Question

In a network whose max segment is 128 bytes, max segment lifetime is 30 sec, and has 8 -bit sequence numbers, what is the maximum data rate per connection?

Short answer

The maximum data rate per connection is 1,092.27 bytes/second.

Step-by-step solution

Identify the key parameters

We are given the following parameters for the network: the maximum segment size is 128 bytes, the maximum segment lifetime is 30 seconds, and the sequence numbers are 8 bits, which means the sequence number space is from 0 to 255 (since 8 bits can represent 256 different values).

Calculate the Sequence Number Space

The sequence number space is determined by the number of bits dedicated to the sequence number. Since we have 8 bits for the sequence numbers, the sequence number space is: \[ 2^8 = 256 \] So the sequence numbers range from 0 to 255.

Calculate the Maximum Window Size

The maximum window size in terms of bytes is equal to the maximum sequence number space (256) multiplied by the maximum segment size (128 bytes). This is:\[ 256 \text{ segments} \times 128 \text{ bytes/segment} = 32,768 \text{ bytes} \]

Calculate the Maximum Data Rate

The maximum data rate (bytes per second) is equal to the maximum window size divided by the maximum segment lifetime which is 30 seconds:\[ \text{Max Data Rate} = \frac{32,768 \text{ bytes}}{30 \text{ seconds}} = 1,092.27 \text{ bytes/second} \]

Key concepts

Sequence Numbers

In computer networks, sequence numbers are used to ensure that data packets are assembled correctly at the receiving end. Sequence numbers keep track of the order in which data packets (segments) are sent and received over the network.
In our scenario, the sequence number is 8 bits long, which allows for 256 unique sequence numbers. This is calculated using the formula for the total number of values represented by a specified number of bits:

• Formula: \(2^n\), where \(n\) is the number of bits.
• For our situation: \(2^8 = 256\).

A sequence number space of 256 means the sequence begins at 0 and ends at 255, making it possible to identify each segment uniquely within this range. This sequence number space is crucial for managing data packets, especially in preventing errors such as duplicate data and ensuring data integrity during transmission.

Segment Size

Segment size in networking refers to the maximum amount of data that can be sent in one segment or packet. In this exercise, the given maximum segment size is 128 bytes.
This size dictates how much data is included in each packet transmitted over the network. Having a specific segment size helps in efficiently managing network traffic and optimizing the use of available bandwidth. Let's break down why segment size is important:

• A larger segment size can increase efficiency by reducing overhead.
• A smaller segment size might lower efficiency because more overhead per data byte exists.

Choosing a segment size of 128 bytes in our example reflects a balance of efficiency and control, ensuring a steady and reliable flow of data across the network.

Window Size

Window size is a critical concept that determines the amount of data that can be sent over the network before requiring an acknowledgment from the receiver.
In our exercise, the window size is derived from combining the sequence number space with the segment size:

• Formula: Window Size = Sequence Number Space \(\times\) Segment Size.
• Calculation: \(256 \text{ segments} \times 128 \text{ bytes/segment} = 32,768 \text{ bytes}\).

This window size influences flow control within networks by allowing the sender to transmit a specific number of bytes (here, 32,768 bytes) before waiting for an acknowledgment. This method helps maximize data rate while minimizing the need for frequent acknowledgments from the receiver.

Data Rate Calculation

The data rate in a network context is the speed at which data is transferred from one place to another. In our given exercise, we need to calculate the maximum achievable data rate given the network conditions.
To do this, we use the formula for maximum data rate:

• Formula: Maximum Data Rate = \(\frac{\text{Window Size}}{\text{Maximum Segment Lifetime}}\)
• Calculation: \(\frac{32,768 \text{ bytes}}{30 \text{ seconds}} = 1,092.27 \text{ bytes/second}\)

This calculation means that the network can theoretically transfer approximately 1,092.27 bytes every second under the given constraints. The data rate is an essential metric for understanding the performance capacity of a connection, impacting how quickly information is transmitted and received across a network.