- Claim:
- The receiver will deliver each frame exactly once, and
- The frames are will be delivered in the order that were transmitted
-
The Sliding Window protocol using
infinite set of sequence numbers
can
guarantee that:
Proof: by showing the following 3 claims:
- Each frame
will be received
at least
once by the receiver.
- A received frame
will be delivered
exactly once
- Received frames are delivered in the transmitted order
- Claim 1:
- A data frame (say: frame x) will be received at least once by the receiver.
Proof:
- Fact 1:
- As long as
data frame x is
outstanding
(= unacknowledged),
the sender will
keep transmitting
the data frame x.
(Sender can timeout on an outstanding frame and re-transmit)
- Rephrased:
as long as x is
inside the
sender window:
the sender will keep sending the data frame
Therefore:
- As long as
data frame x
is inside
the
sender window:
the receiver will have the opportunity to receive the data frame x
- As long as
data frame x is
outstanding
(= unacknowledged),
the sender will
keep transmitting
the data frame x.
- Fact 2:
- A data frame x that
was
not received by
the receiver will
be
inside the
receiver window or
pass the
receiver window:
- A data frame x that
was
not received by
the receiver will
be
inside the
receiver window or
pass the
receiver window:
- Therefore, the
receiver
will
not
receive
a frame x
if:
- The receiver
has not received
the frame x
yet:
- And
the sender will
not transmit the
frame x
any more:
I.e.: frame x must not be inside the send window
In other words:
And this situation is impossible because we have shown that:
- The receive window
will always be
lined up or ahead the
send window !!!
See: click here
- The receiver
has not received
the frame x
yet:
- Claim 2:
- A frame x will be delivered exactly once
Proof:
- While the
frame x is
inside the
receiver window:
the receiver can receive duplicate frame x
- Because
each frame has
a unique sequence number:
- The receiver can remove the duplicates !!!
- When the receiver
delivers the
data frame x,
the receiver window will:
also slide the receiver window pass the value x !!!
- In this state:
Retransmission of data frame x are discard !!!
- Therefore:
- A data frame x will be delivered exactly once !!!
- This cliam is
obvious:
- Data frames are
transmitted in
increasing order by
the sender
- Data frames are
delivered in
increasing order by
the receiver
- There is only
one ordering possible
with a set of
integer values that
is
increasing order
(Namely: x, x+1, x+2, ....)
- There is only
one ordering possible
with a set of
integer values that
is
increasing order
- Therefore:
- Received frames are delivered in the transmitted order
- Data frames are
transmitted in
increasing order by
the sender