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I have been reading on universal law of scalability and found that we can model the relationship between (concurrency vs throughput) and (concurrency vs latency) using the equations derived from universal law of scalability.

I want to know whether we can apply the same equations to model the relationship between (heap size vs throughput) and (heap size vs latnecy).

NOTE Concurrency: Number of threads running simultaneously. Latency: Time difference between sending a request and receiving the response. Throughput: Amount of work done in unit time Heap size: Amount of memory allocated for the application

Thanks

Pasindu Tennage
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  • Can you please describe what scalability, concurrency, latency, and throughput? I'm not sure these are inherent to mathematical modeling, but even if they are it might help to get an answer quicker as more will be able to participate having the information at hand. Sounds interesting though. – marshal craft Jul 30 '18 at 06:52
  • I edited the question – Pasindu Tennage Jul 30 '18 at 07:09
  • So it seem you have work $W(t,n_{threads})$ modeled some how with a function and then something about memory size which I'm not even sure how to define. Sorry I'm just trying to get the ball rolling on this one sense nobody else seem to care. – marshal craft Jul 30 '18 at 10:45
  • It is interesting from c.s. point of view (maybe not math point of view, maybe lattice or differential topology?) If there isomorphic between thread and memory. But it seems a significant issues is just a matter of concretely defining these notions. So that I don't make up some representation, and then someone else comes along illuminating the fact these terms are all standardized elsewhere. From a math point of view this might be one thing, from a c.s. point of view this might all be standard mathematical objects. If you know you can certainly help me out? – marshal craft Jul 30 '18 at 10:59

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If you can define $W_X(t,n_{threads})$ and $W_Y(t,m_{heap})$ where $X,Y$ are sets of functions. If one could hypothesize for any $x,y$ represents different programs' performance. Some $x,y$ it maybe the case the Universal scalability applies equally. In which case memory and thread performance are isomorphic or $x =y$.

So it depends on the program let's say, from a mathematical model perspective.

marshal craft
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