Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mathematical Model for the Optimal Utilization Percentile in M/M/1
  Systems: A Contribution about Knees in Performance Curves   Performance curves of queuing systems can be analyzed by separating them into
three regions: the flat region, the knee region, and the exponential region.
Practical considerations, usually locate the knee region between 70-90% of the
theoretical maximum utilization. However, there is not a clear agreement about
where the boundaries between regions are, and where exactly the utilization
knee is located. An open debate about knees in performance curves was
undertaken at least 20 years ago. This historical debate is mainly divided
between those who claim that a knee in the curve is not a well-defined term in
mathematics, or it is a subjective and not really meaningful concept, and those
who define knees mathematically and consider their relevance and application.
In this paper, we present a mathematical model and analysis for identifying the
three mentioned regions on performance curves for M/M/1 systems; specifically,
we found the knees, or optimal utilization percentiles, at the vertices of the
hyperbolas that relate response time as a function of utilization. Using these
results, we argue that an adaptive and optimal queuing system could be deployed
by keeping load and throughput within the knee region.

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The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