Chapter 3: Problem 32
Suppose a workstation has an I/O bus speed of \(800 \mathrm{Mbps}\) and memory bandwidth of 2 Gbps. Assuming DMA in and out of main memory, how many interfaces to 45-Mbps T3 links could a switch based on this workstation handle?
Short Answer
Expert verified
The switch can handle 17 T3 links.
Step by step solution
01
Understand the Requirements
The problem is asking how many 45-Mbps T3 links can be managed by a system with an I/O bus speed of 800 Mbps and a memory bandwidth of 2 Gbps. The data is transferred using Direct Memory Access (DMA).
02
Determine the Total Data Transfer Rate Required
Each T3 link requires 45 Mbps. If there are multiple T3 links, the total required bandwidth will be the sum of the individual link bandwidths. Let the number of T3 links be represented as 'n'. The total bandwidth required is then: \[ \text{Total Bandwidth Required} = 45n \text{ Mbps} \]
03
Identify the Bottleneck
Compare the required bandwidth to the available system resources. The I/O bus speed is 800 Mbps, and the memory bandwidth is 2 Gbps. The lower of these values will be the bottleneck. In this case, the I/O bus speed of 800 Mbps is the bottleneck.
04
Calculate the Maximum Number of T3 Links
Using the bottleneck bandwidth (I/O bus speed), determine the maximum number of T3 links that can be handled: \[ 45n \text{ Mbps} \ \text{Maximize for } n \] Setting the total bandwidth equal to the I/O bus speed, solve for 'n': \[ 45n \text{ Mbps} = 800 \text{ Mbps} \ n = \frac{800}{45} \approx 17.78 \] Since partial T3 links are not feasible, take the integer part: \[ n = 17 \]
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
I/O Bus Speed
The I/O bus speed refers to the rate at which data can be transferred between the computer's CPU and its peripheral devices. Measured in megabits per second (Mbps) or gigabits per second (Gbps), this speed determines how quickly data can move to and from input/output devices.
The I/O bus speed is crucial because it represents a system's capability to handle external data. In our exercise, the workstation has an I/O bus speed of 800 Mbps.
When considering multiple data streams, the I/O bus speed acts as a limiting factor, or bottleneck. For instance, transferring data from multiple T3 links simultaneously will depend on whether the combined data rate of these links exceeds or meets the I/O bus speed.
The I/O bus speed is crucial because it represents a system's capability to handle external data. In our exercise, the workstation has an I/O bus speed of 800 Mbps.
When considering multiple data streams, the I/O bus speed acts as a limiting factor, or bottleneck. For instance, transferring data from multiple T3 links simultaneously will depend on whether the combined data rate of these links exceeds or meets the I/O bus speed.
Memory Bandwidth
Memory bandwidth is the measure of the data transfer rate between the memory (RAM) and other parts of the computer. It is a key factor affecting a computer's overall performance, especially during high-speed data processing.
The bandwidth is typically measured in Gbps. In the given problem, the workstation has a memory bandwidth of 2 Gbps. This means the memory can handle a data transfer rate of up to 2 gigabits per second.
However, even if the memory bandwidth is high, the actual speed at which data is transferred to and from peripheral devices depends on the I/O bus speed. So, while memory bandwidth is important, the practical data throughput will always be capped by the lower of the I/O bus or memory bandwidth.
The bandwidth is typically measured in Gbps. In the given problem, the workstation has a memory bandwidth of 2 Gbps. This means the memory can handle a data transfer rate of up to 2 gigabits per second.
However, even if the memory bandwidth is high, the actual speed at which data is transferred to and from peripheral devices depends on the I/O bus speed. So, while memory bandwidth is important, the practical data throughput will always be capped by the lower of the I/O bus or memory bandwidth.
T3 Links
T3 links are a type of digital data transmission used in telecommunications. Each T3 link offers a data transmission rate of 45 Mbps. They are commonly used for high-speed internet connections and data transfer between large networks.
When working with multiple T3 links, their combined data rate must be evaluated against the system's capabilities. For example, if each T3 link transmits at 45 Mbps, managing multiple T3 links will require summing up these rates.
In the workstation problem, the goal is to determine how many T3 links the system can handle with an I/O bus speed of 800 Mbps. The bottleneck here is the I/O bus speed, so we calculate the maximum number by dividing the total allowed data rate (800 Mbps) by the rate per T3 link (45 Mbps). The result is around 17.78, meaning the system can handle up to 17 T3 links, as partial links are not feasible.
This calculation ensures that data transfer does not exceed the system's I/O bus capacity, ensuring efficient and uninterrupted data flow between the T3 links and the system.
When working with multiple T3 links, their combined data rate must be evaluated against the system's capabilities. For example, if each T3 link transmits at 45 Mbps, managing multiple T3 links will require summing up these rates.
In the workstation problem, the goal is to determine how many T3 links the system can handle with an I/O bus speed of 800 Mbps. The bottleneck here is the I/O bus speed, so we calculate the maximum number by dividing the total allowed data rate (800 Mbps) by the rate per T3 link (45 Mbps). The result is around 17.78, meaning the system can handle up to 17 T3 links, as partial links are not feasible.
This calculation ensures that data transfer does not exceed the system's I/O bus capacity, ensuring efficient and uninterrupted data flow between the T3 links and the system.
