ChannelSharing and Multicasting

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Chapter 7

• Channel-Sharing and Multicasting

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Outline

• 7.1 Introduction
• 7.2 Background
• 7.3 Shared-Channel Multi-hop GEMNET
• 7.4 Performance Evaluation
• 7.5 Illustrative Example Unicast Traffic
• 7.6 Illustrative Example Multicast Traffic

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Introduction

• W (the number of wavelengths) ?N (the number of
  nodes)
• A general method using channel-sharing is used to
  construct practical multihop networks under this
  limitation.
• Channel-sharing may be achieved through
  time-division multiplexing (TDM).
• Apply to the generalized shuffle-exchange-based
  multihop architecture, called GEMNET

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Multicast

• Multicasting the ability to transmit information
  from a single source node to multiple destination
  nodes
• Application
• (1) multiperson conferences,
• (2) video lectures where a single speaker can
  address a large audience,
• (3) "multipoint-LAN interconnection" which allows
  large companies to treat their many
  geographically distributed LANs as a single large
  network, and
• (4) Collaborative systems. Multicasting is also
  required to make updates in replicated and
  distributed databases.
• (5) Multiprocessor systems also require
  multicasting for cache coherency and message
  passing.
• (6) make updates in replicated and distributed
  databases.

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Introduction

• For the case w lt N, each of the w channels will
  be assumed to be shared by one or more nodes in a
  time-division multiplexed (TDM) fashion.
• Each node is equipped with only a single
  transmitter-receiver pair.
• WDM channels are shared by nodal transmitters
  and receivers in TDM fashion, exhibit an
  interesting and anomalous delay behavior when the
  number of wavelengths is varied.

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Delay Behavior
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Multicast on channel-sharing

• Interestingly, channel-sharing approaches are
  very well suited for multicasting applications in
  a local lightwave network.
• This is because our methods will entail sharing
  at both the transmitting and the receiving ends.
• The latter implies that many nodes will be able
  to simultaneously receive the same information
  from a single transmission, thereby increasing
  the receiver through-put (informally defined as
  the average rate of information received by nodes
  in the network) for multi-destination traffic.

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7.2 Background of Channel-sharing

• The first extensive treatment of the multihop
  approach in WDM optical networks was provided in
  Acam87.
• ShuflieNet logical topology,
• P transmitter-receiver pairs.
• each node has a degree P, and
• networks of size N KPK
• the number of channels w KPK1, where K is the
  number of columns in the ShuffleNet.
• The idea of channel-sharing is achieved through
  the use of TDM all receivers in a common row of
  the ShuffleNet are assigned the same wavelength.

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?1
?1
?5
?5
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Channel-sharing

• these transmitters must take turns (e.g., in TDM
  fashion) to use this channel.
• Any packet of information that these two
  transmitters put onto the channel will be "heard"
  by both nodes 2 and 3.
• The limitation of this strategy is that each node
  requires two transmitter-receiver pairs even in
  the shared case.

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Multicasting

• Single-hop System
• In both BoMu95b and RoAm94, it was shown
  that, for systems with tunable receivers, the
  receiver throughput BoMu95b defined to be the
  number of packets that are delivered in a
  single-transmission slot to various destinations
  in a passive-star network can be greater than
  the transmitter throughput.
• It was also shown in RoAm94 that receiver
  throughput can be much larger than transmitter
  throughput even in systems with tunable
  transmitters provided w lt N channels are used.

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Multicast

• Multihop System
• FT-FR Not only cost effective, but can also
  provode a good basis for comparison with single
  hop system.
• WltN, Nkw
• GEMNET N need not be equal to KPK.
• Analysis feature
• Channel-sharing, TDM, fixed length packets,
  M/D/1.
• Nonzero propagation delay are considered.
• The effect of channel-sharing on the mean total
  delay experienced by a packet in the network can
  be quantified.
• The effect of multicast traffic.

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7.3 Shared-Channel Multihop GEMNET

• A (K, M, P) GEMNET,
• N nodes
• each of degree P
• arranged in a cylinder of K columns and M nodes
  per column so that nodes in adjacent columns are
  arranged according to a generalization of the
  shuffle-exchange connectivity pattern using
  directed links.
• Without channel-sharing, the number of channels
  required in a (K, M, P) GEMNET equals NPKMP.

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Shared Channel Multihop GEMNET

• When each node can have only one fixed
  transmitter-receiver pair and w lt N, the degree
  of the network takes on a new meaning.
  Channel-sharing through TDM implies a higher
  logical nodal degree (viz., ability to reach more
  nodes directly), albeit with a lower capacity on
  each of the logical links.
• The nodal degree is redefined as a logical
  quantity P, where P N/w.
• For analytical convenience, N is assumed to be an
  integral multiple of w to ensure equal and fair
  sharing by all logical links.
• Thus, we define a (K, M, P) SC_GEMNET
  (Shared-Channel GEMNET) as a GEMNET having K
  columns and M rows, where M is an integral
  multiple, n, of P
• (i.e., M nP) and K N/M N/(nP).

