Question

A server hosting a popular chat room sends data to its clients at a rate of \(32 \mathrm{kbps}\). If this data arrives at the clients every \(100 \mathrm{msec}\), what is the packet size used by the server? What is the packet size if the clients receive data every second?

Short answer

Packet size is 3,200 bits for 100 ms intervals and 32,000 bits for 1-second intervals.

Step-by-step solution

Understanding the Data Rate and Time Interval

The server sends data at a rate of 32 kilobits per second (kbps). This means that every second, 32,000 bits are sent because 1 kbps equals 1,000 bits per second. The problem gives two scenarios: data is sent to clients every 100 milliseconds and every second. We need to convert these time intervals into seconds for consistency, knowing that 1 second equals 1,000 milliseconds.

Calculating Packet Size for 100 Milliseconds

For the first scenario, where the data arrives every 100 milliseconds, we convert this time interval to seconds. 100 milliseconds is 0.1 seconds. We calculate how many bits are transmitted in this interval at a rate of 32,000 bits per second using the formula:\[\text{Packet Size} = \text{Data Rate} \times \text{Time Interval} = 32,000 \text{ bits/sec} \times 0.1 \text{ sec}\]Calculating this gives:\[\text{Packet Size} = 3,200 \text{ bits}\]

Calculating Packet Size for 1 Second

For the second scenario, where data arrives every second, the time interval is already in seconds, so we use the same data rate over a 1-second period:\[\text{Packet Size} = \text{Data Rate} \times \text{Time Interval} = 32,000 \text{ bits/sec} \times 1 \text{ sec}\]This calculation gives us:\[\text{Packet Size} = 32,000 \text{ bits}\]

Conclusion

For data arriving every 100 milliseconds, the packet size is 3,200 bits. For data arriving every second, the packet size is 32,000 bits.

Key concepts

Packet Size Calculation

Understanding how packet size is determined is crucial in networking. Packet size is essentially a measure of how much data is sent over the network in a specific time interval. In our example, the server sends data packets to clients, with bits as the smallest unit of data. The formula to find the packet size uses the data rate and the time interval:

• Data Rate: The speed at which data is transmitted, typically measured in bits per second.
• Time Interval: The duration over which data is measured, given in seconds.

The packet size calculation involves multiplying the data rate by the time interval. This simple multiplication will give you the number of bits transmitted during that interval. For instance, at 32 kbps (or 32,000 bits per second) and a time interval of 0.1 seconds (corresponding to 100 milliseconds), the formula becomes:\[\text{Packet Size} = 32,000 \, \text{bits/sec} \times 0.1 \, \text{sec} = 3,200 \, \text{bits}\]This provides the packet size for data sent at 100-millisecond intervals.

Network Time Interval

The network time interval refers to the specific timeframe during which data packets are sent or received over the network. This interval is crucial because it affects both how data is processed and the efficiency of the network.
Here's how to break it down:- **Milliseconds vs. Seconds**: Time intervals can be expressed in different units. In networking, you will often see milliseconds (ms) and seconds (s) used. 1 second equals 1,000 milliseconds. Conversions are often needed to ensure uniform calculations.- **Impact on Packet Size**: Shorter time intervals, like 100 milliseconds, result in smaller packet sizes when using the same data transmission rate than longer intervals, such as 1 second.
Understanding the time interval is essential because it determines how frequently data packets are sent. In our example, when the interval is 100 milliseconds, many smaller packets are sent more frequently. For a 1-second interval, fewer packets of larger size are transmitted.\[\text{Converting 100 milliseconds to seconds: } 100 \, \text{ms} = 0.1 \, \text{s}\]This conversion is essential for calculating packet sizes.

Data Transmission Rate

The data transmission rate is a key factor in understanding how data flows through networks. It's the measure of the amount of digital data transferred from one place to another per unit time. Common units of measure include kilobits per second (kbps), megabits per second (Mbps), and so on.
- **Why It Matters**: The transmission rate determines how quickly data packets are sent across the network. Higher rates mean faster data transfer but may require more bandwidth.- **Impact on Calculations**: When calculating things like packet size, knowing the data rate helps determine how many bits are packed into a given time frame.
In the given exercise, the data transmission rate is 32 kbps, which converts to:\[32 \, \text{kbps} = 32,000 \, \text{bits/sec}\]This conversion is a foundational step in all network data calculations, including determining how the packet size changes depending on the network time interval. The higher the data rate, the more data is transferred, affecting the overall efficiency and performance of the network.