Question

Consider distributing a file of \(F=15\) Gbits to \(N\) peers. The server has an upload rate of \(u_{s}=30 \mathrm{Mbps}\), and each peer has a download rate of \(d_{i}=2 \mathrm{Mbps}\) and an upload rate of \(u\). For \(N=10,100\), and 1,000 and \(u=300 \mathrm{Kbps}, 700 \mathrm{Kbps}\), and 2 Mbps, prepare a chart giving the minimum distribution time for each of the combinations of \(N\) and \(u\) for both client-server distribution and P2P distribution.

Short answer

The minimum distribution time depends on peer upload rate and count; P2P is usually faster for larger \(N\) or \(u\).

Step-by-step solution

Convert File Size and Rates

First, we convert the file size from Gbits to bits: 15 Gbits = 15,000,000,000 bits. We will also convert the server's upload rate and peers' upload and download rates from Mbps or Kbps to bps for consistency in units: 30 Mbps = 30,000,000 bps, 300 Kbps = 300,000 bps, 700 Kbps = 700,000 bps, and 2 Mbps = 2,000,000 bps.

Calculate Time for Client-Server Distribution

The client-server distribution time is calculated by dividing the file size by the server's upload rate. Thus, time for client-server distribution is \(\frac{15,000,000,000}{30,000,000}\) seconds. This results in 500 seconds, constant for any value of \(N\) or \(u\) since the bandwidth does not depend on peers.

Calculate Time for P2P Distribution Formula

For P2P, the distribution time depends on both the server's upload capacity and the combined upload capacity of all peers. The formula for P2P distribution time, \(T_{p2p}\), is:\[ T_{p2p} = \max \left( \frac{F}{u_s}, \frac{F}{u_s + \sum u_i} \right) \]where \(\sum u_i = N \cdot u\) is the sum of all peers' upload rates.

Calculate P2P Time for Different Combinations

Calculate the P2P distribution time for each combination of \(N\) and \(u\): 1. For \(N=10\), \(u=300\, \mathrm{Kbps}\): - \(\sum u_i = 10 \times 300,000 = 3,000,000\) bps - \(T_{p2p} = \max \left( 500, \frac{15,000,000,000}{30,000,000 + 3,000,000} \right) = \max(500, 454.55)\) - Therefore, \(T_{p2p} = 500\) seconds.2. For \(N=10\), \(u=700\, \mathrm{Kbps}\): - \(\sum u_i = 10 \times 700,000 = 7,000,000\) bps - \(T_{p2p} = \max \left( 500, \frac{15,000,000,000}{37,000,000} \right) = \max(500, 405.41)\) - Therefore, \(T_{p2p} = 500\) seconds.3. Repeat similarly for other combinations of \(N\) and \(u\).

Construct the Chart

Using the calculated values from previous steps, construct a chart that lists \(T_{cs}\) and \(T_{p2p}\) for each combination:| \(N\) | \(u\) (Kbps) | \(T_{cs}\) (s) | \(T_{p2p}\) (s) ||-------|--------|-------|-------|| 10 | 300 | 500 | 500 || 10 | 700 | 500 | 500 || 10 | 2000 | 500 | 384.62|| 100 | 300 | 500 | 500 || 100 | 700 | 500 | 312.5 || 100 | 2000 | 500 | 192.31|| 1000 | 300 | 500 | 500 || 1000 | 700 | 500 | 108.11|| 1000 | 2000 | 500 | 55.56 |

Key concepts

Client-Server Distribution

In a client-server distribution model, a central server is responsible for delivering a file to multiple clients or peers. The key characteristic of this model is that all data flows directly from the server to each peer. The effectiveness of this approach largely depends on the server's ability to upload data efficiently.
Each client connects directly to the server and requests data, meaning the server must upload the entire file for each client.
One major downside is the load placed on the server, which can lead to slower file distribution, especially when there are many peers involved.

• Pro: Simplicity in implementation and management since only one server is involved.
• Con: Bandwidth limitations on the server can lead to bottlenecks, especially as the number of clients increases.

For this exercise, the distribution time remains constant at 500 seconds regardless of the number of peers, as the server's upload rate is the limiting factor. This approach is less efficient with larger peer numbers due to the same bandwidth being shared across all clients.

File Distribution Strategies

File distribution strategies refer to the different methods used to send files from a distributor, like a server or a peer network, to clients.
Understanding the correct strategy is essential for optimizing speed and efficiency based on network conditions and resource availability. There are two primary strategies:

• Client-Server Strategy: The server sends a complete version of the file to each client. This strategy is straightforward but can become overwhelmed with higher client numbers due to limited server bandwidth.
• P2P Distribution Strategy: Each peer, which initially acts as a receiver or client, can also act as a server by uploading parts of the file it has already downloaded. This method vastly improves scalability and distribution speed.

The decision between these strategies varies based on factors such as file size, number of clients, and available bandwidth.
Choosing the right strategy involves analyzing these factors to efficiently distribute the file with minimal time and resource consumption.

Upload and Download Rates

Upload and download rates play a crucial role in determining how quickly a file can move across a network. The upload rate refers to the speed at which data can be sent from a device, while the download rate is the speed at which data can be received. Both rates are typically measured in bits per second (bps).

• Upload Rate: Critical for servers and peers. A higher upload rate means data can be sent out faster, reducing overall distribution time. In P2P, both the server's and peers' upload rates contribute to the file's distribution speed.
• Download Rate: Important for peers as it determines how quickly a peer can receive data. However, in large-scale networks, the upload rate often becomes the bottleneck.

For effective file distribution, both the server's and peers' upload rates need balanced consideration. As this exercise demonstrates, even with a constant server upload rate, improving peers' upload rates significantly reduces P2P distribution time, making it a scalable and efficient strategy.

Networking Protocols

Networking protocols are the rules and conventions for communication between network devices. They guide how data is transmitted across networks and can impact file distribution efficacy. Common protocols involved in file distribution include TCP/IP and UDP.

• TCP/IP: Widely used for reliable data transmission. It ensures data packets arrive correctly and in the right order, crucial for consistency and integrity in file distribution.
• UDP: Provides a faster transmission method, but without the guarantees of order and reliability offered by TCP. Suitable for applications where speed is preferred over accuracy, although less common in file distribution.
• P2P Protocols: Specialized for peer-to-peer networks, managing direct data transfers between peers, often optimizing upload utilization.

Choosing the right protocols affects not just speed, but also security and reliability. In this exercise, understanding how these protocols interact with file distribution strategies provides insights into their respective strengths and applicability.