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N12, GEMNET
K12, M1
w6
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W4
w4
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N12, SC_MEMNET
w3
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w2
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average hop distance

• Diameter D
• The upper bound of average hop distance h
• The lower bound of average hop distance h

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• In general, two-column GEMNETs (i.e., K 2) have
  the best performance in terms of the average hop
  distance.
• Therefore, in constructing logical topologies for
  the multihop WDM network, it is, in general, best
  to consider K 2 wherever possible and use the
  next higher value of K as dictated by the
  requirement K N/M N/(nP) w/n, where n is an
  integer which equals the number of channels
  required to provide connectivity between two
  successive column.

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7.4 Performance Evaluation

• Derive an expression for the average delay
  encountered by a packet before it is delivered to
  all of its destinations.
• Assume that communication is time-slotted with a
  slot being equal to the transmission time of a
  packet.
• For example, if a 1-Gbps channel is used with a
  53-byte packet (or cell) as defined in the ATM
  standard, then the slot duration is 0.424µs.
• All other delays in the system are normalized to
  this slot duration.
• Intermediate nodes are capable of examining the
  headers of the packets they receive to determine
  whether the local node is a destination.

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Notations

• N Number of nodes in the system.
• w Number of channels in the system. w is chosen
  such that N/w is an integer.
• R Round-trip propagation delay between a node
  and the passive star. We assume that all nodes
  are equidistant from the passive star. If needed,
  delay lines can be installed so that R is the
  same for all nodes.
• F The frame length is equal to N/w. Since TDM is
  used on each of the channels and N/w is the
  number of nodes which share a single channel, a
  frame comprises F slots in which different nodes
  get to transmit.
• m Multicast destination set size. All packets in
  the network are multicast packets, and each one
  of them has a destination set size specified by a
  constant m.
• hm The average number of transmissions required
  to deliver information to the
• gm The average number of hops separating the
  source from each one of the destinations of a
  multicast packet.

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7.5 Illustrative Example Unicast Traffic

• N12 nodes
• Round-trip delay R2.
• Load ?0.05 packets per slot per node.
• Packet size 53bytes (ATM cell).
• Each channel operates on 100Mbps
• R2(4.24)8.48µs
• Node-to-star distance lt1km
• Load of each node 5Mbps, total 60Mbps.

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Various Delay
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Delay Behavior vs. Variation in ?
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Optimal of wavelength
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Delay Behavior in Larger Network N120
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R0
R1
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R100
R10
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• Larger network do not always requires an equal
  larger number of wavelength.

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7.6 Multicast traffic

• System A
• 39-node
• a single transmitter-receiver pair
• 39 dedicated channels
• node degree 1.
• the entire bandwidth of a channel is available
  to each node.
• logical topology ring.
• System B
• N39, 3 transmitter-receiver pairs
• 117 dedicated channels node degree 3,
• the bandwidth available to each node is 3 times
  the bandwidth of a channel.
• Topology (13, 3, 3)-GEMNET
• System C
• 39-node
• a single transmitter-receiver pair
• 13 dedicated channels (shared)
• node degree 3.
• the entire bandwidth of a channel is available
  to each node.
• Topology (13, 3, 3)-GEMNET.

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• System D
• A 42-node ring network,
• employing a single transmitter-receiver pair at
  each node and
• 42 channels.
• System E
• A (7, 6, 6)-GEMNET, employing six
  transmitter-receiver pairs
• at each node and 42 x 6 252 channels,
• nodal degree of six.
• System F
• A (7, 6, 6)-SC_GEMNET, employing a single
  transmitter-receiver pair at each node and
• seven channels, leading to a nodal degree of six.
• System G
• A (1, 42, 42)-SC_GEMNET, employing a single
  transmitter-receiver pair at each node and one
  channel.
• This is the classical TDM system.

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• We assume that the traffic arrival rate A 0.01
  packets per slot per node,
• propagation delay R 10 ( node-to-star distance
  of about 1 km,)
• Under these conditions, we evaluated the delay
  for the various systems for different values of
  destination set size m.

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A, B, and C

• System A with 39 dedicated channels has the worst
  performance.
• because the only network that can be logically
  implemented for this case is a ring network,
  which can have significant delays due to
  increased hop distance.
• Our shared-channel scheme with only 13 channels
  and a degree of three performs as well as the
  117-channel system also with degree three.
• In shared-channel case, it uses fewer channels
  and/or transceivers than the dedicated-channel
  cases (Systems A and B) however, it does perform
  better in terms of delay.

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