2020-05-17

From Uncertainty Principle to the Dilemma of Efficiency and Service Quality

Recently, listening to some youtube clips about philosophy triggers my memory of Heisenbery's uncertainty principle learnt in high school:

(standard deviation of position) times (standard deviation of momentum) >= Planck constant / 2

It simply states the more certain of the former implies the more uncertain of the latter.
I nearly forgot. But during work, I more often have to deal with the resource (labour or others) efficiency and customer satisfaction (e.g. wait time). Hey! I remember I have learnt queuing theory for M/M/1 model,

the mean queue time is t = ρ / (1-ρ) where ρ = λ / μ
λ is the rate at which packets arrive at the queue (in packets/second), and
μ is the rate at which packets may be served by the queue (in packets/second)
(sorry I in fact forgot the exact formula but I just copy from Wikipedia)

My main point is this has many similarity with uncertainty principle in the sense that the high efficiency you request, the longer wait time will be resulted.

for efficiency, I can view ρ can serve this role because it is always less than one.

The I redefine inefficiency as λ = 1-ρ, then
t = ρ / (1-ρ) ≈ 1 / (1-ρ) (since ρ≈1)
then t • (1-ρ) ≈ 1 or

t • λ ≈ 1
which is my analogy of the uncertainty principle.