Memory and Storage for SI, Part 7: The Five-Minute Rule in Microseconds

In 1987, Jim Gray and Franco Putzolu turned a pricing question into a rule. If a page of data is read again within about five minutes, it’s cheaper to keep it in memory than to fetch it from disk. Zhang and colleagues rebuilt the rule from first principles in a model that uses normalized costs, where the boundary between DRAM and flash falls to a few seconds for GPU hosts paired with SSDs built for small random reads.

The Memory and Storage Hierarchy tells the rule’s history through 2017 and leaves the sum for today undone. Part 4 covered the drives that changed one of its inputs, and Part 6 the drives at the other end of the cluster. This part redoes the sum for flash that answers in microseconds, with each input marked as sourced, modeled, or forecast.

The rule prices one access

Gray’s rule weighs two costs. Keeping a page in DRAM means paying rent on that memory for as long as the page stays there. Reading it from storage instead uses up a slice of the drive each time, because a drive can only serve so many reads per second. Zhang’s team writes the classical rule as one ratio. It sets the break-even interval as the cost of one storage access divided by the cost of holding one page in DRAM. If a page comes back sooner than that, it’s cheaper to keep in memory. If it comes back later, it’s cheaper to leave on the drive.

In Gray and Putzolu’s paper, a disc and half a controller deliver 15 random accesses per second. At Tandem’s prices that put the break-even at one access every 400 seconds for a 1KB record, and they called that five minutes.

For the sums below I use the two-ratio form from Appuswamy and colleagues, and the hierarchy page explains where it comes from. It multiplies one ratio set by the hardware by one set by the market.

interval = (pages per MB of DRAM / reads per second per drive) × (price of a drive / price of a MB of DRAM)

From milliseconds to microseconds

Reads per second is the input that moved the most. A disc doing 15 random accesses a second spends about 67ms on each one. The hierarchy page follows hard drives and flash through 2017, and Figure 7.2 adds today’s drives to that history. Goetz Graefe’s 2007 flash disk served 6,200 reads per second, and Appuswamy’s 2017 SATA SSD served 67,000.

Today’s drives are rated far higher. Micron rates its 9650 at 5.4 million random reads per second, and Kioxia rates its GP1 at up to 10 million per second at 512 bytes. Each read is faster too. Kioxia gives its XL-FLASH a read latency under 5µs, where a 1987 disc spent about 67ms on each access. That sets a die’s read latency against a whole disc’s service time, which are different measures.

Reads per second sit in the first ratio, so ten times the reads cuts the interval by ten, as long as the drive’s price doesn’t climb with them.

Redoing the sum

Appuswamy’s 2017 SATA SSD makes a clean worked example, because every input sits in one table. It serves 67,000 random reads per second and costs 560 USD, and DRAM costs 0.005 USD per MB. A megabyte holds 256 pages of 4KB, so the sum is:

interval = (256 / 67,000) × (560 / 0.005) = about 428s

That’s about 7 minutes, and the paper gives the same seven minutes for 4KB reads. The paper gets 41 seconds for the Intel 750, which was its NVMe drive of the time.

The page shrinks

Changing one input at a time shows what each one does. A megabyte holds 2,048 pages of 512 bytes, which is 8 times as many as at 4KB. At the same price, the same drive then breaks even at 8 times the interval, which works out to about 3,424s, or 57 minutes. If the drive keeps its read rate with the smaller pages, each read still takes the same share of it, while each page now holds an eighth as much DRAM, so a small page is cheap to keep and costly to fetch.

Drives built for small reads work against that. Zhang’s team says makers are developing drives with up to 10x more IOPS per dollar that scale as reads shrink. Their example is 50 million reads per second at 512 bytes against 10 million at 4KB. At the same drive price, five times the reads divides the eightfold rise by five, so in this thought experiment the 512-byte interval ends up 1.6 times the 4KB value.

The prices move

Because the formula divides the drive’s price by DRAM’s, the 2026 shortage moves the answer too. In February 2026, TrendForce forecast conventional DRAM contract prices up 90% to 95% for 1Q26 and enterprise SSD prices up 53% to 58%. That quarter has since ended. If nothing else changed, those two forecasts would cut the interval to about 0.8 of its earlier value in one quarter. That’s a sensitivity on forecast inputs, not a result. A proper 2026 number needs a drive’s rated small-read IOPS and its price from the same date, and none of the sources saved for Part 4 gives a price.

What the revisit adds

Zhang’s team keeps Gray’s balance and adds two costs that only show up with a fast drive. Their calibrated rule also charges for queue handling, interrupts and the rest of the host processor work on each I/O, and for the host DRAM bandwidth each transfer uses. At a few reads per second those costs are too small to notice, but at millions per second they add up to a real share of the total.

Their model takes its costs from die area and process node rather than market prices, which the authors say avoids buyer bias. In those units a server CPU core costs 4 and serves 1 million IOPS. A GPU streaming multiprocessor costs 3 and serves 4 million, and the authors take that GPU figure from NVIDIA’s SCADA work covered in Part 4.

These results come out of a model built on those normalized costs, so the seconds aren’t a price list for any drive you can buy. In the model, an SLC Storage-Next SSD on a CPU host breaks even at about 34s for 512-byte pages and about 10s for 4KB. Moving the same reads to a GPU host cuts the 512-byte figure from about 34s to about 5s, because the GPU serves more I/O for its cost.

Slower flash pushes the other way. As sensing latency grows from 5µs for SLC to 40µs for TLC, the drive’s IOPS per dollar falls and its share of the total cost rises. Relaxing the latency target from 7µs to 85µs shortens the 512-byte GPU interval by only about 1.5s. The paper finds that host processor IOPS matter most.

What to watch

Once one of the Storage-Next drives in Part 4 gets a published price next to its rated small-read IOPS, I can redo the sum on this page with real numbers instead of a sensitivity. To check and vary the model, Zhang’s team built a calibrated SSD simulator called MQSim-Next.

I think an interval measured in seconds makes the economic case for flash tiers like the ones in Part 5. In this model, data that’s read again within seconds is worth keeping in memory, and data that waits longer is cheaper on flash. KV cache blocks aren’t the paper’s pages, though, so their cutoff stays unknown until someone runs the model on them.

In the last part of the series, I step back from the arithmetic and place each memory family by the job it could do.