Abstract
We set on modeling performance of distributed systems analytically. We show that for reasonable assumptions, we can generalize probability calculus to network latency distributions. These distributions may model both network connectivity, and computational performance of the system. We describe their algebra, show how to implement computations on these distributions, and get exact results in most cases. We apply this methodology to model performance of AWS DynamoDB analytically, as well as gossip algorithm.
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Notes
- 1.
We describe how it generalizes these max-plus and min-plus algebras later.
- 2.
Usually called finite difference operators.
- 3.
Antidifference is an inverse of finite difference operator. Backwards difference subtracts immediate predecessor from a successor term in the series.
- 4.
Note that we in this context we are mainly interested in null and unit of multiplication.
- 5.
Note that we considered using \(\textit{matrix}\text {-}{} {\textbf {static}}\), but it does not have typesafe indexing.
- 6.
Sometimes named.
- 7.
This field definition will be used for multiplication of connection matrices.
- 8.
Here \(\textit{liftBinOp}\) is for lifting an operator to a newtype.
- 9.
That we do not reduce loss over remainder yet?
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Gajda, M.J. (2022). Curious Properties of Latency Distributions. In: Arai, K. (eds) Intelligent Computing. SAI 2022. Lecture Notes in Networks and Systems, vol 506. Springer, Cham. https://doi.org/10.1007/978-3-031-10461-9_10
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