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. at the output are used instead of 16 SOA gates in the type-II tunable
filter. However, compared to type-I and type-II tunable filters, the type-III tunable filter has more power loss, caused by the 1 = 4 splitter
and the 4 = 1 combiner.
11.4.5 Ping-Pong Arbitration Unit
As shown in Figure 11.20, a centralized PAU is used in our router. The arbitration is pipelined with packet segment transmission in the OIN. In
other words, while a HOL segment is being transmitted via the OIN, the segment next to it is also sending a request to the arbitration unit. In order to
minimize the delay of forwarding multicast request signals, 256 parallel arbiters are used, each of which is associated with one output and handles
256 input request signals. The 256 incoming multicast request signals must be handled simultaneously within one time slot, that is, 51.2 ns for a 64-byte
data segment sent at 10 Gbitrs.
11.4.5.1 Principles of Ping-Pong Arbitration Consider an N-input
packet switch. To resolve its output contention, a solution is to use an arbiter for each output to fairly select one among those incoming packets and send
back a grant signal to the corresponding input. The arbitration procedure is as follows:
1. During every arbitration cycle, each input submits a one-bit request Ž
. signal to each output arbiter , indicating whether its packet, if any, is
destined for the output. 2. Each output arbiter collects N request signals, among which one input
with active request is granted according to some priority order. 3. A grant signal is sent back to acknowledge the input.
Here, the second step that arbitrates one input among N possible ones is considered.
A simple RR scheme is generally adopted in an arbiter to ensure fair arbitration among the inputs. Imagine there is a token circulating among the
inputs in a certain ordering. The input that is granted by the arbiter is said to grasp the token, which represents the grant signal. The arbiter is responsible
for moving the token among the inputs that have request signals. The traditional arbiters handle all inputs together, and the arbitration time is
proportional to the number of inputs. As a result, the switch size or capacity is limited by the available amount of arbitration time.
Here, it is suggested to divide the inputs into groups. Each group has its own arbiter. The request information of each group is summarized as a group
request signal. Further grouping can be applied recursively to all the group request signals at the current layer, forming a tree structure, as illustrated in
Figure 11.32. Thus, an arbiter with N inputs can be constructed using
Ž .
multiple small-size arbiters ARs in each layer. Different group sizes can be used.
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Ž .
Fig. 11.32
A tree-structured hierarchical arbitration. 䊚1999 IEEE.
Assume N s 2
k
. Figure 11.32 depicts a k-layer complete binary tree with a group size of two when k s 4. Let AR2 represent a two-input AR. An AR2
contains an internal flag signal that indicates which input is favored. Once an input is granted in an arbitration cycle, the other input will be favored in the
next cycle. In other words, the granted request is always chosen between left Ž
. input and right alternately. That is why it is called Ping-Pong arbitration.
The first layer consists of 2
ky1
arbiters called leaf AR2s. The next k y 2 layers consist of arbiters called intermediate AR2s, 2
kyi
of which are in layer i. Finally, the last layer consists of only one arbiter called the root AR2.
Every AR2 has two request signals. An input request signal in layer i is the group request signal of 2
iy1
inputs and can be produced by OR gates either directly or recursively. The grant signal from an AR2 has to be fed
back to all the lower-layer AR2s related to the corresponding input. There- fore, every leaf or intermediate AR2 also has an external grant signal that
ANDs all grant signals at upper layers, indicating the arbitration results of upper layers. The root AR2 needs no external grant signal. At each leaf AR2,
the local grant signals have to combine the arbitration results of the upper
Ž .
layer i.e., form its external grant signal and provide full information on whether the corresponding input is granted or not.
One important use of the external grant signal is to govern the local flag signal update. If the external grant signal is invalid, which indicates that these
Ž . two input requests as a whole are not granted at some upper layer s , then
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Fig. 11.33 Comparison of the PPA with FIFO q RR and output queuing: switch
throughput and total average delay for a speedup factor of two.
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the flag should be kept unchanged in order to preserve the original prefer- ence. As shown in Figure 11.32, the external grant signal of a leaf AR2 can
be added at the final stage to allow other local logical operations to be finished while waiting for the grant signals from upper layers, which mini-
mizes the total arbitration time.
Suppose N inputs are served in increasing order of their input numbers, i.e., 1 ™ 2 ™ ⭈⭈⭈ ™ N ™ 1 under a RR scheme. Each AR2 by itself per-
forms RR service for its two inputs. The Ping-Pong arbitration consisting of the tree of AR2s shown in Figure 11.32 can serve the inputs in the order of
1 ™ 3 ™ 2 ™ 4 ™ 1 when N s 4, for instance, which is still RR, if each input always has a packet to send and there is no conflict between any of the
input request signals. Below its performance is shown by simulations.
11.4.5.2 Performance of PPA
