---

Condition for unambiguity with finite sequence numbers

---

• Pre-requisite to understanding this material: relationship between the send window and receive window
  • Consider the following sliding window setting:

    N = 4   (we use 4 sequence numbers)         Send window size = 3 Receive window size = 3

    ---

    ---

  • Initially:

    The send/receive windows are lined up

    ---

    ---

  • Suppose the receive window is now: [3,0,1]

    Question:

    What are the possible values for the send window ???

    Answer:

    The possible values for the send window are: [0,1,2]        [1,2,3] [2,3,0] [3,0,1] Graphically:

    Reason:

    The send window can fall the farthest behind the receive window as possible: This happens when all ACK frames were lost The send window can line up (= farthest ahead) with the receive window: This happens when all ACK frames were received When some of the ACK frames were received (and some were lost), the send window can be [1,2,3] or [2,3,0]

  ---

  ---

  ---

  ---

• How is ambiguity "created"
  • Fact:

    Ambiguity is "created" (= caused) by a sequence number x when: The sequence number x is inside the receiver window The sender can use the sequence number x to identify   two (2) different (data) frames

    ---

    ---

    Example:

    Initially, the send window and receive window are lined up: Without loss of generality, we can assume that: The sender window and receiver window are lined up at the sequence number 0 (The argument will work for any sequence number. It is easier to understand using as starting sequence number = 0) Suppose the receiver receives 3 frames and slides the receive window forward: Pay attention the sequence number 0 inside the receive window It is now possible for the sender to use confuse the receiver by using sequence number 0: The sender could have fallen behind and re-transmit the frame #1 using the sequence number 0 to the receiver: The sender could have caught up and sends the frame #(N+1) using the sequence number 0 to the receiver:

    ---

    ---

  • How to prevent ambiguity:

    For every sequence number x inside the (= any) receive window We make sure that the sender cannot use sequence number x to identify two different frames !!!!!!

  ---

  ---

  ---

  ---

• A concrete example on how to prevent ambiguity
  • Consider the following sliding window setting:

    N = 4   (we use 4 sequence numbers)         Send window size = 2 Receive window size = 2

    ---

    ---

  • Suppose that the receive window is [2,3]:

    ---

    ---

  • The possible values of the send window of the sender are

    [0,1]       [1,2] [2,3]

    ---

    ---

    ---

  • The sender cannot confuse the receiver because:

    The sender can only use the sequence number 2 to identify frame #3 The sender can only use the sequence number 3 to identify frame #4 The sender cannot use the sequence number 2 or 3 (in the receive window) to identify 2 different frames !!!

    Therefore:

    No ambiguity possible !!!!!!

    This unambiguous case was discussed previously: click here

  ---

  ---

  ---

  ---

  ---

  ---

  ---

  ---

• Another example to how to prevent ambiguity
  • Consider the following sliding window setting:

    N = 4   (we use 4 sequence numbers)         Send window size = 3 Receive window size = 1

    ---

    ---

  • Suppose that the receive window is [3]:

    ---

    ---

  • The possible values of the send window of the sender are:

    [0,1,2]       [1,2,3] [2,3,0] [3,0,1]

    ---

    ---

    ---

  • The sender cannot confuse the receiver because:

    The receive window = [3] That mean: The receiver will only buffer the frame with sequence number 3 !!! Within the range of the send window values: The sender can only transmit the frame #4 using the sequence number 3:

  ---

  ---

  ---

  ---

• Sufficient condition to guarantee unambiguity (with proof)
  • Sufficient condition that guarantee that a sequence number in the send window will uniquely identifies a unique frame:

    Let N = the number of different sequence numbers available Let Wsend = the send window size Let Wrecv = the receive window size If: (1) Wsend + Wrecv ≤ N then: A sequence number in the send window will uniquely identifies one specific frame

    Proof:

    The labeling of the data frames is as follows: Consider an arbitrary receive window: (The proof is similar for other windows, but this specific window make the explanation easier to understand) The farthest behind value for the send window is: The farthest ahead value for the send window is: Within the range of possible values for the send window: each value inside the receive window (Wrecv) is used to identify one (1) specific frame: Therefore: Ambiguity is not possible

  ---

  ---

  ---

  ---

• Commonly used Send/Receive windows
  • If the frame has N bits for sequence/ACK numbers, then:

    Wsend = 2N-1 Wrecv = 2N-1