Question

Compute the fraction of the bandwidth that is wasted on overhead (headers and retransmissions) for protocol 6 on a heavily loaded 50 -kbps satellite channel with data frames consisting of 40 header and 3960 data bits. Assume that the signal propagation time from the earth to the satellite is \(270 \mathrm{msec}\). ACK frames never occur. NAK frames are 40 bits. The error rate for data frames is \(1 \%\), and the error rate for NAK frames is negligible. The sequence numbers are 8 bits.

Short answer

The fraction of the bandwidth wasted on overhead is 2%.

Step-by-step solution

Understand the Problem

In this problem, we are tasked with finding the fraction of bandwidth wasted due to headers and retransmissions on a satellite channel using a specified protocol. We need to account for both overhead introduced by packet headers and retransmissions due to data frame errors.

Calculate the Total Frame Size

Determine the total number of bits in a data frame, which includes both header and data bits. Given, header is 40 bits and data is 3960 bits.\[\text{Total frame size} = 40 \text{ bits (header)} + 3960 \text{ bits (data)} = 4000 \text{ bits}\]

Calculate the Bandwidth for Data Transfer

To find the bandwidth used for data, compute the fraction of the total frame used for data. This is the ratio of data bits to total frame bits.\[\text{Data fraction} = \frac{3960}{4000} = 0.99\]

Determine the Error Impact

Since there's a 1% error rate for data frames, on average, 1 out of every 100 frames needs to be retransmitted. Therefore, we need to add an additional frame for every 100 frames due to retransmissions.\[\text{Retransmission rate} = \frac{1}{100} = 0.01\]

Calculate the Oversize Due to Errors

The amount of bandwidth wasted due to retransmissions is equal to the retransmission rate, since one frame for every 100 is redundant.\[\text{Retransmission bandwidth fraction} = 0.01\]

Sum Up the Total Overhead and Error Waste

Combine the header and retransmission contributions to determine the total bandwidth waste.\[\text{Total wasted bandwidth fraction} = \text{Header fraction} + \text{Retransmission fraction} = (1 - 0.99) + 0.01 = 0.02\]

Calculate the Fraction Wasted on Overhead

Given the total wasted bandwidth fraction is 0.02, this represents 2% of the bandwidth wasted due to overhead and retransmissions.

Key concepts

Bandwidth Efficiency

Bandwidth efficiency is an essential concept in satellite communication protocols, as it determines how effectively the available bandwidth is utilized for transmitting useful data. In the context of the provided exercise, we are examining a 50-kbps satellite channel. This channel has to manage both the useful data payload and the extra bits required as overhead.

• Data Payload: From the given problem, the data frame contains 3960 data bits.
• Total Frame Size: Adding these to the 40 header bits, the total frame size becomes 4000 bits.
• Efficiency Calculation: Bandwidth efficiency can be understood as the ratio of data bits to the total frame size. Here, it's calculated as \[ \frac{3960}{4000} = 0.99 \]. This implies that 99% of each frame is used to carry data, which is a high efficiency.

Understanding bandwidth efficiency helps in optimizing the communication protocol to maximize data throughput and minimize transmission costs.

Frame Overhead

Frame overhead refers to the extra bits that are necessary for communication over a network beyond the actual data. This can include header bits and, occasionally, trailer bits used for maintaining communication.

• Header Bits: In the context of our exercise, each data frame contains 40 header bits that are crucial for managing the data packets as they travel through the network.
• Overhead Impact: Since the header consumes 40 out of every 4000 bits transmitted, the overhead accounts for 1% of the total bits sent, which slightly reduces the bandwidth efficiency.
• Purpose: These headers carry important information such as sequence numbers and error detection codes, essential for data integrity and proper sequencing.

Although the overhead seems minimal in terms of percentage, it plays a crucial role in ensuring reliable communication.

Error Rate Impact

The error rate in data transmission significantly affects the bandwidth efficiency, especially when considering retransmissions. In this exercise, we deal with a 1% error rate for data frames.

• Understanding Error Rates: This implies that, statistically, 1 out of every 100 frames needs to be retransmitted due to errors.
• Effect on Bandwidth: With an error rate of 1%, a retransmission is required for these erroneous frames, adding an additional 1% of overhead.
• Impact Calculation: This impact is calculated as an increase in wasted bandwidth, \[ \text{Retransmission Rate} = \frac{1}{100} = 0.01 \], resulting in extra bandwidth use.

The impact of error rates on protocol efficiency emphasizes the importance of robust error handling and correction mechanisms in satellite communication.

Retransmission

Retransmission is a crucial concept when dealing with error-prone communication channels. It is the process of sending the same data frame again after it has been identified as having errors.

• Fundamental Requirement: With a 1% frame error rate, retransmissions ensure that all data eventually gets through error-free, thus maintaining the integrity of the communication.
• Additional Overhead: As calculated earlier, retransmissions contribute an additional 1% to the bandwidth "waste," raising the total fraction of wasted bandwidth to 2%.
• Influence on Protocol Design: Protocols need to be designed to efficiently handle retransmissions without excessive delay, especially for time-sensitive data.

Efficient retransmission strategies, such as using negative acknowledgments (NAKs), are essential to mitigate the detrimental impact of errors on satellite communication efficiency.