SWITCH ARCHITECTURE CLASSIFICATION
29
Fig. 2.11 Three different topologies of banyan-based switches.
three isomorphic topologiesᎏdelta, omega, and banyan networksᎏbelonging to the banyan-based family. All of them offer equivalent performance and
are discussed in detail in Chapter 5. The banyan-based switch provides several advantages: First, it has a
complexity of paths and switching elements of order N log N, which makes it much more suitable than the crossbar-based and the fully interconnected
switch, whose complexity is of order N
2
, for the construction of large switches. Self-routing is also an attractive feature in that no control mecha-
nism is needed for routing cells. Routing information is contained within each cell, and it is used while the cell is routed along the path. Parallel
structure of the switch provides a benefit in that several cells on different paths can be processed simultaneously. Due to their modular and recursive
structure, large-scale switches can be built by using elementary switching elements without modifying their structures. This can be appropriately real-
ized by VLSI implementation.
The main drawback of the banyan-based switch is that it is an internally blocking switch. Its performance degrades rapidly as the size of the switch
Ž .
increases. The performance may be improved if M = M M 2 switching elements are employed instead of 2 = 2 switching elements. This leads to the
class of delta-based switches. The delta-based switch is a family of self-routing switches constructed
from M = M switching elements with a single path between any input and output port. While the performance of the delta-based switch can be signifi-
cantly better than that of the banyan-based switch, it is still a blocking switch. The performance of the switch is reduced due to internal contention. This
can be improved by increasing the speed of internal links within the switch with respect to that of input and output ports or by introducing buffers into
the switching elements.
2.2.2.2 Multiple-Path Switches
Multiple-path switches are classified as augmented banyan switches, Clos switches, multiplane switches, and recircula-
tion switches, as shown in Figure 2.12.
BASICS OF PACKET SWITCHING
30
Fig. 2.12 Multiple-path space-division switches.
a Augmented Banyan Switches In a regular N = N banyan switch, cells
pass through log N stages of switching elements before reaching their desti- Ž .
nations. The augmented banyan switch, as illustrated in Figure 2.12 a , has more stages than the regular banyan switch. In the regular banyan switch,
once a cell is deflected to an incorrect link and thus deviates from a predetermined unique path, the cell is not guaranteed to reach its requested
output. Here, in the augmented banyan switch, deflected cells are provided more chances to be routed to their destinations again by using later aug-
mented stages. When the deflected cells do not reach their destinations after the last stage, they are discarded.
The advantage of the augmented banyan switch is that by adding aug- mented stages, the cell loss rate is reduced. The performance of the switch is
improved. The disadvantage of this switch type is its complicated routing scheme. Cells are examined at every augmented stage to determine whether
they have arrived at their requested output ports. If so, they are sent to the output interface module. Otherwise, they are routed to the next stage and
will be examined again. Another disadvantage is that the number of aug- mented stages needs to be sufficiently large. Adding each augmented stage to
the switch causes increased hardware complexity. The tandem banyan switch
w x w x
14 and dual shuffle exchange switch 9 are examples of the augmented banyan switches.
b Three-Stage Clos Switches The structure of three-stage Clos switches,
Ž . as shown in Figure 2.12 b , consists of three stages of switch modules. At the
SWITCH ARCHITECTURE CLASSIFICATION
31
Fig. 2.13 Example of internal blocking in a three-stage Clos switch.
first stage, N input lines are broken up into r groups of n lines. Each group of lines goes into each first-stage switch module. There are m outputs in the
first-stage switch module; each connects to all m middle-stage switch mod- ules. Similarly, each middle-stage switch module has t outputs, so that it
connects to all t third-stage switch modules. At the third stage, N output lines are provided as t groups of s lines.
A consideration with the three-stage Clos switch is that it may be blocking. It should be clear that a crossbar-based switch is nonblocking; that is, a path
is always available to connect an idle input port to an idle output port. This is not always true for the three-stage Clos switch. Figure 2.13 shows a three-stage
Clos switch with N s 9, n s 3, and m s 3. The bold lines indicate paths that
are already in use. It is shown that input port 9 cannot be connected to either output port 4 or 6, even though both of these output lines are available.
