Write a simulation program to find the average dwell(stay) time w¯(n) of the M/M/1 queueing system and the 95% confidence interval of the true average dwell(stay) time wˆ
(The programming language is arbitrary(Python is preferable))

- Simulation method: Single-run method
- Sample interval length: 100,000 (packets), sample size n: 10
- Service rate µ = 100, 000
- Assumption: ( Line bandwidth: 1Gb/s, average packet length: 1,250 bytes → average processing time 1/µ= 10 (µs))

Under the above conditions, plot the relationship between w¯(n), the 95% confidence interval, and the utilization rate ρ.

Compare and discuss this with the value obtained analytically from queueing theory (Equation (38)).

Equation (38) is 

E[T] = E[W] + 1/ µ = 1/ (µ(1 − ρ))

E[T]:The average time it takes for a customer arriving at the system to be processed or Time (packet transfer delay) 

E[W]:Average waiting time