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Go-back-n : example
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The sliding window
Sliding window example
In practice, as the frame header includes an `n` bits field to encode the sequence number, only the sequence numbers between :math:`0` and :math:`2^{n}-1` can be used. This implies that, during a long transfer, the same sequence number will be used for different frames and the sliding window will wrap. This is illustrated in the figure below assuming that `2` bits are used to encode the sequence number in the frame header. Note that upon reception of `OK1`, the sender slides its window and can use sequence number `0` again.
Utilisation of the sliding window with modulo arithmetic
Unfortunately, frame losses do not disappear because a reliable protocol uses a sliding window. To recover from losses, a sliding window protocol must define :
a heuristic to detect frame losses
a `retransmission strategy` to retransmit the lost frames
The figure below shows the FSM of a simple `go-back-n` receiver. This receiver uses two variables : `lastack` and `next`. `next` is the next expected sequence number and `lastack` the sequence number of the last data frame that has been acknowledged. The receiver only accepts the frame that are received in sequence. `maxseq` is the number of different sequence numbers (:math:`2^n`).
The operation of `go-back-n` is illustrated in the figure below. In this figure, note that upon reception of the out-of-sequence frame `D(2,c)`, the receiver returns a cumulative acknowledgment `C(OK,0)` that acknowledges all the frames that have been received in sequence. The lost frame is retransmitted upon the expiration of the retransmission timer.
Go-back-n : example
The main advantage of `go-back-n` is that it can be easily implemented, and it can also provide good performance when only a few frames are lost. However, when there are many losses, the performance of `go-back-n` quickly drops for two reasons :
the `go-back-n` receiver does not accept out-of-sequence frames
the `go-back-n` sender retransmits all unacknowledged frames once it has detected a loss
`Selective repeat` is a better strategy to recover from losses. Intuitively, `selective repeat` allows the receiver to accept out-of-sequence frames. Furthermore, when a `selective repeat` sender detects losses, it only retransmits the frames that have been lost and not the frames that have already been correctly received.
A `selective repeat` receiver maintains a sliding window of `W` frames and stores in a buffer the out-of-sequence frames that it receives. The figure below shows a five-frame receive window on a receiver that has already received frames `7` and `9`.
The receiving window with selective repeat
A `selective repeat` receiver discards all frames having an invalid CRC, and maintains the variable `lastack` as the sequence number of the last in-sequence frame that it has received. The receiver always includes the value of `lastack` in the acknowledgments that it sends. Some protocols also allow the `selective repeat` receiver to acknowledge the out-of-sequence frames that it has received. This can be done for example by placing the list of the correctly received, but out-of-sequence frames in the acknowledgments together with the `lastack` value.
When a `selective repeat` receiver receives a data frame, it first verifies whether the frame is inside its receiving window. If yes, the frame is placed in the receive buffer. If not, the received frame is discarded and an acknowledgment containing `lastack` is sent to the sender. The receiver then removes all consecutive frames starting at `lastack` (if any) from the receive buffer. The payloads of these frames are delivered to the user, `lastack` and the receiving window are updated, and an acknowledgment acknowledging the last frame received in sequence is sent.
The `selective repeat` sender maintains a sending buffer that can store up to `W` unacknowledged frames. These frames are sent as long as the sending buffer is not full. Several implementations of a `selective repeat` sender are possible. A simple implementation associates one retransmission timer to each frame. The timer is started when the frame is sent and canceled upon reception of an acknowledgment that covers this frame. When a retransmission timer expires, the corresponding frame is retransmitted and this retransmission timer is restarted. When an acknowledgment is received, all the frames that are covered by this acknowledgment are removed from the sending buffer and the sliding window is updated.
The figure below illustrates the operation of `selective repeat` when frames are lost. In this figure, `C(OK,x)` is used to indicate that all frames, up to and including sequence number `x` have been received correctly.
Selective repeat : example
Pure cumulative acknowledgments work well with the `go-back-n` strategy. However, with only cumulative acknowledgments a `selective repeat` sender cannot easily determine which frames have been correctly received after a data frame has been lost. For example, in the figure above, the second `C(OK,0)` does not inform explicitly the sender of the reception of `D(2,c)` and the sender could retransmit this frame although it has already been received. A possible solution to improve the performance of `selective repeat` is to provide additional information about the received frames in the acknowledgments that are returned by the receiver. For example, the receiver could add in the returned acknowledgment the list of the sequence numbers of all frames that have already been received. Such acknowledgments are sometimes called `selective acknowledgments`. This is illustrated in the figure above.
In the figure above, when the sender receives `C(OK,0,[2])`, it knows that all frames up to and including `D(0,...)` have been correctly received. It also knows that frame `D(2,...)` has been received and can cancel the retransmission timer associated to this frame. However, this frame should not be removed from the sending buffer before the reception of a cumulative acknowledgment (`C(OK,2)` in the figure above) that covers this frame.
Maximum window size with `go-back-n` and `selective repeat`
A reliable protocol that uses `n` bits to encode its sequence number can send up to :math:`2^n` successive frames. However, to ensure a reliable delivery of the frames, `go-back-n` and `selective repeat` cannot use a sending window of :math:`2^n` frames. Consider first `go-back-n` and assume that a sender sends :math:`2^n` frames. These frames are received in-sequence by the destination, but all the returned acknowledgments are lost. The sender will retransmit all frames. These frames will all be accepted by the receiver and delivered a second time to the user. It is easy to see that this problem can be avoided if the maximum size of the sending window is :math:`{2^n}-1` frames. A similar problem occurs with `selective repeat`. However, as the receiver accepts out-of-sequence frames, a sending window of :math:`{2^n}-1` frames is not sufficient to ensure a reliable delivery. It can be easily shown that to avoid this problem, a `selective repeat` sender cannot use a window that is larger than :math:`\frac{2^n}{2}` frames.

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../../principles/reliability.rst:763
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locale/cs/LC_MESSAGES/principles/reliability.po, string 184