0

Let's say we're shipping boxes of stuff every 10-min, and if a shipped box is more than X% full, then for next shipment we will choose a box Y% bigger than the previous one. If the previous one was less than X% full, then we will use the same box size again.

This means that if boxes are consistently filled over the threshold X%, then our n-th box size will be given by exponential growth function box_size(n) = initial_size*pow(1+Y, n)

However, if some boxes were not filled enough, then we will have skipped some increases and we could say it will grow like:

box_size(n) = initial_size*pow(1+Y, n - n_underutilized).

This requires memory of the entire past, so how do you call this? Some kind of aggregate function?

bca-0353f40e
  • 121
  • 3
    I doubt this is something that has a common name that is already in use. Unless you can make your question more specific, you could call this whatever you find appropriate. – Mees de Vries Dec 16 '22 at 12:41
  • If it doesn't have a common name, then I'm looking for help in correctly describing it. Is it correct to say that box_size(n) is an aggregate function over the interval (0,n)? Can it be called an iterative function? – bca-0353f40e Dec 16 '22 at 13:11
  • The box_size(n) is -as you wrote- initial_size times 1+Y raised to the power of the number of steps until n in which the size was not under utilized. It is acceptable in a single document to call that just the 'box-size function' as long as the precise mathematical definition is included in that document. No mathematician will guess from another name alone what exactly you mean. – Kurt G. Dec 16 '22 at 13:24
  • The sequence of sufficient utilization can be intermittent... 100 boxes utilized, then 10 not, then 20 utilized then 10 not, then 30 yes, so it'd be pow(1+Y, 100+20+30), skipping growth for those periods of low utilization, but utilization bar is a proportion of the size so you need to compute the function for each boxing in order to know yes/no. So, an intermittent growth function? Monotonic box size function? – bca-0353f40e Dec 16 '22 at 13:30
  • Ok I think I found my words, how does this sound:

    The proposed algorithm can be described as intermittent exponential growth function. In exponential growth, the new size is obtained by multiplying the old size with a constant for every time interval. With the proposed algorithm, there will be time intervals where there is no growth, if conditions for growth are not met.

     – bca-0353f40e Dec 17 '22 at 07:25
  • 1
    "Intermittent" is a very good description. I thank you, on behalf of your readers, for having taken the trouble to come up with good terminology. – JonathanZ Dec 17 '22 at 17:18

1 Answers1

2

I've settled for "intermittent exponential growth" as the name for my algorithm, which can be described with:

The proposed algorithm can be described as intermittent exponential growth function. In exponential growth, the new size is obtained by multiplying the old size with a constant for every time interval. With the proposed algorithm, there will be time intervals where there is no growth, if conditions for growth are not met.

I think the figure below best illustrates why it is an adequate name.

Intermittent Exponential Growth

bca-0353f40e
  • 121