A Silicon Valley company is looking to increase the performance of its workstations. Analysis of the applications that its customers are using has shown that the average response time breaks down into three main categories: CPU time, memory system time, and host/client communication time.
A meeting is convened to discuss how the response time can be improved. At the meeting, the network people are quite embarrassed by the proportion of host/client time, and they promise that by using a more suitable network, host/client communications will be sped up by 10 times.
Next, the memory designers speak, and they predict that by using a new design the memory system time can be reduced to 10% of the total response time. (Assuming that the other two components are not changed.)
a) If after only the network changes, the response time is distributed 74%, 25%, and 1% between the CPU, memory system, and communication respectively, how much faster are the original workstations after both the network and memory system improvements?
b) Lastly, the CPU designers take the podium, and they announce (having carefully listened to the previous two groups) that including their enhancements to the CPU, the total speedup (after all the group’s improvement will be two times. How much are the CPU designers planning to speed up the CPU?
a)
If initially, the response time is distributed as 74% for CPU, 25% for memory system, and 1% for communication, and after the network changes, the communication portion becomes 1/10th of its original time, we can calculate the new distribution.
New distribution after network changes:
CPU time = 74%
Memory system time = 25%
Communication time = 1% / 10 = 0.1%
Next, memory system designers claim that the memory system time can be reduced to 10% of the total response time. Assuming the other two components remain unchanged, we can calculate the new distribution.
New distribution after both network and memory system improvements:
CPU time = 74%
Memory system time = 25% * 10% = 2.5%
Communication time = 0.1%
To calculate the overall performance improvement, we can compare the sum of the old distribution percentages (CPU + Memory system + Communication) with the sum of the new distribution percentages.
Old sum = 74% + 25% + 1% = 100%
New sum = 74% + 2.5% + 0.1% = 76.6%
The overall speed increase can be calculated as the ratio of the old sum to the new sum:
Speed increase = (Old sum / New sum) = (100% / 76.6%) ≈ 1.305
Therefore, the original workstations are approximately 1.305 times faster after both the network and memory system improvements.
b)
The CPU designers are planning to achieve a total speedup of 2 times, including the improvements from the network and memory system changes.
If we assume the original speed of the CPU is "x", the new speed will be 2 times the original speed, which is 2x.
Therefore, the CPU designers are planning to speed up the CPU by a factor of 2x / x = 2.
To calculate the improvement in the original workstation's performance after both the network and memory system improvements, we need to follow these steps:
a) Calculate the new distribution of response time after the network changes:
Since the network was improved by 10 times, the new distribution of response time would be 74% for the CPU, 25% for the memory system, and 1% for the communication, but with the communication time 10 times faster than before.
Therefore, the new distribution becomes: 74% for the CPU, 25% for the memory system, and 0.1% for the communication.
b) Calculate the new distribution of response time after the memory system changes:
Since the memory system time is reduced to 10% of the total response time, the new distribution of response time would be 74% for the CPU, 10% for the memory system, and 0.1% for the communication.
c) Calculate the speedup of the original workstations after both the network and memory system improvements:
To calculate this, we need to find the ratio of the original total response time to the new total response time.
The original total response time can be calculated as the sum of the response times for each component: CPU + memory system + communication.
The new total response time can be calculated using the new distribution of response time:
New Total Response Time = CPU time + memory system time + communication time
Now, let's calculate the speedup using the following steps:
1. Calculate the original total response time:
Original Total Response Time = (original CPU time) + (original memory system time) + (original host/client communication time)
Assuming the original distribution is 74%, 25%, and 1% respectively, the original total response time can be calculated as:
Original Total Response Time = 74% + 25% + 1% = 100%
2. Calculate the new total response time after the network changes:
New Total Response Time (after network changes) = 74% + 25% + 0.1% = 99.1%
3. Calculate the new total response time after the memory system changes:
New Total Response Time (after network and memory system changes) = 74% + 10% + 0.1% = 84.1%
4. Calculate the speedup:
Speedup = Original Total Response Time / New Total Response Time (after network and memory system changes)
Speedup = 100% / 84.1% = 1.19
Therefore, the original workstations are 1.19 times faster after both the network and memory system improvements.
b) To determine how much the CPU designers are planning to speed up the CPU, we need to calculate the remaining 0.81 (1 - 0.19) of the total speedup that is expected after all the group's improvements.
The total expected speedup after all the improvements is given as 2 times.
Therefore, the CPU designers are planning to speed up the CPU by:
Speedup of the CPU = Total Expected Speedup - Speedup after network and memory system improvements
Speedup of the CPU = 2 - 1.19 = 0.81
The CPU designers are planning to speed up the CPU by 0.81 times.