Queuing Model = mminf, Arrival Rate `lambda=96` per 1 day, Service Rate `mu=1` per 10 min
Solution:
Arrival Rate `lambda=96` per 1 day and Service Rate `mu=1` per 10 min (given)
So, Arrival Rate `lambda=96/(24xx60)=0.06666667` per min and Service Rate `mu=0.1` per min
Queuing Model : M/M/`oo`
Arrival Rate `lambda=0.06666667,` Service Rate `mu=0.1` (given)
1. Traffic Intensity
`rho=lambda/mu`
`=(0.06666667)/(0.1)`
`=0.6666667`
2. Probability of no customers in the system
`P_0=e^(-rho)`
`=e^(-0.6666667)`
`=0.5134171` or `0.5134171xx100=51.34171%`
3. Probability that there are n customers in the system
`P_n=rho^n/(n!)*P_0`
`P_n=(0.6666667)^n/(n!)*P_0`
`P_1=((0.6666667)^1)/(1!)*P_0=0.6666667/1*0.5134171=0.34227809`
`P_2=((0.6666667)^2)/(2!)*P_0=0.44444449/2*0.5134171=0.1140927`
`P_3=((0.6666667)^3)/(3!)*P_0=0.29629634/6*0.5134171=0.02535393`
`P_4=((0.6666667)^4)/(4!)*P_0=0.1975309/24*0.5134171=0.00422566`
`P_5=((0.6666667)^5)/(5!)*P_0=0.13168728/120*0.5134171=0.00056342`
`P_6=((0.6666667)^6)/(6!)*P_0=0.08779152/720*0.5134171=0.0000626`
4. Average number of customers in the system
`L_s=rho`
`=0.6666667`
5. Average number of customers in the queue
`L_q=0`
6. Average time spent in the system
`W_s=1/mu`
`=1/(0.1)`
`=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.
Any bug, improvement, feedback then