Ž By increasing the value of m the number of outputs from each first-stage
. switch module or the number of middle-stage switch modules , the probabil-
ity of blocking is reduced. To find the value of m needed for a nonblocking three-stage switch, let us refer to Figure 2.14.
We wish to establish a path from input port a to output port b. The worst situation for blocking occurs if all of the remaining n
y 1 input lines and n
y 1 output lines are busy and are connected to different middle-stage Ž
. Ž
. switch modules. Thus a total of n
y 1 q n y 1 s 2n y 2 middle-stage switch modules are unavailable for creating a path from a to b. However, if
one more middle-stage switch module exists, an appropriate link must be available for the connection. Thus, a three-stage Clos switch will be non-
blocking if
m G 2n y 2 q 1 s 2n y 1.
Ž .
BASICS OF PACKET SWITCHING
32
Fig. 2.14
Nonblocking condition for a three-stage Clos switch.
The total number N of crosspoints in a three-stage Clos switch when it is
x
Ž .
symmetric that is, when t s r and s s n is
2
N N
s 2 Nm q m .
x
ž
n Substituting m
s 2n y 1 into N , we obtain
x 2
N N
s 2 N 2n y 1 q 2n y 1 .
Ž .
Ž .
x
ž
n for a nonblocking switch. For a large switch size, n is large. We can
approximate
2 2
N N
N , 2 N 2n q 2n
s 4Nn q 2 .
Ž .
x
ž
ž
n n
SWITCH ARCHITECTURE CLASSIFICATION
33
To optimize the number of crosspoints, differentiate N with respect to
x
1 2
Ž .
n and set the result equal to 0. The result will be n f Nr2 . Substituting
into N ,
x
3 3
2 2
N s 4 2 N s O N .
Ž .
x
The three-stage Clos switch provides an advantage in that it reduces the Ž
2
. hardware complexity from O N
in the case of the crossbar-based switch to
3 2
Ž .
O N , and the switch can be designed to be nonblocking. Furthermore, it also provides more reliability since there is more than one possible path
through the switch to connect from any input port to any output port. The main disadvantage of this switch type is that some fast and intelligent
mechanism is needed to rearrange the connections in every cell time slot according to arrival cells so that internal blocking can be avoided. This will
be the bottleneck when the switch size becomes large. In practice, it is difficult to avoid internal blocking although the switch itself is nonblocking.
Once contention on the internal links occurs, the throughput is reduced. This can be improved by increasing the number of internal links between switch
modules so that there are more paths for routing cells. Increasing the bandwidth of internal links is also helpful in that instead of having one cell
for each internal link in each time slot, now more than one cell from the input module that are destined to the same third-stage module can be
routed. Another way to reduce the internal blocking is routing cells in a random manner. If the center-stage switch modules have buffers, careful
provision has to be made at the output ports in order to preserve cell sequencing.
Ž . c Multiplane Switches
As shown in Figure 2.12 c , multiplane switches Ž
. refer to the switches that have multiple usually identical switch planes.
Multiplane switches are mainly proposed as a way to improve system throughput. By using some mechanisms to distribute the incoming traffic
loading, cell collisions within the switches can be reduced. Additionally, more than one cell can be transmitted to the same output port by using each
switch plane, so the output lines do not have to operate at higher speed than the input lines. Another advantage of multiplane switches is that they can be
used for achieving reliability, since the loss of a whole switch plane will reduce the capacity but not the connectivity of the switches. However, cell
sequencing may be disturbed unless cells belonging to the same connection are forced to use the same plane. The parallel banyan switch and the
w x Sunshine switch 4 are examples of multiplane switches.
d Recirculation Switches
Recirculation switches, as shown in Figure Ž .
2.12 d , are designed to handle the output port contention problem. By recirculating the cells that did not make it to their output ports during
the current time slot back to the input ports via a set of recirculation paths,
BASICS OF PACKET SWITCHING
34
the cell loss rate can be reduced. This results in system throughput improve- ment. The disadvantage of recirculation switches is that they require a large
switch to accommodate the recirculation ports. Also, recirculation may cause out-of-sequence errors. Some mechanisms are needed to preserve the cell
sequencing among the cells in the same connection. The best-known recircu-
w x w x
lation switches are the Starlite switch 6 and the Sunshine switch 4 .
2.2.3 Buffering Strategies
