7.2 Amdahl's Law

Each time a (particular) microprocessor company announces its latest and greatest CPU, headlines sprout across the globe heralding this latest leap forward in technology. Cyberphiles the world over would agree that such advances are laudable and deserving of fanfare. However, when similar advances are made in I/O technology, the story is apt to appear on page 67 of some obscure trade magazine. Under the blare of media hype, it is easy to lose sight of the integrated nature of computer systems. A 40% speedup for one component certainly will not make the entire system 40% faster, despite media implications to the contrary.

In 1967, George Amdahl recognized the interrelationship of all components with the overall efficiency of a computer system. He quantified his observations in a formula, which is now known as Amdahl's Law. In essence, Amdahl's Law states that the overall speedup of a computer system depends on both the speedup in a particular component and how much that component is used by the system. In symbols:

where

S is the speedup;

f is the fraction of work performed by the faster component; and

k is the speedup of a new component.

Let's say that most of your daytime processes spend 70% of their time running in the CPU and 30% waiting for service from the disk. Suppose also that someone is trying to sell you a processor array upgrade that is 50% faster than what you have and costs $10,000. The day before, someone had called you on the phone offering you a set of disk drives for $7,000. These new disks promise two and a half times the throughput of your existing disks. You know that the system performance is starting to degrade, so you need to do something. Which would you choose to yield the best performance improvement for the least amount of money?

For the processor option we have:

We therefore appreciate a total speedup of 130% with the new processor for $10,000.

For the disk option we have:

The disk upgrade gives us a speedup of 122% for $7,000.

All things being equal, it is a close decision. Each 1% of performance improvement resulting from the processor upgrade costs about $333. Each 1% with the disk upgrade costs about $318. This makes the disk upgrade a slightly better choice, based solely upon dollars spent per performance improvement percentage point. Certainly, other factors would influence your decision. For example, if your disks are nearing the end of their expected life, or if you're running out of disk space, you might consider the disk upgrade even if it were to cost more than the processor upgrade.

Before you make that disk decision, however, you need to know your options. The sections that follow will help you to gain an understanding of general I/O architecture, with special emphasis on disk I/O. Disk I/O follows closely behind the CPU and memory in determining the overall effectiveness of a computer system.