Window Sizes and Flow Control

1
Window Sizes and Flow Control

• Two factors that can affect each other are
• the maximum window size allowed by a protocol
• the number of bits available for sequence numbers
• If m bits are available for sequence numbers,
  then there are 2m possible sequence numbers (0
  ... 2m -- 1).
• We want to avoid the situation where a window
  could include two messages that are different,
  but have the same sequence number.
• Clearly, the window size W should be such that W
  lt 2m
• However, there may be additional constraints, so
  this is not the final value.

2
Window sizes at the receiver

• Although window sizes are usually with reference
  to the sender, there is effectively a receiving
  window as well.
• The receivers window size is determined by the
  set of messages it is willing to accept at any
  given time.
• For Go-back-N, the receivers window size is
  straightforward it is always 1.
• Suppose that a receiver is expecting message N
  .
• Any message with sequence number lt N is assumed
  to have been received already, and the message is
  a duplicate created by a resend.
• Any message with sequence number gt N is discarded
  as being out of order.
• In this context, the lt and gt operators take
  into account that for m bit sequence numbers,
  2m1 lt 0 lt 1

3
Go-back-N window limits

• Since Go-back-N does not look ahead, all other
  sequence numbers are considered to be
  distinguishable.
• If the protocols acknowledgements are for the
  next expected sequence number, we cannot use the
  entire space.
• 3 bit sequence numbers, send 0 through 7 ?
  acknowledgment number is 0.
• Is it that 0 through 7 were received, or that no
  messages were received?
• 5 bit sequence number, send 0 through 6 ?
  acknowledgement number is 0
• Can only be interpreted as no messages
  received.
• 5 bit sequence number, send 0 through 6 ?
  acknowledgment number is 7
• Can only be interpreted as all messages
  received.
• Result The maximum window size for go-back-N is
  2m 1 when sequence numbers have m bits.

4
Window sizes, Go-back-N
5
Selective Repeat Receivers Window (1)

• For Selective Repeat, the receivers window size
  is more complicated.
• There are three types of messages that could be
  received. Suppose that a receiver is expecting
  message M. It could actually receive
• the message we are expecting M
• a resend of a previous message lt M
• a message ahead of the one we expect gt M
• Since our space of sequence numbers is circular
  through 0, there has to be a limit on how far we
  can look ahead from message M for acceptable
  messages.
• That is, there needs to be a division point at
  which we distinguish a previous message from a
  future message.
• Why? If we have unlimited look ahead, message M
  1 might be saved as a future message even
  though it is more likely to be a resend.

6
Selective Repeat Receivers Window (2)

• To distinguish the past from the future, we
  will divide the sequence number space in halves,
  based on our current expected sequence number.
• If we have 2m possible sequence numbers
• 2m1 sequence numbers lt N are considered to be
  the past
• 2m1 1 sequence numbers gt N are considered to
  be the future.
• One sequence number, N, is our expected message.
• Out of the entire space, 2m1 sequence numbers
  will be accepted and 2m1 sequence numbers will
  be rejected.
• In this context, the lt and gt operators take
  into account that for m bit sequence numbers,
  2m1 lt 0 lt 1

7
Selective Repeat Receivers Window (3)

• Example 3 bit sequence numbers, next expected
  message is 2
• Past 6, 7, 0, 1
• Present 2
• Future 3, 4, 5
• If a message with sequence number 6, 7, 0, or 1
  arrives, it will be assumed to be a resend and
  discarded.
• If a message with sequence number 2, 3, 4, or 5
  arrives, it will be saved in buffer and accepted.
• Result The maximum window size for selective
  repeat is 2m1 when sequence numbers have m bits.

8
Window sizes, selective repeat
9
Question

• Suppose that a protocol is using Go-Back-N flow /
  error control, and the protocol uses 5 bits of
  sequence numbers. What is the largest sending
  window size that can be used safely? What could
  go wrong if a larger window size is used?
• What if Selective Repeat was being used?

