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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