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 queuesize) 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.

Scheduling in Non-Blocking Buffered Three-Stage Switching Fabrics

“…The unbalanced traffic experiments use Bernoulli arrivals, and an unbalance factor determined by w [19]: when w is equal to zero (0) traffic is uniform, whereas when w is equal to one (1) traffic consists of persistent (non-conflicting) input-output port connections. Under hotspot traffic, each destination belonging to a designated set of "hot spots" receives (smooth or bursty 13 traffic at 100% collective load, uniformly from all sources; the rest of the destinations receive uniform or bursty traffic as above. Hotspots are randomly selected out of the fabric-output ports.…”

Linear-Time Approximation for Maximum Weight Matching

“…In each cycle one partial permutation can be realized. Existing algorithms for choosing these matchings, such as iSLIP [McKeown 1999] and PIM [Anderson et al 1993], guarantee 1 2 -MCMs and it has been shown [Giaccone et al 2005;McKeown et al 1996] that (approximate) MWMs have good throughput guarantees, where edge weights are based on queue-length. See also Leonardi et al [2003], Shah and Kopikare [2002], and .…”

A low complexity scheduling algorithm for a crosspoint buffered switch with 100% throughput

“…Since there is at most one arrival or departure from each X ij in each time slot, we obtain that for any schedule P where the last inequality is from (7).…”

“…In [7], the authors proposed a distributed scheduling algorithm and derived a relationship between throughput and the size of crosspoint buffers. However, to achieve 100% throughput, it needed a buffer of infinite size.…”