10
Solution

• Largest window size that can be used safely is 31
  (25 1).
• Why? Here is what could go wrong if we could
  send 32 messages.
• Suppose that the receiver tells us that the next
  message expected is message 0. We send messages
  0 through 31 that is, 32 messages in total
  and the receiver tells us that it now expects
  message 0.
• This could be interpreted by the sender in two
  ways
• All 32 messages that we sent were received
  successfully, and so the receiver is now
  expecting message (311) 0, assuming that only
  5 bits are available to store sequence numbers.
• All 32 messages were lost, and the receiver is
  still expecting the original message 0. Wait
  for the timeout and resend the messages.

11
Solution (if the window size is 25)
28
29
30
31
0
1
2
3
4
5
28
29
30
31
0
1
2
3
32 messages were sent
Sender cant tell if the messages were lost or
received
1
2
3
28
29
30
31
0
Send 0
12
Solution

• There there could be several causes for why it
  appears to the sender that all 32 messages are
  lost
• All 32 messages were, in fact, lost
• All of the acknowledgments were lost, but the
  messages were actually received successfully.
• Various combinations of the above.
• Note that the sender cannot tell the difference
  between a lost message and a lost acknowledgment.
  It has to assume the message is lost and await a
  timeout to resend.

13
Solution (if the window size is 25-1)
28
29
30
31
0
1
2
3
4
5
28
29
30
31
0
1
2
3
31 messages were sent
Sender knows which 0 to send
28
29
30
31
0
1
2
3
Send 0
14
Solution

• 31 messages in the window is safe.
• If all 31 messages, presumably numbered 0
  through 30, are lost, the receiver will tell us
  it still expects message 0.
• Since there is at least one sequence number we
  havent used (i.e. 31), the receiver cannot be
  expecting the next 0 and so it must be
  expecting the previous 0.
• All of this only applies to Go-back-N

15
Same question, selective repeat

• If we are using Selective Repeat, then only half
  of the sequence number space can be used, because
  the receiver is willing to look ahead for
  messages out of sequence.
• Allow the receiver to use half of the sequence
  number space for taking in out of sequence
  messages, and the other half for resends.
• With 32 sequence numbers available
• If we are currently expecting message 16 from the
  receivers point of view, then at the receiver
• Messages with sequence numbers 0 to 15 arriving
  at the receiver are assumed to be resends.
• A message with sequence number 16 is what we
  want.
• Messages with sequence numbers 16 to 31 are
  assumed to be new messages to be kept while
  waiting for message 16 to arrive.

16
Selective Repeat (window size is 25-1)
Sender Window
7
8
9
17
18
20
10
11
12
13
14
16
19
15
21
22
23
31
24
25
26
27
28
30
29
Frames sent but not received ACK
Frames that can be sent
Receiver Window
7
8
9
17
18
20
10
11
12
13
14
16
19
15
21
22
23
31
24
25
26
27
28
30
29
Frames already received
Frames that can be received and stored
Next Expected Frame
Frames which have arrived out of order
17
Selective Repeat Solution

• In the case where a message 0 through 14 arrives,
  it may be because
• The message was selectively rejected, and the
  receiver had asked for a resend.
• An acknowledgment had been lost, and the sender
  timed out. Even though the receiver has the
  message, it has appeared again.
• If a message 2 shows up, the receiver needs to
  be able to distinguish between the previous 2
  and the next 2.
• Result maximum window size for sender is 2m1,
  where m is the number of bits in the sequence
  number. Therefore, if we have 5 bits in the
  sequence number, the maximum selective reject
  window size is 25-1 24 16.

18
What about the receiver?

• From the receivers point of view, the window
  size is
• 1 for Go-back-N
• There is only one message sequence number that
  will be accepted by the receiver.
• 2m1 for Selective repeat
• Up to this many sequence numbers can be accepted
  by the receiver.