Question

Consider the GBN protocol with a sender window size of 4 and a sequence number range of 1,024 . Suppose that at time \(t\), the next in-order packet that the receiver is expecting has a sequence number of \(k\). Assume that the medium does not reorder messages. Answer the following questions: a. What are the possible sets of sequence numbers inside the sender's window at time \(t\) ? Justify your answer. b. What are all possible values of the ACK field in all possible messages currently propagating back to the sender at time \(t\) ? Justify your answer.

Short answer

a. Sequence numbers: \( \{ k, k+1, k+2, k+3 \} \); b. ACK field: \( k \).

Step-by-step solution

Understanding the Sender's Window

Given that the sender window size is 4 and the sequence number range is 1,024, we need to determine the sequence numbers that can be present in the sender's window when the receiver is expecting packet sequence number \( k \). Since the receiver is expecting the \( k \)-th packet, the last packet acknowledged was \( k-1 \), and the sender can send up to 4 more packets. This means the sender window can contain packets with sequence numbers \( k, k+1, k+2, \) and \( k+3 \). Thus, the possible sets of sequence numbers are \( \{ k, k+1, k+2, k+3 \} \).

Analyzing the ACK Field Values

Given that the receiver expects the next packet with sequence number \( k \), the receiver has acknowledged all packets up to \( k-1 \). In the Go-Back-N protocol, the Receiver sends ACK for the last in-order packet received, which is \( k-1 \). Therefore, the ACK messages propagating back to the sender will contain the sequence number \( k \) indicating all packets up to \( k-1 \) are acknowledged. If there were any ACKs in transit, they also represent sequence number \( k \). Thus, the ACK field is consistently \( k \) for all messages in transit.

Key concepts

Sender Window Size

In the Go-Back-N (GBN) protocol, understanding the sender window size is crucial for efficient data transmission.
The sender window size determines how many packets can be sent without waiting for an acknowledgment (ACK) from the receiver.
For example, if the sender window size is 4, it means the sender can send up to four packets in succession before requiring confirmation that the receiver successfully received them.

• This makes the sender window size a critical factor in how fast data can be pushed through a network.
• A larger window size allows for more packets to be in transit, potentially increasing throughput, especially in reliable and stable networks.
• However, a window size that is too large can flood the network, particularly if the network has high error rates, leading to many retransmissions.

In the context of the exercise, where the sender window size is specified as 4, it means four packets from the current sequence number, say starting at packet number \(k\), can be sent consecutively. These packets would have sequence numbers \(k, k+1, k+2,\) and \(k+3\). This setup helps in maintaining a balance between efficiency and network load, especially considering the potential for packet loss and the need for retransmissions.

Sequence Number Range

The sequence number range in a Go-Back-N protocol is an essential feature that defines how many unique sequence numbers are available for use.
In the exercise, the sequence number range is given as 1,024, which means there are 1,024 different numbers that can be used to uniquely identify packets before these numbers start to repeat.

• This large range is beneficial as it minimizes the chances of packet numbers clashing, particularly when older packets are still being processed as new packets are sent.
• The wrapping of sequence numbers allows continuous data flow without a long stoppage to reset sequence numbers, supporting uninterrupted communication.
• A larger sequence number range can effectively support a larger sender window size because it helps in reducing the risk of sequence number overlap between consecutive sender windows.

When the receiver expects a packet with a sequence number \(k\) in a system with a sequence number range of 1,024, it implies the sequence can cycle back to zero if packets continue beyond 1,023,
making careful management of these numbers important to avoid ambiguity.

ACK Field

The ACK (Acknowledgment) field in the Go-Back-N protocol is used to inform the sender which packets have been successfully received.
In this protocol, a cumulative acknowledgment is used, which means the receiver sends an ACK for the highest in-order sequence number received correctly.

• For instance, if the receiver has correctly received all packets up to sequence number \(k-1\), it sends an ACK with the value \(k\).
• This indicates that all packets up to \(k-1\) are acknowledged and the sender can proceed with sending subsequent packets.
• If an error is detected in any packet within the window, subsequent packets need to be retransmitted, adhering to the protocol's name "Go-Back-N."

In this context, at time \(t\), the ACK field in all acknowledgments currently traveling back to the sender carries the sequence number \(k\), confirming all packets up to \(k-1\) were received properly. It's important to understand that multiple ACKs with the same \(k\) number may exist in different stages of transit, but they all communicate the same state of readiness for the next packet \(k\).

Retransmission

Retransmission in the GBN protocol is triggered when the sender does not receive the expected ACK within a certain time frame.
This mechanism ensures reliable delivery in the case of packet loss, network congestion, or errors.

• As soon as the sender detects a missing ACK for an in-order packet, it resends all packets starting from that sequence number, even if some were received successfully, leading to potential redundant transmissions.
• This approach, while potentially inefficient due to duplicated data in transit, ensures that any lost or corrupted packets are successfully re-delivered, maintaining data integrity.
• Furthermore, retransmission underpins the concept of the sender window, as the window does not advance until the earliest packet in the current window is acknowledged.

Effective retransmission is essential in environments with unpredictable packet behavior, as it guarantees that all data eventually reaches its destination in correct sequence, a key feature of reliable data transfer protocols like GBN.