We consider the problem of providing flexible, ratebased, quality of service guarantees for a particular class of multistage switch networks that includes Banyan networks. We focus on solving a type of on-line, traffic scheduling problem, whose input at each time step is a set of desired traffic rates through the switch network. These traffic rates in general cannot be exactly achieved since they treat the incoming data as fluid, that is, they assume arbitrarily small fractions of packets can be transmitted at each time step. The goal of the traffic scheduling problem is to closely approximate the given sequence of traffic rates by a sequence of switch uses throughout the network in which only whole packets are sent. The focus of this paper is bounding the costs incurred in using such an approximation, in terms of the additional buffer size, called backlog, required. Our contributions in this paper apply to a class of multistage

We consider a problem motivated by the desire to provide flexible, rate-based, quality of service guarantees for packets sent over input queued switches and switch networks. Our focus is solving a type of online traffic scheduling problem, whose input at each time step is a set of desired traffic rates through the switch network. These traffic rates in general cannot be exactly achieved since they assume arbitrarily small fractions of packets can be transmitted at each time step. The goal of the traffic scheduling problem is to closely approximate the given sequence of traffic rates by a sequence of transmissions in which only whole packets are sent. We prove worst-case bounds on the additional buffer use, which we call backlog, that results from using such an approximation. We first consider the, input queued, crossbar switch. Our main result is an online packet-scheduling algorithm using no speedup that guarantees backlog at most @ CIA P R packets at each input port and each output port. Upper bounds on worst-case backlog have been proved for the case of constant fluid schedules, such as the P P CP bound of Chang, Chen, and Huang (INFOCOM, 2000). Our main result for the crossbar switch is the first, to our knowledge, to bound backlog in terms of switch size for arbitrary, time-varying fluid schedules, without using speedup. Our main result for Banyan networks is an exact characterization of the speedup required to maintain bounded backlog, in terms of polytopes derived from the network topology.

SUMMARY Proportional fair bandwidth allocation in packet switches is a fundamental issue for quality of service (QoS) support in IP networks. Input-queued switches performing packet-mode scheduling deliver all the segments of a packet contiguously from the input port to the output port, thus greatly simplify the output reassembly and yield performance advantage over switches with cellmode scheduling under certain conditions[1]. An important issue of packet-mode scheduling is how to achieve fair bandwidth allocation among flows with different packet sizes. This paper presents a packet-mode fair scheduling (pFS) algorithm to guarantee each flow a bandwidth proportional to its reserved share regardless of the packet size distribution and the system load. Simulations show that our approach achieves high throughput as well as good delay performance. Compared to algorithms without fairness mechanism, pFS yields significant performance improvement in terms of average packet delay under heterogeneous traffic. An hardware implementation is presented to show that the computation of the algorithm can be completed within a single clock, which makes pFS applicable to high speed switches. key words: scheduling, fairness, switch, input-queued, packet-mode. 1.