Question

An upper-layer packet is split into 10 frames, each of which has an \(80 \%\) chance of arriving undamaged. If no error control is done by the data link protocol, how many times must the message be sent on average to get the entire thing through?

Short answer

Approximately 9.35 transmissions are needed on average.

Step-by-step solution

Understand the problem

We have a packet split into 10 frames. Each frame has an 80% chance of arriving undamaged. The task is to find the average number of times the message needs to be sent for all frames to arrive error-free.

Calculate the probability of one successful transmission

The probability of one frame being undamaged is 0.8. Hence, the probability that all 10 frames arrive undamaged in a single transmission is given by raising the individual success probability to the power of 10, i.e., \( P( ext{all undamaged}) = 0.8^{10} \).

Compute numerical value

Calculate \( 0.8^{10} \) using a calculator or computational tool. \( 0.8^{10} = 0.1073741824 \). Thus, the probability of all frames being undamaged in one transmission is approximately 0.107.

Determine average number of transmissions

To find the average number of transmissions required for a successful message delivery, take the reciprocal of the probability calculated in Step 3. Therefore, \( ext{Average transmissions} = \frac{1}{0.107} \).

Compute final result

Calculate the value from Step 4: \( \frac{1}{0.107} \approx 9.35 \). Hence, on average, about 9.35 transmissions are required for the entire packet to be sent undamaged.

Key concepts

Packet Transmission

Packet transmission is a method used to send data across a network. When a large data piece, like a message or a file, needs to be sent, it is usually broken down into smaller chunks called packets or frames.
Each frame is sent individually across the network to the destination. In this process, it's crucial to ensure that frames arrive correctly and in the right order so they can be put back together by the receiver.

• Fragmentation: Large packets are divided into frames for easier handling and processing.
• Reassembly: At the receiving end, frames are reassembled to reproduce the original data.
• Transmission: Frames travel across the network, potentially taking different paths.

This exercise involves transmitting 10 frames, each with an 80% chance of arriving undamaged. Effective packet transmission is vital for ensuring accurate and efficient communication, especially in environments with error-prone conditions.

Probability of Success

In the context of packet transmission, the probability of success refers to the likelihood of all frames arriving undamaged at the destination.
In our exercise, each frame has an 80% chance of arriving undamaged. Since there are 10 frames, calculating the probability that every single frame reaches intact in one transmission involves raising the individual probability to the power of the number of frames: \[ P(\text{all undamaged}) = 0.8^{10} \].

• Single Frame Probability: The probability of one frame being undamaged is 0.8.
• All Frames Probability: For all 10 frames, the probability is calculated as the individual success probability raised to the 10th power.

Practically, it translates to approximately a 10.7% chance that all frames will arrive undamaged when sent at once.
Understanding these probabilities helps in determining how often a retransmission might be needed when no error control is applied.

Data Link Protocols

Data link protocols are a set of rules that dictate how data is formatted for transmission and how it is handled at the link layer in networking.
These protocols include methods for controlling data flow, error handling, and ensuring data integrity during transmission.

• Flow Control: Manages the speed of data transmission to prevent a fast sender from overwhelming a slow receiver.
• Error Detection and Correction: Some protocols include checks to detect errors in frames and request retransmissions.
• Frame Sequencing: Ensures packets are delivered in the correct order and without duplication.

In scenarios like our exercise, when no error control is used, the dependence is purely on the probability of successful frame transmission. This increases the need for multiple retransmissions to ensure the entire message gets through error-free.
Using sophisticated data link protocols can significantly reduce the need for retransmission by incorporating mechanisms to detect and fix errors during packet transmission.