| Summary: | 博士 === 國立清華大學 === 通訊工程研究所 === 96 === Load-balanced switches have received a great deal of attention recently as they are much more scalable than other existing switch architectures in the literature. However, as there exist multiple paths for flows of packets to traverse through load-balanced switches, packets in such switches may be delivered out of order. The UFS scheme in [23] proposed by Stanford University and the mailbox switches in [10] proposed by our research team are scalable solutions to solve such an out-of-sequence problem. Though the UFS scheme is shown to achieve 100% throughput [23], the packet delay is large (even in light traffic). This is known as the starvation problem. On the other hand, the mailbox switch (with δ= 0 in [10]) was shown to have only 58% throughput. The advantage of the mailbox switch is its low packet delay in light traffic.
Our first contribution is to find the throughput limitations in the mailbox switch. We found that there are two kinds of throughput limitations in the two extreme schemes of the mailbox switches, i.e., the δ=0 scheme and the δ=∞ scheme. In theδ=0 scheme, we study the throughput for the frame-based mailbox switches with frame size F. We find that the throughput goes to 1.0 in the order of 1/√F as F goes to ∞. On the other hand, in the δ=∞ scheme, we found that the maximum stable throughput is 0.6748. An interesting phenomenon is that the throughput keeps growing with the arrival rate when the arrival rate is greater than the maximum stable throughput. In particular, we show that the maximum unstable throughput is 0.6786 when the arrival rate reaches 1.0.
The main contribution of our research is to propose a switch architecture, called the CR switch, that can have the advantages of both the UFS scheme in [23] and the mailbox switch withδ= 0 in [10]. We show that the CR switch achieves 100% throughput and delivers packets in order (as in the UFS scheme), while maintaining low packet delay in light traffic (as in the mailbox switch with δ= 0). The main idea, as pointed out in the pioneer work by Tobagi and Kleinrock [51] for a multiple access channel, is to have the CR switch operating in two modes: the contention mode (in light traffic) and the reservation mode (in heavy traffic). The difference between our scheme and [51] is that our system has multiple parallel channels while there is only one in [51]. The challenge in multiple CR (Contention and Reservation) channels is to maintain packets in sequence. The key innovation that enables us to do this is a new buffer management scheme, called I-VOQ (virtual output queue with insertion). With the I-VOQ technique, we give rigorous mathematical proofs for 100% throughput and in order packet delivery of the CR switch. By computer simulations, we also demonstrate that the average packet delay of the CR switch in light traffic is almost the same as that in the mailbox switch and it is considerably smaller than that in the UFS scheme. Moreover, when compared with the Padded Frame scheme [21], an improved scheme proposed by the University of Illinois at Urbana Champaign for the starvation problem in the UFS scheme, our delay performance is also much better in light traffic and comparable in heavy traffic.
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