Survey of Performance Analysis
on Banyan Networks
Written By Nathan D. Truhan
Kent State University
Outline
•
•
•
•
•
•
•
•
Introduction & Banyan Networks
Replicated & Dilated Banyan Networks
Plane Interconnected Parallel Network
Buffered Banyan Network
Output-buffered Banyan Network
Input-buffered Banyan Network
Conclusions
References
Introduction & Banyan Networks
• Banyan networks have been a topic of
discussion in high-speed networks due to
its low cost and simple implementation
• Belongs to a family of multistage
interconnection networks which also
include Omega, Shuffle-exchange, and
others
Introduction & Banyan Networks
• Has the properties of having a unique path
from source to destination, constructed out
of m-stages of uniform switches, selfrouting, modular, having a constant delay
for all input-output port pairs, in-order
delivery of packets
Introduction & Banyan Networks
• Consists of O(N log N) switching
elements, split into O(log N) stages
• Standard Banyan has no buffers
• Will concentrate on 2 x 2 switches
[1]
Replicated & Dilated Banyan Networks
• Expands a Banyan network by adding
switching elements or links
• A Replicated Banyan network adds d
copies of the Banyan network connected
by a multiplexer and de-multiplexer
Replicated & Dilated Banyan Networks
• When a packet enters the network at the
input port I, a layer in d is chosen and the
packet is routed to this layer
• Layers in a replicated Banyan network are
selected in one of three methods Random, round robin and network load
Replicated & Dilated Banyan Networks
[2]
Replicated & Dilated Banyan Networks
• Once a packet has traversed its assigned
layer it reaches the output de-multiplexer
• The de-multiplexers can take packets in
two ways - Multiple and single acceptance
• One adverse side-effect is that the Banyan
network could lose its in-order delivery of
packets
Replicated & Dilated Banyan Networks
• Can force all packets in same connection
to same layer
• Can be more expensive to deploy, having
an O(d x (N log N)), where d is number of
layers in the network
Replicated & Dilated Banyan Networks
• Can compromise between standard
Banyan and replicated Banyan by using
partially replicated networks
• Replication occurs only in layers that see
congestion
Replicated & Dilated Banyan Networks
[2]
Replicated & Dilated Banyan Networks
Throughput of replicated Banyan network
[2]
Replicated & Dilated Banyan Networks
Delay of replicated Banyan network
[2]
Replicated & Dilated Banyan Networks
• A Dilated Banyan network adds d lines to
each port to allow multiple packets to flow
between switching elements at the same
time which results in 2d x 2d switching
elements
• It has also been shown in Architecture and
Performance Analysis of DIRSMIN [8] that
to meet the low-latency and high
performance requirement, d = log log N
dilation is optimal.
Replicated & Dilated Banyan Networks
[3]
Plane Interconnected Parallel Network
• Introduced by Moustafa Youssef, Mohamed ElDerini and Hussien Aly from Alexandria
University [4]
• Standard PIPN network created as split Banyan
network with two sub-networks of size N/2 x N/2
and n – 1 stages
• Non uniform traffic throughput is measured with
2
[4]:
X PIPN 


X banyan  1  1 
2 

Plane Interconnected Parallel Network
[4]
Plane Interconnected Parallel Network
• Can use features of replication and dilation
of Banyan networks
[4]
Plane Interconnected Parallel Network
[4]
Plane Interconnected Parallel Network
• Performance in a dilated PIPN network can be shown
with dilation 2 and 4
[4]
Outline
•
•
•
•
•
•
•
•
Introduction & Banyan Networks
Replicated & Dilated Banyan Networks
Plane Interconnected Parallel Network
Buffered Banyan Network
Output-buffered Banyan Network
Input-buffered Banyan Network
Conclusions
References
Buffered Banyan Network
• Most common method to deal with
contention is add a queue to some location
in the switching element
[5]
Buffered Banyan Network
• Queues can be placed at the input or
output buffers and will have an impact on
the performance on the network
[5]
Buffered Banyan Network
• Cannot completely remove contention, since if
packets are headed to the same queue we still
have contention
• Contended packets are not dropped, but held in
the buffer until it can be transmitted, unless the
buffer is full
Buffered Banyan Network
[7]
Buffered Banyan Network
• Processing a network buffer occurs in a two
stage clock cycle
• At time 0, the network is empty
• In the first cycle the network checks for
availability of free queue slot to transfer the
head-of-line slot packet
• In the second cycle the routing of the HOL
packet occurs
Buffered Banyan Network
• Buffers based off of a three-stage
Markovian model [6] to show state of
head-of-line packet
– State “e” is empty, no packets in buffer
– State “n” denotes new packet which is
different from previous cycle
– State “b” denotes packet in buffer is same as
last cycle and was blocked
Buffered Banyan Network
• At the beginning of an operation cycle a buffer in stage k, may be in
(2B + 1) possible combinations of states, where 0  k  m , and B is
the number of buffers in the queue:
• 0, e , 1, n , 1, b , B  1, n , B  1, b , B, n , B, b
[5]
    




