Little's Law establishes the relationship between concurrency C, throughput T, and response time R, where C = T * R. Amdahl's Law states that parallelizing work can provide speedup, but there is a limit to speedup based on the portion of work that remains serialized. For databases and disk performance, throughput is affected by coordination between nodes completing units of work, as concurrency is decremented during entry and exit, represented by a kappa factor of less than 95%.

1. Mathematical thinking of
database/disk Performance
Little ‘s Law
Concurrency C = T (Stable long term throughput)
X R (Stable long term Response Time)
C = T X R
All three C,T,R are interdependent

2. Mathematical thinking of
database/disk Performance
AMDAHL ‘s Law
Where sigma represent portion of
Unit of Work serialized
(SQL queries in case of DB,
Disk access I/O in case of Disk)
Take away: parallelizing speed up 95% if 5 % is
serailized

3. Mathematical thinking of
Database/Disk Performance
Here K kappa factor represent Cross talk between
coordinating nodes of unit of work.
e.g as query Enters DB the concurrency is
decremented while leaving decremented.
Throughput count of unit of work between arrival
& completion. So K factor less than 95%.