Question

Assume a quad-core computer system can process database queries at a steady state rate of requests per second. Also assume that each transaction takes, on average, a fixed amount of time to process. The following table shows pairs of transaction latency and processing rate.

Average Transaction Latency	Minimum transaction processing rate
1 ms	5000/sec
2 ms	5000/sec
1 ms	10,000/sec
2 ms	10,000/sec

For each of the pairs in the table, answer the following questions:

(6.20.1) On average, how many requests are being processed at any given instant?

(6.20.2) If move to an 8-core system, ideally, what will happen to the system throughput (i.e., how many queries/second will the computer process)?

(6.20.3) Discuss why we rarely obtain this kind of speedup by simply increasing the number of cores.

Short answer

(6.20.1)

Average Transaction Latency	Minimum transaction processing rate	Average number of requests being processed
1 ms	5000/sec	1.25
2 ms	5000/sec	2.5
1 ms	10,000/sec	2.5
2 ms	10,000/sec	5

(6.20.2)

The system throughput doubles with 8-core system.

(6.20.3)

Memory contention is the reason for not obtaining speedup by simply increasing the number of cores.

Step-by-step solution

Identify the formula for average number of requests for 5000 transaction processing rate.

(6.20.1)

The processor is quad-core. That means the number of cores is 4. To find the average number of requests being processed at any given instant, use the following formula:

Calculate the average number of requests

For average transaction latency equal to 1, the average number of requests is:

Similarly, for average transaction latency equal to 2, the average number of requests is:

Identify the formula for average number of requests for 10000 transaction processing rate 

With number of cores equal to 4, the average number of requests being processed is calculated as:

Calculate the average number of requests for 10000 transaction processing rate

For average transaction latency equal to 1, the average number of requests is:

Similarly, for average transaction latency equal to 2, the average number of requests is:

Hence, the average number of requests processed are:

Average Transaction Latency	Minimum transaction processing rate	Average number of requests being processed
1 ms	5000/sec	1.25
2 ms	5000/sec	2.5
1 ms	10,000/sec	2.5
2 ms	10,000/sec	5

Identify what will happen to the system throughput if 8-core processor is used

(6.20.2)

A system throughput is the amount of information that can be processed in a given amount of time. With the increase in the number of cores, the information that can be processed also increases. The greater number of cores on a processor means more information can be processed simultaneously. The system throughput is proportional to the number of cores. Therefore, if the number of cores is doubled, the maximum transaction processing rate also doubles.

Identify the reason for not getting speedup generally by increasing the number of cores

(6.20.3)

In shared memory system, it is possible for more than one process to access the same memory block. Increasing the number of cores results in more processors being executed simultaneously. In such scenarios, if more than one process is accessing the shared memory block, the situation of memory contention arises. This is the reason for not getting speedup by just increasing the number of cores.