If it is known that key values will always increase monotonically, an alternative approach to consistent hashing is possible.

Now we recall that the function and are both monotonically increasing.

A sequence is said to be monotonically increasing if each term is greater than or equal to the one before it.

One sees that efficiency does not simply increase monotonically with the receiver temperature.

Assume (3) applies and that is monotonically increasing with .

So the initialization vectors must be monotonically increasing in value over time.

And the stream IDs always increase monotonically in each direction.

Examples of functions that are convex but not monotonically increasing include and .

Both numbers are monotonically increasing with time; they only ever increase.

It may also be observed that, if, is monotonically increasing.