Queuing Model = mminf, Arrival Rate `lambda=4` per 1 hr, Service Rate `mu=1` per 10 min
Solution:
Arrival Rate `lambda=4` per 1 hr and Service Rate `mu=1` per 10 min (given)
So, Arrival Rate `lambda=4` per hr and Service Rate `mu=0.1xx60=6` per hr
Queuing Model : M/M/`oo`
Arrival Rate `lambda=4,` Service Rate `mu=6` (given)
1. Traffic Intensity
`rho=lambda/mu`
`=(4)/(6)`
`=0.66666667`
2. Probability of no customers in the system
`P_0=e^(-rho)`
`=e^(-0.66666667)`
`=0.51341712` or `0.51341712xx100=51.341712%`
3. Probability that there are n customers in the system
`P_n=rho^n/(n!)*P_0`
`P_n=(0.66666667)^n/(n!)*P_0`
`P_1=((0.66666667)^1)/(1!)*P_0=0.66666667/1*0.51341712=0.34227808`
`P_2=((0.66666667)^2)/(2!)*P_0=0.44444444/2*0.51341712=0.11409269`
`P_3=((0.66666667)^3)/(3!)*P_0=0.2962963/6*0.51341712=0.02535393`
`P_4=((0.66666667)^4)/(4!)*P_0=0.19753086/24*0.51341712=0.00422566`
`P_5=((0.66666667)^5)/(5!)*P_0=0.13168724/120*0.51341712=0.00056342`
`P_6=((0.66666667)^6)/(6!)*P_0=0.0877915/720*0.51341712=0.0000626`
4. Average number of customers in the system
`L_s=rho`
`=0.66666667`
5. Average number of customers in the queue
`L_q=0`
6. Average time spent in the system
`W_s=1/mu`
`=1/(6)`
`=0.16666667` hr or `0.16666667xx60=10` 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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