• The last stage, m, is special as it cannot be in state b, therefore it
only has (B + 1) states, giving us the following:
• 0, e , 1, n , 2, n , B  1, n , B, n
[5]
  
 


Buffered Banyan Network
• if two packets are contending for the same
input of the switching element in the next
stage, but are destined for two separate
outputs, with input buffering they would
contend and cause congestion
• however with output queuing they would
be permitted to enter the next stage and
be placed in their separate output queues
Output-buffered Banyan Network
• Output-buffered Banyan has extra buffer
stage at the inputs, while the rest reside at
the outputs of the switching elements
• This leads to having m + 1 stages
considering queuing
Output-buffered Banyan Network
• Performance is modeled similar to dilated
PIPN network
[5]
Input-buffered Banyan Network
• Unlike output-buffered network, all queues
are at the inputs
• This leads to having exactly m stages
Input-buffered Banyan Network
[6]
Outline
•
•
•
•
•
•
•
•
•
Introduction & Banyan Networks
Replicated & Dilated Banyan Networks
Plane Interconnected Parallel Network
Buffered Banyan Network
Output-buffered Banyan Network
Input-buffered Banyan Network
Conclusions
Questions
References
Conclusions
• In this survey paper we have looked at several methods to improve
a Banyan network
• Dilating and replication provide marginal increases as well as the
PIPN network which combines these methods. The main problem
with these designs is the lack of buffer, which still causes contention
to occur and packets to be lost
• This contention problem is greatly reduced by adding buffers to the
network, be it one buffer slot or multiple. There is not a foolproof
way to eliminate contention because adding buffers may also add
congestion
• All methods shown provide a marginal difference in performance,
and even through they take different approaches to enhancing
performance they are have all similar results, as demonstrated in the
figures above
Questions?
References
[1]
[2]
[3]
[4]
C. Bouras, C. Gkantsidis. Cost of implementing Banyan networks for use
in ATM switching fabrics.
<http://www.cc.gatech.edu/people/home/gantsich/Other/CostOfImplemen
tingBanyanNetworksForUseInATMSwitchingFabrics.pdf>
D. Tutsch, G. Hommel. Multilayer Multistage Interconnection Networks
<http://pdv.cs.tu-berlin.de/~dietmart/Publications/DASD2003.pdf>
M. Youssef, M. El-Derini, H. Aly. Performance Enhancement Techniques
of a Banyan Network Based Interconnection Structure. 1999.
<http://www.cs.umd.edu/~moustafa/papers/aej99.pdf>
A. Somani, T. Zhang. Architecture and Performance Analysis of
DIRSMIN: A Fault-Tolerant Switch using Dilated Reduced-Stage MIN.
1995. <http://citeseer.ist.psu.edu/607007.html>
References
[5]
[6]
[7]
K. Chan, et. al. A Refined Model for Performance Analysis of Outputbuffered Banyan Networks. <http://citeseer.ist.psu.edu/234601.html>.
K. Chan, K. Yeung, S. Chan. A Refined Model for Performance Analysis
of Buffered Banyan Networks with and without Priority Control. In IEICE
Transactions, January 1999, Vol.E82-B.
<http://citeseer.ist.psu.edu/chan99refined.html>.
D. Koppelman. Congested Banyan Network Analysis Using CongestedQueue States amd Neighboring-Queue Effects. 1995.
<http://citeseer.ist.psu.edu/30043.html>.