Alternating Bit Protocol
m[2],0
m[1],1
m[0],0
m[0],0
R
S
ack, 0
ABP is a link layer protocol. Works on FIFO channels only.
Guarantees reliable message delivery with a 1-bit sequence
number (this is the traditional version with window size = 1).
Study how this works.
Alternating Bit Protocol
program ABP;
{program for process S}
define sent, b : 0 or 1; next : integer;
initially next = 0, sent = 1, b = 0, and channels are empty;
do sent ≠b 
send (m[next], b);
next := next+1; sent := b
 (ack, j) is received  if j = b  b := 1-b
 j ≠ b  skip
fi
timeout (R,S)
 send (m[next-1], b)
od
{program for process R}
define j : 0 or 1; {initially j = 0};
do
(m[ ], b) is received 
if j = b  accept the message;
send (ack, j); j:= 1 - j
 j ≠ b  send (ack, 1-j)
fi
od
S
m[2],0
m[1],1
a,0
m[0],0
m[0],0
R
How TCP works
Supports end-to-end logical connection between any two
computers on the Internet. Basic idea is the same as those of
sliding window protocols. But TCP uses bounded sequence
numbers!
It is safe to re-use a sequence number when it is unique. With a
high probability, a random 32 or 64-bit number is unique. Also,
current sequence numbers are flushed out of the system after a
time = 2d, where d is the round trip delay.
How TCP works
Sender
Receiver
SY N seq = x
SY N, seq=y, ack = x+1
ACK, ack =y+1
send (m, y+1)
ack (y+2)
How TCP works
• Three-way handshake. Sequence numbers are unique w.h.p.
• Why is the knowledge of roundtrip delay important?
• What if the window is too small / too large?
• What if the timeout period is too small / toolarge?
• Adaptive retransmission: receiver can throttle sender
and control the window size to save its buffer space.
Distributed Consensus
Reaching agreement is a fundamental problem in distributed
computing. Some examples are
Leader election / Mutual Exclusion
Commit or Abort in distributed transactions
Reaching agreement about which process has failed
Clock phase synchronization
Air traffic control system: all aircrafts must have the same view
If there is no failure, then reaching consensus is trivial. All-to-all broadcast
Followed by a applying a choice function … Consensus in presence of
failures can however be complex.
Problem Specification
input
output
p0
u0
v
p1
v
p2
u1
u2
p3
u3
v
v
Here, v must be equal to the value at some input line.
Also, all outputs must be identical.
Problem Specification
Termination.
Every non-faulty process must eventually decide.
Agreement.
The final decision of every non-faulty process
must be identical.
Validity.
If every non-faulty process begins with the same
initial value v, then their final decision must be v.
Asynchronous Consensus
Seven members of a busy household decided to hire a cook, since they do not
have time to prepare their own food. Each member separately interviewed
every applicant for the cook’s position. Depending on how it went, each
member voted "yes" (means “hire”) or "no" (means “don't hire”).
These members will now have to communicate with one another to reach a
uniform final decision about whether the applicant will be hired. The process
will be repeated with the next applicant, until someone is hired.
Consider various modes of communication…
Asynchronous Consensus
Theorem.
In a purely asynchronous distributed system,
the consensus problem is impossible to solve
if even a single process crashes
Famous result due to Fischer, Lynch, Patterson
(commonly known as FLP 85)
Proof
Bivalent and Univalent states
A decision state is bivalent, if starting from that state, there exist
two distinct executions leading to two distinct decision values 0 or 1.
Otherwise it is univalent.
A univalent state may be either 0-valent or 1-valent.
Proof
Lemma.
No execution can lead from a 0-valent to a 1-valent
state or vice versa.
Proof.
Follows from the definition of 0-valent and 1-valent states.
Proof
Lemma. Every consensus protocol must have a bivalent initial state.
Proof by contradiction. Suppose not. Then consider the following scenario:
s[0]
s[n-1]
0 0 0 0 0 0 …0 0 0
0 0 0 0 0 0 …0 0 1
0 0 0 0 0 0 …0 1 1
…
…
…
1 1 1 1 1 1 …1 1 1
{0-valent)
…
{1-valent}
s[j] is 0-valent
s[j+1] is 1-valent
(differ in jth position)
What if process (j+1) crashes at the first step?
Proof
Lemma.
Q
In a consensus protocol,
starting
from
any
initial
bivalent state, there must
exist a reachable bivalent
state T, such that every
action taken by some process
bivalent
The adversary tries to prevent
The system from reaching
consensus
bivalent
bivalent
S
R
action 0
R0
o-valent
bivalent
U
action 1
R1
1-valent
bivalent
T
action 0
T0
o-valent
action 1
T1
1-valent
p in state T leads to either a
0-valent or a 1-valent state.
Actions 0 and 1 from T must be
taken by the same process p. Why?