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 \(\mathrm{ACK}\) field in all possible messages cur rently propagating back to the sender at time \(t ?\) Justify your answer.

Short answer

a. {k, k+1, k+2, k+3}; b. The ACK value is k in all ACK messages sent.

Step-by-step solution

Understanding the Sender's Window Size

The Go-Back-N (GBN) protocol has a sender window size which limits the number of unacknowledged packets a sender can transmit. In this case, the sender window size is 4.

Identifying Sequence Number Range

GBN uses sequence numbers in a range from 0 to 1023, giving a total of 1024 sequence numbers. This is a modulo operation in practice, where after reaching the sequence number 1023, it wraps around back to 0.

Defining the Receiver's Expected Packet

The receiver is expecting packet with sequence number \( k \). This means the last received and correctly acknowledged packet was \( k-1 \).

Calculating Possible Sequence Numbers in Sender's Window

At time \( t \), the sequence numbers in the sender's window range from \( k \) to \( (k+3) \) because the window size is 4. Thus, the possible set of sequence numbers is \( \{k, k+1, k+2, k+3\} \). Each sequence number is valid as long as it's within the sequence range \([0, 1023]\).

Determining Possible ACK Values

The ACK field in any ACK message sent by the receiver acknowledges the next sequence number it expects. Since the receiver is waiting for sequence number \( k \), the highest ACK number for any message being propagated is \( k \), meaning all ACKs being sent acknowledge up to \( k-1 \).

Key concepts

Sender Window Size

In the Go-Back-N (GBN) protocol, the sender's window size is crucial because it determines how many packets the sender can transmit without receiving an acknowledgment from the receiver. This ensures that the sender does not overwhelm the network and can efficiently manage the flow of packets.

In the exercise provided, the window size is set at 4. This means the sender can have up to 4 packets that are sent but unacknowledged by the receiver.

The concept of the window size is vital for understanding how data packets are controlled and managed during transmission, avoiding congestion, and ensuring reliable data communication.

Sequence Numbers

Sequence numbers are unique identifiers assigned to packets to ensure they are received in the correct order. In the GBN protocol, they play a crucial role in maintaining the integrity of data transmission over the network.

The sequence number range in this example is from 0 to 1023, providing 1024 unique sequence numbers. This range allows the protocol to handle a large number of packets efficiently.

Since the sequence numbers are handled using modulo arithmetic, when it reaches 1023, it wraps around to 0. This keeps the sequence manageable and helps in tracking the ordered delivery of packets. At time \( t \), if the receiver expects the packet numbered \( k \), the sender's window of sequence numbers could range from \( k \) to \( (k+3) \).

This wrapping mechanism is key to the design of GBN, allowing the system to reuse sequence numbers once earlier packets are acknowledged, optimizing the sliding window mechanism.

ACK Field

The ACK (Acknowledgment) field is used by the receiver to inform the sender that it has successfully received packets up to a certain sequence number. In the GBN protocol, this field is essential for the error control mechanism.

The exercise describes scenarios involving acknowledged packets. The receiver will send an ACK with the sequence number of the next packet it expects, indicating that it has received all previous packets in order. For instance, if it expects sequence number \( k \), all propagating ACKs will have the value \( k \), acknowledging delivery up to \( k-1 \).

This mechanism ensures that if any packet is lost or received out of order, the sender can retransmit the necessary packets, maintaining the data flow's reliability and consistency.

Packet Transmission

Packet transmission in the GBN protocol involves efficient sending and acknowledgment of data packets. This process is guided by the sender's window, sequence numbers, and ACKs.

The sender transmits packets up to the window size, and each packet carries a sequence number. As the receiver acknowledges each packet through the ACK field, the sender shifts its window forward, maintaining the flow of new data.

If a packet is lost or an error is detected (an ACK is not received), the GBN protocol will require the sender to retransmit all packets from the last acknowledged packet. This ensures reliable delivery but may lead to increased retransmissions if packets frequently get lost. Such a mechanism highlights the balance between efficiency and reliability inherent in the GBN protocol.