1. Queuing Model = mminf, Arrival Rate `lambda=8` per 1 hr, Service Rate `mu=9` per 1 hr

Solution:
Arrival Rate `lambda=8` per 1 hr and Service Rate `mu=9` per 1 hr (given)

Queuing Model : M/M/`oo`


Arrival Rate `lambda=8,` Service Rate `mu=9` (given)


1. Traffic Intensity
`rho=lambda/mu`

`=(8)/(9)`

`=0.88888889`


2. Probability of no customers in the system
`P_0=e^(-rho)`

`=e^(-0.88888889)`

`=0.41111229` or `0.41111229xx100=41.111229%`


3. Probability that there are n customers in the system
`P_n=rho^n/(n!)*P_0`

`P_n=(0.88888889)^n/(n!)*P_0`

`P_1=((0.88888889)^1)/(1!)*P_0=0.88888889/1*0.41111229=0.36543315`

`P_2=((0.88888889)^2)/(2!)*P_0=0.79012346/2*0.41111229=0.16241473`

`P_3=((0.88888889)^3)/(3!)*P_0=0.70233196/6*0.41111229=0.04812288`

`P_4=((0.88888889)^4)/(4!)*P_0=0.62429508/24*0.41111229=0.01069397`

`P_5=((0.88888889)^5)/(5!)*P_0=0.55492896/120*0.41111229=0.00190115`

`P_6=((0.88888889)^6)/(6!)*P_0=0.49327018/720*0.41111229=0.00028165`

`P_7=((0.88888889)^7)/(7!)*P_0=0.43846239/5040*0.41111229=0.00003577`


4. Average number of customers in the system
`L_s=rho`

`=0.88888889`


5. Average number of customers in the queue
`L_q=0`


6. Average time spent in the system
`W_s=1/mu`

`=1/(9)`

`=0.11111111` hr or `0.11111111xx60=6.66666667` min


7. Average Time spent in the queue
`W_q=0`