Good afternoon, colleagues. How to get a couple of formulas from the questions. Here we are given a queuing system with initial parameters: $$\begin{matrix}\text{intake intensity} & \lambda\\ \text{service channels} & m\\ \text{service intensity} & \mu\\ \text{maximum queue size} &n\end{matrix}$$

And we know how to get these parameters:

a) Probability of denial of service $$ p_{denial} = p_{n+m} $$ b) Relative intensity of service $$ q=1-p_{n+m} $$ c) Absolute intensity of service $$ A = q\cdot\lambda $$ d) Average queue length $$ L_{queue}=\sum^n_{i=1}ip_{m+i} $$ e) Average time in queue $$ T_{queue}=\sum^{n-1}_{i=0}\frac{i+1}{m\mu}p_{m+i} $$ f) Average number of busy channels $$N_{channels}=\sum^{m}_{i=1}ip_i+\sum^{m+n}_{i=m+1}mp_i $$

But with these, I did not find the necessary information in the relevant literature. Maybe they are derived from the above, or do they need additional calculations?

g) Probability that an incoming request will not wait at queue

h) Average downtime of the queuing system

i) Average time when there is no queue in the system