Question

In this problem, we consider sending real-time voice from Host A to Host B over a packet-switched network (VoIP). Host A converts analog voice to a digital \(64 \mathrm{kbps}\) bit stream on the fly. Host A then groups the bits into 56 -byte packets. There is one link between Hosts A and B; its transmission rate is 2 Mbps and its propagation delay is \(10 \mathrm{msec}\). As soon as Host A gathers a packet, it sends it to Host B. As soon as Host B receives an entire packet, it converts the packet's bits to an analog signal. How much time elapses from the time a bit is created (from the original analog signal at Host A) until the bit is decoded (as part of the analog signal at Host B)?

Short answer

17.224 milliseconds

Step-by-step solution

Calculate Packet Generation Time

First, we determine the time it takes for Host A to create a packet. The digital stream is 64 kbps, meaning 64,000 bits are created per second. Each packet contains 56 bytes, which is equal to \(56 \times 8 = 448\) bits. Therefore, the time to generate one packet is given by:\[ \text{Packet generation time} = \frac{448 \text{ bits}}{64,000 \text{ bits per second}} = 0.007 \text{ seconds or } 7 \text{ milliseconds}. \]

Calculate Transmission Time

Next, we calculate how long it takes to transmit this packet over the single link. The transmission rate is 2 Mbps, or 2,000,000 bits per second. To find the transmission time for a 448-bit packet, we use:\[ \text{Transmission time} = \frac{448 \text{ bits}}{2,000,000 \text{ bits per second}} = 0.000224 \text{ seconds or } 0.224 \text{ milliseconds}. \]

Calculate Propagation Delay

The propagation delay is given in the problem as 10 milliseconds. This is the time it takes for the first bit to travel from Host A to Host B after it has been sent and is not affected by packet length or transmission rate.

Calculate Total End-to-End Delay

Now, we sum up all the delays to find the total time from the creation of a bit at Host A to its decoding at Host B:\[ \text{Total delay} = \text{Packet generation time} + \text{Transmission time} + \text{Propagation delay} \]This gives:\[ \text{Total delay} = 7 \text{ ms} + 0.224 \text{ ms} + 10 \text{ ms} = 17.224 \text{ milliseconds}. \]

Conclusion

The time elapsed from when a bit is created at Host A to when it is decoded at Host B is 17.224 milliseconds.

Key concepts

Packet-Switched Network

A packet-switched network is a type of digital communication network where data is sent in small packets over a shared network path. In contrast to circuit-switched networks, where a dedicated line is open for communication, packet-switched networks divide data into packets that can travel across various routes to reach their destination. Each packet carries not only a part of the data but also the destination address, which allows it to be re-assembled at the destination.

These networks are highly efficient and flexible, as the same network infrastructure can be used by many users simultaneously. The Internet, for example, is a massive packet-switched network, allowing for diverse forms of communications such as VoIP (Voice over Internet Protocol), which we are discussing here. VoIP uses packet-switched networks to send voice data, improving efficiency and reducing costs compared to traditional telephony.

• Data is divided into packets.
• Packets can take different paths to the destination.
• Enables efficient use of network resources.

Transmission Rate

Transmission rate refers to the speed at which data is transferred from one point to another in a network, typically measured in bits per second (bps). In the context of our exercise, Host A transmits packets to Host B with a transmission rate of 2 Mbps, meaning it can send 2 million bits every second.

The transmission rate is crucial because it determines how quickly data can move across a network. A higher transmission rate means that more data can be sent in less time. For instance, the quicker Hosta can transmit its 448-bit packet, the faster it can start sending the next one.

Knowing the transmission rate helps in predicting network performance and calculating how long it will take to transmit a packet, which is an essential factor in determining the overall delay in a network communication scenario.

• Measured in bits per second (bps).
• Affects how quickly data is sent.
• Higher rates mean faster data transfer.

Propagation Delay

Propagation delay is the time it takes for a single bit to travel from the sender to the receiver over the network medium. This delay is primarily influenced by the physical distance between the two hosts and the speed at which the signal travels through the medium (often close to the speed of light for fiber optics).

In the given problem, we are told the propagation delay between Host A and Host B is 10 milliseconds. This indicates that, regardless of how fast a packet is sent, the first bit will always take 10 milliseconds to reach its destination.

Understanding propagation delay is important because it affects how quickly information travels from one point to another. In real-time applications like VoIP, minimal propagation delay is desired to avoid noticeable lag in conversation.

• Determined by distance and medium speed.
• Influences total communication delay.
• Critical for real-time applications.

End-to-End Delay

End-to-end delay is the total time taken for data to travel from the source to the destination. It includes all the variables involved in the transmission process: packet generation time, transmission time, and propagation delay.

In our exercise, we've computed the end-to-end delay as the sum of these three components, resulting in 17.224 milliseconds. This metric is essential for understanding the overall efficiency of a communication system, especially for time-sensitive applications like VoIP.

A breakdown of the components:

• Packet Generation Time: Time to form packets (7 ms).
• Transmission Time: Time to send packets (0.224 ms).
• Propagation Delay: Time for data to travel to its location (10 ms).

Improving end-to-end delay involves optimizing each of these areas to enhance the communication quality. Reducing delay ensures a smooth, coherent communication experience and is critical for user satisfaction and application performance.