Totally Ordered Broadcast

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Totally Ordered Broadcast

• Algorithms for Distributed System
• Semester Project
• (Nam Thoai)

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Totally Ordered Broadcast

• Broadcast
• Broadcast Service Qualities
• ordering single-source FIFO, totally ordered,
  causally ordered
• reliability
• Implementing a broadcast service
• Algorithm for Totally Ordered Broadcast
• Modified Algorithm for Totally Ordered Broadcast

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Broadcast

• Point-to-Point links provides One-to-One
  communication one processor sends a message on
  an incident link to a single other processor
• Broadcast(multicast) provides one-to-all
  (one-to-many) communication a processor sends a
  message to all processors
• Broadcast (multicast) can be simulated by sending
  a number of point-to-point messages

M
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The Basic Service Specification (broadcast)

• bc-sendi(m,qos) An input event of processor pi,
  which sends a message m to all processors,
  containing an indication of the sender qos is a
  parameter describing the quality of service
  required.
• bc-recvi(m,j,qos) An output event in which
  processor pi receives the message m previously
  broadcast by pj qos, as above, describes the
  quality of service provided.
• Basic broadcast service each bc-recvi(m,j,qos)
  event is mapped to an earlier bc-sendi(m,qos)
  event, every message received was previously sent
  (Integrity), and every message that is sent is
  received once (Liveness) and only once (No
  Duplicates) at every processor.

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Broadcast Service Qualities

• Broadcast properties can be organized along two
  axes
• Ordering Do processors see all messages in the
  same order or just see the messages from a single
  processor in the order they were sent ? Does the
  order in which messages are received by the
  broadcast service preserve the happens-before
  relation ?
• Reliability Do all processors see the same set
  of messages even if failures occur in the
  underlying system? Do all processors see all the
  messages broadcast by a nonfaulty processor?

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Ordering

• Single-Source FIFO For all messages m1 and m2
  and all processors pi and pj, if pi sends m1
  before sends m2, then m2 is not received at pj
  before m1 is.
• Totally Ordered For all messages m1 and m2 and
  all processors pi and pj, if m1 is received at pi
  before m2 is, then m2 is not received at pj
  before m1 is.
• Causally Ordered For all messages m1 and m2 and
  every processor pi, if m1 happens before m2, then
  m2 is not received at pi before m1 is.
• Note message m1 is said to happen before message
  m2 if either
• the bc-recv event for m1 happens before the
  bc-send event for m2, or
• m1 and m2 are sent by the same processor and m1
  is sent before m2.

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Ordering

• Causally Ordered implies Single-Source FIFO

a
a
b
a,b
b,a
b
b,a
b,a
(1) causally ordered (totally ordered)
(2) totally ordered (causally ordered,
single-source ordered)
a
b,a
b
a,b
(1) single-source FIFO (totally ordered, causally
ordered)
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Reliability

• In the presence of faulty processors, the
  Liveness property needs to be weakened.
• There are at most f faulty processors and the
  mapping ? from bc-recv(m) events to bc-send(m)
  events.
• Integrity For each processor pi, 0 ? i ? n-1,
  the restriction of ? to bc-recvi events is
  well-defined. That is, every message received was
  previously sent - no message is received out of
  thin air.
• No Duplicates For each processor pi, 0 ? i ?
  n-1, the restriction of ? to bc-recvi events is
  one-to-one. That is, no message is received more
  than once at any single processor.

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Reliability

• Nonfaulty Liveness When restricted to bc-send
  and bc-recv events at nonfaulty processors, ? is
  onto. That is, all messages broadcast by a
  nonfaulty processor are eventually received by
  all nonfaulty processors.
• Faulty Liveness If one nonfaulty processor has a
  bc-recv event that maps to a particular bc-send
  event of a faulty processor, then every nonfaulty
  processor has a bc-recv event that maps to the
  same bc-send event. That is, every messages sent
  by a faulty processor is either received by all
  nonfaulty processors or by none of them.
• Atomic broadcast is a reliable broadcast with
  total ordering atomic broadcast is also called
  total broadcast. FIFO atomic broadcast is an
  atomic broadcast with single-source FIFO
  ordering. Causal atomic broadcast is an atomic
  broadcast with preserves causality.

Pn-1
m1
m1
m1
. . .
P0
P1
Pn-1-f
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Implementing a Broadcast Service

• Basic Broadcast Service
• Using the underlying point-to-point message
  system to send a copy of m to all processors.
• Single-Source FIFO Ordering

message(data, N)
N
N N1 bc-send(data, N)
Message(data, n) is received if all message(i)
(0 ? i lt n) are received
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Totally Ordered Broadcast

• An Asymmetric Algorithm
• Processor pi sends m using the basic broadcast
  service to a unique central site at processor pc.
• Processor pc assigns a sequence number to each
  message and then sends it to all processors using
  the basic broadcast service.
• Message(k) is received if all messages(i) (0 ? i
  lt k) are received

c
a
b
?
?
?
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Totally Ordered Broadcast

• A Symmetric Algorithm
• Based on assigning timestamps to messages.
• Assume that the underlying communication system
  provides single-source FIFO broadcast.
• Each processor maintains an increasing counter
  (timestamp), which is tagged on messages.
• Each processor also maintains a vector with
  estimates of the timestamps of all other
  processes. Processor pi updates its entry for pj
  using the tags on messages received from pj and
  using special timestamp update message sent by
  pj.

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Totally Ordered Broadcast

• (Code for pi, 0 ? i ? n-1)
• Initially tsj0, 0 ? j ? n-1, and pending is
  empty
• 1 when bc-sendi(m,to) occurs // quality of
  service to means totally ordered
• 2 tsi tsi1
• 3 add ?m, tsi, i? to pending
• 4 enable bc-sendi(?m, tsi?, ssf) //
  quality of service to means single-source FIFO
• 5 when bc-recvi(?m, T?, j, ssf), j?i, occurs //
  j indicates sender ignore messages from self
• 6 tsj T
• 7 add ?m, T, j? to pending
• 8 if T gt tsi then
• 9 tsi T
• 10 enable bc-sendi(?ts-up, T?, ssf) //
  bcast timestamp update message
• 11 when bc-recvi(?ts-up, T? , j, ssf), j?i,
  occurs // ignore message from self
• 12 tsj T
• 13 enable bc-recvi(m, j, to) when

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Totally Ordered Broadcast (implementation)

• (Code for pi, 0 ? i ? n-1)
• Initially tsj0, tnj0 (0 ? j ? n-1), N0,
  and pending is empty
• 1 when bc-sendi(m,to) occurs // quality of
  service to means totally ordered
• 2 tsi tsi1
• N N1
• 3 add ?m, tsi, N, i? to pending
• 4 enable bc-sendi(?m, tsi, N?, basic) //
  quality of service to means basic
• 5 when bc-recvi(?m, T, N?, j, basic), j?i,
  occurs // j indicates sender ignore messages
  from self
• 6 tsj T
• 7 add ?m, T, N, j? to pending
• 8 if T gt tsi then
• 9 tsi T
• 10 enable bc-sendi(?ts-up, T?,
  basic) // bcast timestamp update message
• 11 when bc-recvi(?ts-up, T? , j, basic), j?i,
  occurs // ignore message from self
• 12 tsj T
• 13 enable bc-recvi(m, j, to) when