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2. Queuing Theory, M/M/1/N Queuing Model (M/M/1/K) example
( Enter your problem )
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Algorithm and examples
- Formula
- Example-1: `lambda=8`, `mu=9`, `N=3`
- Example-2: `lambda=6`, `mu=7`, `N=3`
- Example-3: `lambda=1`, `mu=1.2`, `N=6`
- Example-4: `lambda=25`, `mu=40`, `N=12`
- Example-5: `lambda=1.5`, `mu=2.1`, `N=10`
- Example-6: `lambda=1/10`, `mu=1/4`, `N=5`
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1. Formula
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Queuing Model : M/M/1/N
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Arrival rate `lambda,` Service rate `mu,` Capacity `N`
1. Traffic Intensity
`rho=lambda/mu`
2. Probability of no customers in the system
`P_0=(1-rho)/(1-rho^(N+1))`
3. Probability of N customers in the system
`P_N=rho^N*P_0`
4. Average number of customers in the system
`L_s=rho/(1-rho) - ((N+1)*rho^(N+1))/(1-rho^(N+1))`
5. Effective Arrival rate
`lambda_e=lambda(1-P_N)`
6. Average number of customers in the queue
`L_q=L_s-(lambda_e)/(mu)=L_s-(lambda(1-P_N))/(mu)`
7. Average time spent in the system
`W_s=(L_s)/(lambda_e)=(L_s)/(lambda(1-P_N))`
8. Average Time spent in the queue
`W_q=(L_q)/(lambda_e)=(L_q)/(lambda(1-P_N))`
9. Utilization factor
`U=L_s-L_q`
10. Probability that there are n customers in the system
`P_n=rho^n*P_0`
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This material is intended as a summary. Use your textbook for detail explanation.Any bug, improvement, feedback then Submit Here |
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