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Home > Operation Research > Queuing Theory > Queuing Theory M/M/Infinity Queuing Model example
7. Queuing Theory, M/M/infinity Queuing Model example ( Enter your problem )
( Enter your problem )
Algorithm and examples
  1. Formula
  2. Example-1: `lambda=8,mu=9`
  3. Example-2: `lambda=6,mu=7`
  4. Example-3: `lambda=10` per 8 hr, `mu=1` per 30 min
  5. Example-4: `lambda=4` per 1 hr, `mu=1` per 10 min
  6. Example-5: `lambda=30` per 1 day, `mu=1` per 36 min
  7. Example-6: `lambda=96` per 1 day, `mu=1` per 10 min

1. Formula


Queuing Model : M/M/`oo`

Arrival Rate `lambda,` Service Rate `mu`


1. Traffic Intensity
`rho=lambda/mu`


2. Probability of no customers in the system
`P_0=e^(-rho)`


3. Probability that there are n customers in the system
`P_n=rho^n/(n!)*P_0`


4. Average number of customers in the system
`L_s=rho`


5. Average number of customers in the queue
`L_q=0`


6. Average time spent in the system
`W_s=1/mu`


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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