Queuing Model = mminf, Arrival Rate `lambda=10` per 8 hr, Service Rate `mu=1` per 30 min
Solution:
Arrival Rate `lambda=10` per 8 hr and Service Rate `mu=1` per 30 min (given)
So, Arrival Rate `lambda=1.25` per hr and Service Rate `mu=0.03333333xx60=2` per hr
Queuing Model : M/M/`oo`
Arrival Rate `lambda=1.25,` Service Rate `mu=2` (given)
1. Traffic Intensity
`rho=lambda/mu`
`=(1.25)/(2)`
`=0.625`
2. Probability of no customers in the system
`P_0=e^(-rho)`
`=e^(-0.625)`
`=0.53526143` or `0.53526143xx100=53.526143%`
3. Probability that there are n customers in the system
`P_n=rho^n/(n!)*P_0`
`P_n=(0.625)^n/(n!)*P_0`
`P_1=((0.625)^1)/(1!)*P_0=0.625/1*0.53526143=0.33453839`
`P_2=((0.625)^2)/(2!)*P_0=0.390625/2*0.53526143=0.10454325`
`P_3=((0.625)^3)/(3!)*P_0=0.24414062/6*0.53526143=0.02177984`
`P_4=((0.625)^4)/(4!)*P_0=0.15258789/24*0.53526143=0.0034031`
`P_5=((0.625)^5)/(5!)*P_0=0.09536743/120*0.53526143=0.00042539`
`P_6=((0.625)^6)/(6!)*P_0=0.05960464/720*0.53526143=0.00004431`
4. Average number of customers in the system
`L_s=rho`
`=0.625`
5. Average number of customers in the queue
`L_q=0`
6. Average time spent in the system
`W_s=1/mu`
`=1/(2)`
`=0.5` hr or `0.5xx60=30` 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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