Queuing Model = mminf, Arrival Rate `lambda=6` per 1 hr, Service Rate `mu=7` per 1 hr
Solution:
Arrival Rate `lambda=6` per 1 hr and Service Rate `mu=7` per 1 hr (given)
Queuing Model : M/M/`oo`
Arrival Rate `lambda=6,` Service Rate `mu=7` (given)
1. Traffic Intensity
`rho=lambda/mu`
`=(6)/(7)`
`=0.85714286`
2. Probability of no customers in the system
`P_0=e^(-rho)`
`=e^(-0.85714286)`
`=0.42437285` or `0.42437285xx100=42.437285%`
3. Probability that there are n customers in the system
`P_n=rho^n/(n!)*P_0`
`P_n=(0.85714286)^n/(n!)*P_0`
`P_1=((0.85714286)^1)/(1!)*P_0=0.85714286/1*0.42437285=0.36374815`
`P_2=((0.85714286)^2)/(2!)*P_0=0.73469388/2*0.42437285=0.15589207`
`P_3=((0.85714286)^3)/(3!)*P_0=0.62973761/6*0.42437285=0.04454059`
`P_4=((0.85714286)^4)/(4!)*P_0=0.53977509/24*0.42437285=0.00954441`
`P_5=((0.85714286)^5)/(5!)*P_0=0.46266437/120*0.42437285=0.00163618`
`P_6=((0.85714286)^6)/(6!)*P_0=0.39656946/720*0.42437285=0.00023374`
`P_7=((0.85714286)^7)/(7!)*P_0=0.33991668/5040*0.42437285=0.00002862`
4. Average number of customers in the system
`L_s=rho`
`=0.85714286`
5. Average number of customers in the queue
`L_q=0`
6. Average time spent in the system
`W_s=1/mu`
`=1/(7)`
`=0.14285714` hr or `0.14285714xx60=8.57142857` 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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