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`
This material is intended as a summary. Use your textbook for detail explanation.
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