MULTICAST COPY NETWORKS
137
running sums as follows: SCN s RS ,
and min N y RS
, RS y RS if RS
- N
Ž .
iy1 i
iy1 iy1
SCN s
i
½
otherwise
5.6.6.2 Concentration The starting point in a CRAN may not be port 0,
and the resulting sequence of routing addresses in the RBN may not be continuous monotone. As illustrated in Figure 5.36, internal collisions may
occur in the RBN.
Fig. 5.36 Cyclic monotone addresses give rise to cell collisions in a reverse banyan
network. Port 2 and port 6 are idle.
Fig. 5.37 An additional RAN is used to concentrate active cells. The starting point is
marked by encircling its copy request.
BANYAN-BASED SWITCHES
138
This problem can be solved if an additional RAN with fixed starting point Ž
. port 0 is added in front of the RBN. As shown in Figure 5.37, this
additional RAN will recalculate the running sums of RAs so that the resulting sequence of RAs becomes continuous monotone.
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H. Jonathan Chao, Cheuk H. Lam, Eiji Oki Copyright 䊚 2001 John Wiley Sons, Inc.
Ž .
Ž .
ISBNs: 0-471-00454-5 Hardback ; 0-471-22440-5 Electronic
CHAPTER 6
KNOCKOUT-BASED SWITCHES
Ž As shown in Chapter 2, output buffer switches including the shared-memory
. switches provide the best delay᎐throughput performance. The problem of
the output-buffered switches is that their capacity is limited by the memory speed. Consider the case of an ATM switch with 100 ports. We should ask
ourselves what is the probability of all 100 cells arriving at the same output port in the same time slot. If the probability is very low, why do we need to
have the output buffer able to receive all 100 cells at the same slot? A group of researchers in Bell Labs in the late 1980s tried to solve this problem by
limiting the number of cells that can arrive at an output port in each time slot and thus the speed requirement of the memory at the output ports. Excess
cells are discarded by the switch fabric. The concept is called the knockout principle. The question is how many cells should be delivered to the output
port in each time slot. If it is too many, memory speed may be the bottleneck. If too few, the cell loss rate in the switch fabric may be too high to be
acceptable. For a given cell loss rate, this number can be determined. The number is found to be 12 for a cell loss rate of 10
y10
, independent of the switch size.
This result seems very encouraging in that the memory speed is no longer the bottleneck for the output-buffered switch. However, there are no com-
mercial switches implemented with the knockout principle. This is because the results obtained assume that input traffic distributions from different
inputs are uncorrelated, which may be unrealistic in the real world. Secondly, people are not comfortable with the idea that cells are discarded by the
switch fabric. Usually, cells are discarded when a buffer is filled or exceeds some predetermined threshold.
141
KNOCKOUT-BASED SWITCHES
142
Although the knockout principle has not been used in real switching systems, it has attracted many researchers in the past, and various architec-
tures based on it have been proposed. Some of them are discussed in this chapter. Section 6.1 describes the knockout principle and an implementation
and architecture of a knockout switch. Section 6.2 describes a useful and powerful concept, channel grouping, to save routing links in the switch fabric.
A generalized knockout principle that extends the original one by integrating the channel grouping concept is described. Section 6.3 describes a two-stage
multicast output-buffered switch that is based on the generalized knockout principle. Section 6.4 describes a fault-tolerant multicast output-buffered
ATM switch. Section 6.5 is an appendix that shows the derivation of some equations used in this chapter.
6.1 SINGLE-STAGE KNOCKOUT SWITCH
6.1.1 Basic Architecture
w x The knockout switch 28 is illustrated in Figure 6.1. It is composed of a
completely broadcasting interconnection fabric and N bus interfaces. The interconnection fabric for the knockout switch has two basic characteristics:
Ž . Ž .
1 each input has a separate broadcast bus, and 2 each output has access to all broadcast buses and thus all input cells.
With each input having a direct path to every output, no switch blocking occurs within the interconnection fabric. The only congestion in the switch
takes place at the interface to each output, where cells can arrive simultane- ously on different inputs destined for the same output. The switch architec-
ture is modular in that the N broadcast buses can reside on an equipment backplane with the circuitry for each of the N input᎐output pairs placed on a
single plug-in circuit card.
Fig. 6.1 Knockout switch interconnection fabric.
